Technische Universität München

Kudela, László; Kollmannsberger, Stefan; Almac, Umut; Rank, Ernst Show abstract Direct Structural Analysis of Domains Defined by Point Clouds
Computer Methods in Applied Mechanics and Engineering 358, 2020 - Status: Verlagsversion / published



This contribution presents a method that aims at the numerical analysis of solids represented by oriented point clouds. The proposed approach is based on the Finite Cell Method, a highorder immersed boundary technique that computes on a regular background grid of Finite elements and requires only inside-outside information from the geometric model. It is shown that oriented point clouds provide sufficent information for these point-membership classifications. Further, we address a tessellation-free formulation of contour integrals that allows to apply Neumann boundary conditions on point clouds without having to recover the underlying surface. Two-dimensional linear elastic benchmark examples demonstrate that the method is able to provide the same accuracy as those computed with conventional, continuous surface descriptions, because the associated error can be controlled by the density of the cloud. Three-dimensional examples computed on point clouds of historical structures show how the method can be employed to establish seamless connections between digital shape measurement techniques and numerical analyses.

Jomo, J.; de Prenter, F.; Elhaddad, M.; D'Angella, D.; Verhoosel, C.; Kollmannsberger, S.; Kirschke, J.; Nübel, V.; van Brummelen, H.; Rank, E. Robust and parallel scalable iterative solutions for large-scale finite cell analyses
Finite Elements in Analysis and Design - Status: Accepted for publication, 2019
DOI: 10.1016/j.finel.2019.01.009

Paolini, A.; Kollmannsberger, S.; Rank, E.; Horger, T.; Wohlmuth, B. Show abstract A mortar formulation including viscoelastic layers for vibration analysis
Computational Mechanics 63 (1), pp. 23-33, 2019
DOI: 10.1007/s00466-018-1582-9 - Status: Verlagsversion / published



In order to reduce the transfer of sound and vibrations in structures such as timber buildings, thin elastomer layers can be embedded between their components. The influence of these elastomers on the response of the structures in the low frequency range can be determined accurately by using conforming hexahedral finite elements. Three-dimensional mesh generation, however, is yet a non-trivial task and mesh refinements which may be necessary at the junctions can cause a high computational effort. One remedy is to mesh the components independently from each other and to couple them using the mortar method. Further, the hexahedral mesh for the thin elastomer layer itself can be avoided by integrating its elastic behavior into the mortar formulation. The present paper extends this mortar formulation to take damping into account such that frequency response analyses can be performed more accurately. Finally, the proposed method is verified by numerical examples.

Kollmannsberger, S.; Carraturo, M.; Reali, A.; Auricchio, F. Show abstract Accurate prediction of melt pool shapes in laser powder bed fusion by the non-linear temperature equation including phase changes
Integrating Materials and Manufacturing Innovation, 2019
DOI: 10.1007/s40192-019-00132-9 - Status: Verlagsversion / published



In this contribution, we validate a physical model based on a transient temperature equation (including latent heat) w.r.t. the experimental set AMB2018-02 provided within the additive manufacturing benchmark series, established at the National Institute of Standards and Technology, USA. We aim at predicting the following quantities of interest: width, depth, and length of the melt pool by numerical simulation and report also on the obtainable numerical results of the cooling rate. We first assume the laser to posses a double ellipsoidal shape and demonstrate that a well calibrated, purely thermal model based on isotropic thermal conductivity is able to predict all the quantities of interest, up to a deviation of maximum 7.3% from the experimentally measured values. However, it is interesting to observe that if we directly introduce, whenever available, the measured laser profile in the model (instead of the double ellipsoidal shape) the investigated model returns a deviation of 19.3% from the experimental values. This motivates a model update by introducing anisotropic conductivity, which is intended to be a simplistic model for heat material convection inside the melt pool. Such an anisotropic model enables the prediction of all quantities of interest mentioned above with a maximum deviation from the experimental values of 6.5%. We note that, although more predictive, the anisotropic model induces only a marginal increase in computational complexity

Paolini, A.; Kollmannsberger, S.; Rank, E. Show abstract Additive manufacturing in construction: A review on processes, applications, and digital planning methods
Additive Manufacturing, 2019
DOI: 10.1016/j.addma.2019.100894 - Status: Postprint / reviewed



The application of additive manufacturing (AM) in construction has been increasingly studied in recent years. Large robotic arm- and gantry-systems have been created to print building parts using aggregate-based materials, metals, or polymers. Significant benefits of AM are the automation of the production process, a high degree of design freedom, and the resulting potential for optimization. However, the building components and 3D-printing processes need to be modeled appropriately. In this paper, the current state of AM in construction is reviewed. AM processes and systems as well as their application in research and construction projects are presented. Moreover, digital methods for planning 3D-printed building parts and AM processes are described.

Ginting, B.M. Show abstract Central-Upwind Scheme for 2D Turbulent Shallow Flows using High-Resolution Meshes with Scalable Wall Functions
Computers & Fluids 179, pp. 394-421, 2019
DOI: 10.1016/j.compfluid.2018.11.014 - Status: Verlagsversion / published



In this paper, the Reynolds-averaged Navier Stokes equations supplemented by the algebraic stress model are solved using the central-upwind scheme for simulating 2D turbulent shallow flows. The model is of spatially and temporally second-order accurate. To increase the accuracy, high-resolution meshes up to 3.4 million cells (6.8 million edges) are used. Consequently, a strategy combining the hydrostatic and topography reconstructions and the scalable wall functions – is proposed to accurately simulate wet–dry phenomena near the interfaces (moving boundary geometries) thus ensuring a proper calculation for the turbulence properties. This strategy has been proven to be accurate and to not deteriorate the results for such very fine meshes thus giving flexibility to users in generating meshes.

Ginting, B.M.; Mundani, R.-P. Show abstract Parallel Flood Simulations for Wet–Dry Problems Using Dynamic Load Balancing Concept
Journal of Computing in Civil Engineering (ASCE) 33 (3), pp. 1-18, 2019
DOI: 10.1061/(ASCE)CP.1943-5487.0000823 - Status: Verlagsversion / published



In this paper, a shared-memory parallel simulation of flood modeling is presented. The model used has second-order spatial and temporal accuracy, where the Monotonic Upwind Scheme for Conservation Laws (MUSCL) method is applied for spatial discretization and the Runge-Kutta second-order method is employed for temporal discretization. A cell-centered finite-volume model is used and solved in an edge-based data structure. The model is well-balanced and able to efficiently simulate flood cases on complex topography with wet–dry problems. A cell–edge reordering strategy is designed to ease vectorization and parallelization of the code. To tackle load imbalances among threads due to wet–dry problems, a novel weighted-dynamic load balancing is proposed. The model shows accurate results, and the strategy proposed shows very good parallel efficiencies for problems of different sizes (up to 6.4 million cells/12.8  million edges) on varying numbers of cores (up to 64 cores). As such, this load balancing technique could become a promising strategy for efficient parallel simulations of real flood cases.

Kollmannsberger, Stefan; D'Angella, Davide; Rank, Ernst; Garhuom, Wadhah; Hubrich, Simeon; Düster, Alexander; Stolfo, Paolo Di; Schröder, Andreas Show abstract Spline- and hp-basis functions of higher differentiability in the finite cell method
GAMM-Mitteilungen 0 (0), pp. e202000004, 2019
DOI: 10.1002/gamm.202000004 - Status: Verlagsversion / published



In this paper, the use of hp-basis functions with higher differentiability properties is discussed in the context of the finite cell method and numerical simulations on complex geometries. For this purpose, Ck hp-basis functions based on classical B-splines and a new approach for the construction of C1 hp-basis functions with minimal local support are introduced. Both approaches allow for hanging nodes, whereas the new C1 approach also includes varying polynomial degrees. The properties of the hp-basis functions are studied in several numerical experiments, in which a linear elastic problem with some singularities is discretized with adaptive refinements. Furthermore, the application of the Ck hp-basis functions based on B-splines is investigated in the context of nonlinear material models, namely hyperelasticity and elastoplasicity with finite strains.

Nagaraja, S.; Elhaddad, M.; Ambati, M.; Kollmannsberger, S.; De Lorenzis, L.; Rank, E. Show abstract Phase-field modeling of brittle fracture with multi-level hp-FEM and the finite cell method
Computational Mechanics 63 (63), pp. 1-18, Springer, 2019
DOI: 10.1007/s00466-018-1649-7 - Status: Postprint / reviewed



The difficulties in dealing with discontinuities related to a sharp crack are overcome in the phase-field approach for fracture by modeling the crack as a diffusive object being described by a continuous field having high gradients. The discrete crack limit case is approached for a small length-scale parameter that controls the width of the transition region between the fully broken and the undamaged phases. From a computational standpoint, this necessitates fine meshes, at least locally, in order to accurately resolve the phase-field profile. In the classical approach, phase-field models are computed on a fixed mesh that is a priori refined in the areas where the crack is expected to propagate. This on the other hand curbs the convenience of using phase-field models for unknown crack paths and its ability to handle complex crack propagation patterns. In this work, we overcome this issue by employing the multi-level hp-refinement technique that enables a dynamically changing mesh which in turn allows the refinement to remain local at singularities and high gradients without problems of hanging nodes. Yet, in case of complex geometries, mesh generation and in particular local refinement becomes non-trivial. We address this issue by integrating a two-dimensional phase-field framework for brittle fracture with the finite cell method (FCM). The FCM based on high-order finite elements is a non-geometry-conforming discretization technique wherein the physical domain is embedded into a larger fictitious domain of simple geometry that can be easily discretized. This facilitates mesh generation for complex geometries and supports local refinement. Numerical examples including a comparison to a validation experiment illustrate the applicability of the multi-level hp-refinement and the FCM in the context of phase-field simulations.

Wassermann, B.; Kollmannsberger, S.; S., Yin; L., Kudela; E., Rank Show abstract Integrating CAD and Numerical Analysis: ’Dirty Geometry’ handling using the Finite Cell Method
Computer Methods in Applied Mechanics and Engineering, 2019 - Status: Verlagsversion / published



This paper proposes a computational methodology for the integration of Computer Aided De- sign (CAD) and the Finite Cell Method (FCM) for models with “dirty geometries”. FCM, being a fictitious domain approach based on higher order finite elements, embeds the physical model into a fictitious domain, which can be discretized without having to take into account the bound- ary of the physical domain. The true geometry is captured by a precise numerical integration of elements cut by the boundary. Thus, an e ff ective Point Membership Classification algorithm that determines the inside-outside state of an integration point with respect to the physical domain is a core operation in FCM. To treat also “dirty geometries”, i.e. imprecise or flawed geometric models, a combination of a segment-triangle intersection algorithm and a flood fill algorithm be- ing insensitive to most CAD model flaws is proposed to identify the a ffi liation of the integration points. The present method thus allows direct computations on geometrically and topologically flawed models. The potential and merit for practical applications of the proposed method is demonstrated by several numerical examples.

Ginting, B.M.; Ginting, H. Show abstract Hybrid Artificial Viscosity--Central-Upwind Scheme for Recirculating Turbulent Shallow Water Flows
Journal of Hydraulic Engineering (ASCE) x (x), pp. 1-54, 2019
DOI: 10.1061/(ASCE)HY.1943-7900.0001639



In this paper, a hybrid artificial viscosity--central-upwind (AV-CU) scheme is proposed for simulating recirculating turbulent shallow water flows by combining the artificial viscosity (AV) technique with the central-upwind (CU) scheme. The two-dimensional (2D) depth-averaged Reynolds-averaged Navier Stokes (DA-RANS) equations are solved using the AV technique, whereas the CU scheme is employed to compute the $ąppa$-$\epsilon$ model. The model is of spatially and temporally second-order accurate. The scalable wall functions (ScWF) are employed, thus becoming flexible in generating meshes without having to estimate the wall friction velocity at initial time step as if the standard wall functions (StWF) are used. The results benefit strongly from this hybrid approach being more accurate than the CU and Harten-Lax-van LeerContact (HLLC) schemes ---and 1.52$\times$ cheaper than the HLLC scheme for such recirculating turbulent flows. As such, the proposed approach could become a promising method for practical engineering purposes to simulate turbulent shallow water flows more efficiently and accurately.

Ginting, B.M.; Mundani, R.-P. Show abstract Comparison of Shallow Water Solvers: Applications for Dam-Break and Tsunami Cases with Reordering Strategy for Efficient Vectorization on Modern Hardware
Water 11 (4), pp. 639, 2019
DOI: 10.3390/w11040639



We investigate in this paper the behaviors of the Riemann solvers (Roe and Harten-Lax-van Leer-Contact (HLLC) schemes) and the Riemann-solver-free method (central-upwind scheme) regarding their accuracy and efficiency for solving the 2D shallow water equations. Our model was devised to be spatially second-order accurate with the Monotonic Upwind Scheme for Conservation Laws (MUSCL) reconstruction for a cell-centered finite volume scheme—and be temporally fourth-order accurate using the Runge–Kutta fourth-order method. Four benchmark cases of dam-break and tsunami events dealing with highly-discontinuous flows and wet–dry problems were simulated. To this end, we applied a reordering strategy for the data structures in our code supporting efficient vectorization and memory access alignment for boosting the performance. Two main features are pointed out here. Firstly, the reordering strategy employed has enabled highly-efficient vectorization for the three solvers investigated on three modern hardware (AVX, AVX2, and AVX-512), where speed-ups of 4.5–6.5× were obtained on the AVX/AVX2 machines for eight data per vector while on the AVX-512 machine we achieved a speed-up of up to 16.7× for 16 data per vector, all with singe-core computation; with parallel simulations, speed-ups of up to 75.7–121.8× and 928.9× were obtained on AVX/AVX2 and AVX-512 machines, respectively. Secondly, we observed that the central-upwind scheme was able to outperform the HLLC and Roe schemes 1.4× and 1.25×, respectively, by exhibiting similar accuracies. This study would be useful for modelers who are interested in developing shallow water codes

Niiranen, J.; Khakalo, S. Variational Formulations and Galerkin Methods for Strain Gradient Elasticity
Encyclopedia of Continuum Mechanics, 2018

Balobanov, V.; Niiranen, J. Locking-free variational formulations and isogeometric analysis for the Timoshenko beam models of strain gradient and classical elasticity
Computer Methods in Applied Mechanics and Engineering 339, pp. 137--159, 2018
DOI: 10.1016/j.cma.2018.04.028 - Status: Verlagsversion / published

Shahzad, S.; Niiranen, J. Analytical solution with validity analysis for an elliptical void and a rigid inclusion under uniform or nonuniform anti-plane loading
Theoretical and Applied Fracture Mechanics 97, pp. 62--72, 2018
DOI: 10.1016/j.tafmec.2018.07.009

Koskela, L.; Ferrantelli, A.; Niiranen, J.; Pikas, E.; Dave, B. Epistemological explanation of lean construction
Journal of Construction Engineering and Management, 2018
DOI: 10.24928/2017/0336 - Status: Verlagsversion / published

Paolini, A.; Frischmann, F.; Kollmannsberger, S.; Rabold, A.; Horger, T.; Wohlmuth, B.; Rank, E. Show abstract BIM gestützte strukturdynamische Analyse mit Volumenelementen höherer Ordnung
Bauingenieur 93 (4), pp. 160-166, 2018 - Status: Verlagsversion / published



Building Information Modeling ermöglicht die automatisierte Erstellung von Simulationsmodellen und schafft somit eine wichtige Grundlage, Zeit und Kosten einzusparen sowie die Qualität der Planung von Gebäuden zu erhöhen. Die Art des Simulationsmodells hängt jedoch wesentlich von der konkreten Problemstellung ab. Für Schwingungsanalysen bei Massivholzkonstruktionen ist eine mechanisch korrekte Beschreibung der Stoßstellen zwischen den Bauteilen von großer Bedeutung. Dafür eignen sich Modelle aus hexaedrischen finiten Elementen erheblich besser als Schalenelemente. Ein konformes Hexaedernetz kann allerdings mit verfügbaren Netzgeneratoren nur bei bestimmten Gebäudegeometrien automatisch erzeugt werden und weist an Stoßstellen eine große Anzahl von Elementen auf, was zu einem hohen Rechenaufwand führen kann. Im vorliegenden Beitrag wird deshalb ein alternatives Verfahren vorgestellt, mit dem ein hexaedrisches Finite Elemente Modell automatisch aus einem Bauwerksinformationsmodell (BIM) abgeleitet werden kann. Die im BIM definierten Bauteile werden dabei getrennt voneinander vernetzt und deren Verbindungen zueinander mit Hilfe der Mortar-Methode abgebildet. Eine große Recheneffizienz wird durch die Verwendung von Ansatzfunktionen höherer Ordnung in Kombination mit einem relativ groben Netz erreicht. Nach der Beschreibung des Verfahrens wird seine Anwendbarkeit an einem mehrgeschossigen Massivholzgebäude demonstriert.

Kudela, L.; Frischmann, F.; Yossef, O.; Uzan, A.; Kollmannsberger, S.; Yosibash, Z.; Rank, E. Image-based mesh generation of tubular geometries under circular motion in refractive environments
Machine Vision and Applications, 2018 - Status: Verlagsversion / published

Kollmannsberger, S.; Özcan, A.; Carraturo, M.; Zander, N.; Rank, E. Show abstract A hierarchical computational model for moving thermal loads and phase changes with applications to Selective Laser Melting
Computers & Mathematics with Applications 75 (5), pp. 1483-1497, 2018
DOI: 10.1016/j.camwa.2017.11.014 - Status: Verlagsversion / published



Computational heat transfer analysis often involves moving fluxes which induce traveling fronts of phase change coupled to one or more field variables. Examples are the transient simulation of melting, welding or of additive manufacturing processes, where material changes its state and the controlling fields are temperature and structural deformation. One of the challenges for a numerical computation of these processes is their multi-scale nature with a highly localized zone of phase transition which may travel over a large domain of a body. Here, a transient local adaptation of the approximation, with not only a refinement at the phase front, but also a de-refinement in regions, where the front has past is of advantage because the de-refinement can assure a bounded number of degrees of freedom which is independent from the traveling length of the front. We present a computational model of this process which involves three novelties: a) a very low number of degrees of freedom which yet yields a comparatively high accuracy. The number of degrees of freedom is, additionally, kept practically constant throughout the duration of the simulation. This is achieved by means of the multi-level hp-finite element method. Its exponential convergence is verified for the first time against a semi-analytic, three-dimensional transient linear thermal benchmark with a traveling source term which models a laser beam. b) A hierarchical treatment of the state variables. To this end, the state of the material is managed on a separate, octree-like grid. This material grid may refine or coarsen independently of the discretization used for the temperature field. This methodology is verified against an analytic benchmark of a melting bar computed in three dimensions in which phase changes of the material occur on a rapidly advancing front. c) The combination of these technologies to demonstrate its potential for the computational modeling of selective laser melting processes. To this end, the computational methodology is extended by the finite cell method which allows for accurate simulations in an embedded domain setting. This opens the new modeling possibility that neither a scan vectors no a layer of material needs to conform to the discretization of the finite element mesh but can form only a fraction within the discretization of the field and state variables.

Özcan, A.; Kollmannsberger, S.; Jomo, J; De Lorenzis, L.; Rank, E. Residual stresses in metal deposition modeling: discretizations of higher order
Computers and Mathematics with Applications, 2018 - Status: Postprint / reviewed

D'Angella, D.; Kollmannsberger, S.; Rank, E.; Reali, A. Multi-level Bézier extraction for hierarchical local refinement of Isogeometric Analysis
Computer Methods in Applied Mechanics and Engineering, 2018 - Status: Verlagsversion / published

Elhaddad, M.; Zander, N.; Bog, T.; Kudela, L.; Kollmannsberger, S.; Kirschke, J.S.; Baum, T.; Ruess, M.; Rank, E. Multi-level hp-finite cell method for embedded interface problems with application in biomechanics
International Journal for Numerical Methods in Biomedical Engineering 34 (4), pp. e2951, Wiley, 2017
DOI: 10.1002/cnm.2951 - Status: Verlagsversion / published

Jomo, J.; Zander, N.; Elhaddad, M.; Özcan, A.; Kollmannsberger, S.; Mundani, R-P.; Rank, E. Parallelization of the multi-level hp-adaptive finite cell method
Computers and Mathematics with Applications 74 (1), pp. 126-142, Elsevier, 2017
DOI: 10.1016/j.camwa.2017.01.004 - Status: Verlagsversion / published

Ranjbar, M.; Mashayekhi, M.; Parvizian, J.; Düster, A.; Rank, E. Finite cell method implementation and validation of a nonlocal integral damage model
International Journal of Mechanical Sciences, 2017
DOI: 10.1016/j.ijmecsci.2017.05.008

Hubrich, S.; Di Stolfo, P.; Kudela, L.; Kollmannsberger, S.; Rank, E.; Schröder, A.; Düster, A. Numerical integration of discontinuous functions: moment fitting and smart octree
Computational Mechanics, pp. 1-19, Springer, 2017
DOI: 10.1007/s00466-017-1441-0 - Status: Verlagsversion / published

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Show abstract Weak imposition of frictionless contact constraints on automatically recovered high-order, embedded interfaces using the finite cell method
Computational Mechanics, 2017 - Status: Postprint / reviewed



The finite cell method (FCM) is a fictitious domain approach that greatly simplifies simulations involving complex structures. Recently, the FCM has been applied to contact problems. The current study continues in this field by extending the concept of weakly enforced boundary conditions to inequality constraints for frictionless contact. Furthermore, it formalizes an approach that automatically recovers highorder contact surfaces of (implicitly defined) embedded geometries by means of an extended Marching Cubes (MC) algorithm. To further improve the accuracy of the discretization, irregularities at the boundary of contact zones are treated with multi-level hp-refinements. Numerical results and a systematic study of h-, p- and hprefinements show that the FCM can efficiently provide accurate results for problems involving contact.

Wassermann, B.; Kollmannsberger, S.; Bog, T.; Rank, E. Show abstract From geometric design to numerical analysis: A direct approach using the Finite Cell Method on Constructive Solid Geometry
Computers & Mathematics with Applications, 2017



During the last ten years, increasing efforts were made to improve and simplify the process from Computer Aided Design (CAD) modeling to a numerical simulation. It has been shown that the transition from one model to another, i.e. the meshing, is a bottle-neck. Several approaches have been developed to overcome this time-consuming step, e.g. Isogeometric Analysis (IGA), which applies the shape functions used for the geometry description (typically B-Splines and NURBS) directly to the numerical analysis. In contrast to IGA, which deals with boundary represented models (B-Rep), our approach focuses on parametric volumetric models such as Constructive Solid Geometries (CSG). These models have several advantages, as their geometry description is inherently watertight and they provide a description of the models interior. To be able to use the explicit mathematical description of these models, we employ the Finite Cell Method (FCM). Herein, the only necessary input is a reliable statement whether an (integration-) point lies inside or outside of the geometric model. This paper mainly discusses such point-in-membership tests on various geometric objects like sweeps and lofts, as well as several geometric operations such as filleting or chamfering. We demonstrate that, based on the information of the construction method of these objects, the point-in-membership-test can be carried out effciently and robustly.

Bas, O.; De-Juan-Pardo, E.; Meinert, C.; D'Angella, D.; Baldwin, J.; Bray, L.; Wellard R.; Kollmannsberger, S.; Rank, E. Werner, C.; Klein, T.; Catelas I.; Hutmacher, D.W. Biofabricated soft network composites for cartilage tissue engineering
Biofabrication, Biofabrication, 2017
DOI: 10.1088/1758-5090/aa6b15 - Status: Verlagsversion / published

Onur Bas; Davide D'Angella; Jeremy G. Baldwin; Nathan J. Castro; Felix M. Wunner; Navid T. Saidy; Stefan Kollmannsberger; Alessandro Reali; Ernst Rank; Elena M. De-Juan-Pardo; Dietmar W. Hutmacher Show abstract An integrated design, material and fabrication platform for engineering biomechanically and biologically functional soft tissues
ACS Appl. Mater. Interfaces, 2017
DOI: 10.1021/acsami.7b08617 - Status: Verlagsversion / published



The development of advanced soft materials can be faciliated through bioinspired design methodologies. Translating the fibre-reinforcement approach of nature, biologically functional soft network composites with enhanced compressive mechanical properties have been achieved. However, design and fabrication concepts addressing the mechanical requirements of tissues which are predominantly functioning under tensile loading (e.g., skin, tendon, ligament, muscle, etc.) are under studied in the current literature. In this communication, to our knowledge for the first time we describe and validate a design library combined with a innovative biomaterials & 3D printing platform which meets the requirements for tissue engineering applications subjected to tensile loads. Herein, we present a library of fibre elements to be used as building blocks for the development of tailored fibrous networks. These fibrous networks are then combined with a tunable interpenetrating polymer network (IPN) system that mimics highly flexible natural extracellular matrices (ECMs). Our holistic design allows the selection and fabrication of customised reinforcing fibre networks and matrices to match both complex tissue-specific biomechanical and biological properties. We mechanically validate our approach through an exemplary soft network composite model which is charactarized to be flexible yet ~125 times stronger (E = 3.19 MPa) and ~100 times tougher (WExt = ~2000 kJ m-3) than its bare hydrogel counterpart.

Paolini, A.; Kollmannsberger, S.; Winter, C.; Buchschmid, M.; Müller, G.; Rabold, R.; Mecking, S.; Schanda, U.; Rank, E. Show abstract A high order finite element model for vibration analysis of cross laminated timber assemblies
Building Acoustics 24 (3), pp. 135-158, 2017
DOI: 10.1177/1351010X17727126 - Status: Verlagsversion / published



The vibration behavior of cross laminated timber (CLT) components in the low frequency range can be predicted with high accuracy by the finite element method. However, the modeling of assembled CLT components has been studied only scarcely. The three-dimensional p-version of the finite element method, which is characterized by hierachical high order shape functions, is well suited to consider coupling and support conditions. Furthermore, a small number of degrees of freedom can be obtained in case of thin-walled structures by using p-elements with high aspect ratios and anisotropic ansatz spaces. In this paper, a model for CLT assemblies made of volumetric high order finite elements is presented. Two representative types of connections are investigated, one with an elastomer between the CLT components and the other without. The model is validated and suitable ranges for the stiffness parameters of the finite elements which represent the junction are identified.

Düster, Alexander; Rank, Ernst; Szabó, Barna The p-Version of the Finite Element and Finite Cell Methods
Encyclopedia of Computational Mechanics Second Edition, John Wiley & Sons, Ltd, 2017

Ertl, C.; J., Frisch; Mundani, R.-P. Show abstract Design and optimisation of an efficient HDF5 I/O Kernel for massive parallel fluid flow simulations
Concurrency and Computation: Practice and Experience, 2017
DOI: 10.1002/cpe.4165



More and more massive parallel codes running on several hundreds of thousands of cores are entering the computational science and engineering domain, allowing high‐fidelity computations on up to trillions of unknowns for very detailed analyses of the underlying problems. Such runs typically produce gigabytes of data, hindering both efficient storage and (interactive) data exploration. Advanced approaches based on inherently distributed data formats such as hierarchical data format version 5 become necessary here to avoid long latencies when storing the data and to support fast (random) access when retrieving the data for visual processing. This paper shows considerations and implementation aspects of an I/O kernel based on hierarchical data format version 5 that supports fast checkpointing, restarting, and selective visualisation using a single shared output file for an existing computational fluid dynamics framework. This functionality is achieved by including the framework's hierarchical data structure in the file, which also opens the door for additional steering functionality. Finally, the performance of the kernel's write routines are presented. Bandwidths close to the theoretical peak on modern supercomputing clusters were achieved by avoiding file‐locking and using collective buffering.

Zander, N.; Bog, T.; Elhaddad, M.; Frischmann, F.; Kollmannsberger, S.; Rank, E. The multi-level hp-method for three-dimensional problems: Dynamically changing high-order mesh refinement with arbitrary hanging nodes.
Computer Methods in Applied Mechanics and Engineering 310, pp. 252-277, 2016
DOI: 10.1016/j.cma.2016.07.007

Seidl, R.; Rank, E. Show abstract Iterative time reversal based flaw identification
Computers & Mathematics with Applications 72 (4), pp. 879-892, 2016
DOI: 10.1016/j.camwa.2016.05.036



In the field of ultrasonic non-destructive testing, ultrasonic impulses are used to detect flaws in components without causing damage. Based on performing experiments alone, it is possible to infer the state of the component–but this usually provides only limited details about the interior damage such as its position, dimension or orientation. Furthermore, the amount of sensors that can be used to record the signals is restricted to only a few because of the shape and the dimensions of a typical specimen and considerations such as costs, additional mass and structural integrity. Further information about the flaw is hidden in the recorded experimental signals. The idea of the proposed method is to use the experimental data together with a wave speed model of a healthy component and to try to adapt the model to generate these experimental measurements. Formally, the problem is posed as a nonlinear optimization, and the wave speed model is adapted in such a way that the discrepancy between the experimental measurements and the model output is minimized. Moreover, to overcome the problem of only a few available sensor measurements, a combination of multiple simulations corresponding to generally performed multiple experiments in SHM practice is used to improve the accuracy. Following this approach, the position, dimension and orientation of a flaw can be detected for an emulated damaged aluminum plate. For cases when there are only few sensors available, it is shown how a combination of similar experiments can be used to improve the inversion results.

Wille, Hagen; Ruess, Martin; Rank, Ernst; Yosibash, Zohar Show abstract Uncertainty quantification for personalized analyses of human proximal femurs
Journal of Biomechanics 49 (4), pp. 520-527, Elsevier, 2016
DOI: 10.1016/j.jbiomech.2015.11.013 - Status: Verlagsversion / published



Computational models for the personalized analysis of human femurs contain uncertainties in bone material properties and loads, which affect the simulation results. To quantify the influence we developed a probabilistic framework based on polynomial chaos (PC) that propagates stochastic input variables through any computational model. We considered a stochastic E-p relationship and a stochastic hip contact force, representing realistic variability of experimental data. Their influence on the prediction of principal strains (e1 and e3) was quantified for one human proximal femur, including sensitivity and reliability analysis. Large variabilities in the principal strain predictions were found in the cortical shell of the femoral neck, with coeffcients of variation of ≈ 40%. Between 60-80% of the variance in e1 and e3 are attributable to the uncertainty in the E-p relationship, while ≈ 10% are caused by the load magnitude and 5-30% by the load direction. Principal strain directions were unaffected by material and loading uncertainties. The antero-superior and medial inferior sides of the neck exhibited the largest probabilities for tensile and compression failure, however all were very small (pf < 0:001). In summary, uncertainty quantification with PC has been demonstrated to effciently and accurately describe the influence of very different stochastic inputs, which increases the credibility and explanatory power of personalized analyses of human proximal femurs.

D'Angella, D.; Zander, N.; Kollmannsberger, S.; Frischmann, F.; Rank, E.; Schröder, A.; Reali, A. Show abstract Multi-Level hp-Adaptivity and Explicit Error Estimation
Advanced Modeling and Simulation in Engineering Sciences, pp. 1-18, Springer, 2016
DOI: 10.1186/s40323-016-0085-5 - Status: Verlagsversion / published



Recently, a multi-level hp-version of the Finite Element Method (FEM) was proposed to ease the difficulties of treating hanging nodes, while providing full hp-approximation capabilities. In the original paper, the refinement procedure made use of a-priori knowledge of the solution. However, adaptive procedures can produce discretizations which are more effective than an intuitive choice of element sizes h and polynomial degree distributions p. This is particularly prominent when a-priori knowledge of the solution is only vague or unavailable. The present contribution demonstrates that multi-level hp-adaptive schemes can be efficiently driven by an explicit a-posteriori error estimator. To this end, we adopt the classical residual-based error estimator. The main insight here is that its extension to multi-level hp-FEM is possible by considering the refined-most overlay elements as integration domains. We demonstrate on several two- and three-dimensional examples that exponential convergence rates can be obtained.

Kudela, László; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst Smart octrees: accurately integrating discontinuous functions in 3D
Computer Methods in Applied Mechanics and Engineering, 2016 - Status: Verlagsversion / published

Di Stolfo, P.; Schröder, A.; Zander, N.; Kollmannsberger, S. Show abstract An easy treatment of hanging nodes in hp-finite elements
Finite Elements in Analysis and Design 121, pp. 101-117, 2016
DOI: 10.1016/j.finel.2016.07.001 - Status: Verlagsversion / published



We present an easy treatment of (multi-level) hanging nodes in hp-finite elements in two dimensions. Its simplicity is due to the fact that the connectivity matrices can directly be computed in a row-wise fashion. This is achieved by treating a global degree of freedom as a local degree of freedom on each element in an appropriate union of elements. This forms a type of support which is larger than the one used in the conventional approach and generalizes the recently presented multi-level hp-method. Numerical experiments compare the new approach with respect to accuracy and the conditioning of the resulting linear system. We conclude that this new approach achieves nearly the same properties as the conventional approach in all investigated examples and provides an excellent trade-off between implementational complexity and solvability.

Zander, N.; Ruess, M.; Bog, T.; Kollmannsberger, S.; Rank, E. Multi-Level hp-Adaptivity for Cohesive Fracture Modelling
International Journal for Numerical Methods in Engineering 109 (3), pp. 1723-1755, 2016
DOI: 10.1002/nme.5340 - Status: Verlagsversion / published

Seidl, R.; Rank, E. Show abstract Iterative time reversal based flaw identification
Computers & Mathematics with Applications, 2016 - Status: Postprint / reviewed



In the field of ultrasonic non destructive testing ultrasonic impulses are used to detect cracks in components without causing damage. When performing only experiments it is possible to infer the state of the component but usually no additional details about the interior damage like position, dimension or orientation are available. Furthermore, the amount of sensors that can be used to record the signals is limited to only a few because of the shape and dimension of typical specimen. The information about these details is hidden in the recorded experimental signals. The idea of the proposed method is to use this experimental data together with a wave speed model of the healthy component and to try to adapt the model to generate these experimental measurements. Formally, the problem is posed as nonlinear optimization and the wave speed model is adapted such that the discrepancy between experimental measurements and the model output is minimized. Moreover, to overcome the problem of only few available sensor measurements, a combination of multiple experiments is used to improve accuracy. Following this approach, the position, dimension and orientation of a crack is detected for an emulated cracked aluminum plate. When only few sensors are available, it is shown how a combination of similar experiments can be used to improve the inversion results.

Mundani, R.-P.; Frisch, J.; Varduhn, V.; Rank, E. A Sliding Window Technique for Interactive High-Performance Computing Scenarios
Advances in Engineering Software 84, pp. 21--30, 2015
DOI: 10.1016/j.advengsoft.2015.02.003

Dauge, M.; Düster, A.; Rank, E. Show abstract Theoretical and Numerical Investigation of the Finite Cell Method
J. Sci. Comput., 2015
DOI: 10.1007/s10915-015-9997-3 - Status: Verlagsversion / published



We present a detailed analysis of the convergence properties of the finite cell method which is a fictitious domain approach based on high order finite elements. It is proved that exponential type of convergence can be obtained by the finite cell method for Laplace and Lamé problems in one, two as well as three dimensions. Several numerical examples in one and two dimensions including a well-known benchmark problem from linear elasticity confirm the results of the mathematical analysis of the finite cell method.

Yosibash, Zohar; Wille, Hagen; Rank, Ernst Show abstract Stochastic description of the peak hip contact force during walking free and going upstairs
Journal of Biomechanics 48, pp. 1015--1022, 2015
DOI: 10.1016/j.jbiomech.2015.01.041



Uncertainty quantification for the response of a patient specific femur is mandatory when advocating finite element (FE) models in clinical applications. Reliable stochastic descriptions of physiological hip contact forces are an essential prerequisite for such an endeavor. We therefore analyze the in-vivo available data of seven individuals from HIP98 and OrthoLoad with the objective of characterizing the variability of the peak hip contact force magnitude and two corresponding spatial angles (in sagittal and frontal plane) during walking free and going upstairs. Regression analyses with linear mixed-effects models were performed resulting in six normal random variables, one for each force component and activity. Importantly, the statistical analysis accounts for the fact that same individuals performed both activities. The mean of the peak force magnitude was found to be linearly dependent on the body weight with an additional, activity-specific intercept and all variances were dominated by the inter-patient variability. No distinct correlation was found between the two angles and the force magnitude. The proposed stochastic description of the peak hip contact force during walking free and going upstairs contributes towards future uncertainty quantification of patient-specific FE models.

Frisch, J.; Mundani, R.-P.; Rank, E.; van Treeck, C. Show abstract Engineering-Based Thermal CFD Simulations on Massive Parallel Systems
Computation 3 (2), pp. 235-261, 2015
DOI: 10.3390/computation3020235 - Status: Verlagsversion / published



The development of parallel Computational Fluid Dynamics (CFD) codes is a challenging task that entails efficient parallelization concepts and strategies in order to achieve good scalability values when running those codes on modern supercomputers with several thousands to millions of cores. In this paper, we present a hierarchical data structure for massive parallel computations that supports the coupling of a Navier–Stokes-based fluid flow code with the Boussinesq approximation in order to address complex thermal scenarios for energy-related assessments. The newly designed data structure is specifically designed with the idea of interactive data exploration and visualization during runtime of the simulation code; a major shortcoming of traditional high-performance computing (HPC) simulation codes. We further show and discuss speed-up values obtained on one of Germany’s top-ranked supercomputers with up to 140,000 processes and present simulation results for different engineering-based thermal problems.

Kudela, L.; Zander, N.; Bog, T.; Kollmannsberger, S.; Rank, E. Show abstract Efficient and accurate numerical quadrature for immersed boundary methods
Advanced Modeling and Simulation in Engineering Sciences 2 (1), Springer International Publishing, 2015
DOI: 10.1186/s40323-015-0031-y - Status: Verlagsversion / published



One question in the context of immersed boundary or fictitious domain methods is how to compute discontinuous integrands in cut elements accurately. A frequently used method is to apply a composed Gaussian quadrature based on a spacetree subdivision. Although this approach works robustly on any geometry, the resulting integration mesh yields a low order representation of the boundary. If high order shape functions are employed to approximate the solution, this lack of geometric approximation power prevents exponential convergence in the asymptotic range. In this paper we present an algorithmic subdivision approach that aims to be as robust as the spacetree decomposition even for close-to-degenerate cases—but remains geometrically accurate at the same time. Based on 2D numerical examples, we will show that optimal convergence rates can be obtained with a nearly optimal number of integration points.

Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Schillinger, Dominik; Rank, Ernst Show abstract Multi-Level hp-Adaptivity: High-Order Mesh Adaptivity without the Difficulties of Constraining Hanging Nodes
Computational Mechanics 55 (3), pp. 499ff., 2015
DOI: 10.1007/s00466-014-1118-x - Status: Verlagsversion / published



The implementation of hp-adaptivity is challenging as hanging nodes, edges, and faces have to be constrained to ensure compatibility of the shape functions. For this reason, most hp-code frameworks restrict themselves to 1-irregular meshes to ease the implementational effort. This work alleviates these difficulties by introducing a new formulation for high-order mesh adaptivity that provides full local hp-refinement capabilities at a comparably small implementational effort. Its main idea is the extension of the hp-d method such that it allows for high-order overlay meshes yielding a hierarchical, multi-level hp-formulation of the Finite Element Method. This concept enables intuitive refinement and coarsening procedures, while linear independence and compatibility of the shape functions are guaranteed by construction. The proposed method is demonstrated to achieve exponential rates of convergence for problems with non-smooth solutions, is used alongside the Finite Cell Method to simulate the heat flow around moving objects on a non-conforming background mesh and is combined with an energy-based refinement indicator for automatic hp-adaptivity.

Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Show abstract Normal contact with high order finite elements and a fictitious contact material
Computers & Mathematics with Applications 70 (7), pp. 1370–1390, 2015
DOI: 10.1016/j.camwa.2015.04.020 - Status: Verlagsversion / published



Contact problems in solid mechanics are traditionally solved using the h-version of the finite element method. The constraints are enforced along the surfaces of e.g. elastic bodies under consideration. Standard constraint algorithms include penalty methods, Lagrange multiplier methods and combinations thereof. For complex scenarios, a major part of the solution time is taken up by operations to identify points that come into contact. This paper presents a novel approach to model frictionless contact using high order finite elements. Here, we employ an especially designed material model that is inserted into two- respectively three- dimensional regions surrounding contacting bodies. Contact constraints are thus enforced on the same manifold as the accompanying structural problem. The application of the current material formulation leads to a regularization of the Karush-Kuhn-Tucker conditions. Our formulation can be classified as a barrier-type method. Results are obtained for two- and three-dimensional prob- lems, including a Hertzian contact problem. Comparisons to a commercial FEA package are provided. The proposed formulation works well for non-matching discretizations on adjacent contact interfaces and handles self-contact naturally. Since the non-penetrating conditions are solved in a physically consistent man- ner, there is no need for an explicit contact search.

Elhaddad, M.; Zander, N.; Kollmannsberger, S.; Shadavakhsh, A.; Nübel, V.; Rank, E. Show abstract Finite Cell Method: High order structural dynamics for complex geometries
International Journal for Structural Stability and Dynamics 15 (7), pp. 1-25, 2015
DOI: 10.1142/S0219455415400180 - Status: Verlagsversion / published



In this contribution, the finite cell method (FCM) is applied to solve transient problems of linear elastodynamics. The mathematical formulation of FCM for linear elastodynamics is presented, following from the weak formulation of the initial/boundary-value problem. Semi-discrete time integration schemes are briefly discussed, and the choice of implicit time integration is justified. A one-dimensional benchmark problem is solved using FCM, illustrating the method's ability to solve problems of linear elastodynamics obtaining high rates of convergence. Furthermore, a numerical example of transient analysis from an industrial application is solved using FCM. The numerical results are compared to the results obtained using state-of-the-art commercial software, employing linear finite elements, in conjunction with explicit time integration. The results illustrate the potential of FCM as a powerful tool for transient analysis in elastodynamics, offering a high degree of accuracy at a moderate computational effort.

Kollmannsberger, S.; Özcan, A.; Baiges, J.; Ruess, M.; Rank, E.; Reali,A. Parameter-free, weak imposition of Dirichlet boundary conditions and coupling of trimmed and non-conforming patches
International Journal For Numerical Methods In Engineering, 2015
DOI: 10.1002/nme.4817

Wanga, Yang; Zhao, Fu-Yun; Kuckelkorn, Jens; Spliethoff, Hartmut; Rank, Ernst Show abstract School building energy performance and classroom air environment implemented with the heat recovery heat pump and displacement ventilation system
Applied Energy 114, pp. 58 - 68, 2014
DOI: 10.1016/j.apenergy.2013.09.020



Recent built low energy school buildings have adopted a novel heat recovery heat pump and classroom ventilation system. School building energy conservation performance and classroom air quality enhancement will be simultaneously investigated in the present work. Heat recovery efficiency of the heat recovery facility and energy conservation ratio of the heat pump unit were analytically modeled, taking the classroom ventilation network into account. Following that, classroom displacement ventilation and its thermal stratification have been investigated concerning the effects of delivering ventilation flow rate and supplying air temperature. Representative thermal comfort parameters, percentage dissatisfied, temperature difference between ankle and head, and draft dissatisfaction have been evaluated. Indoor air quality indicated by the CO2 concentration was also investigated in terms of different levels of ventilation flow rate. Classroom energy demands for ventilation and winter heating have been shown to decrease with the promotion of heat recovery efficiency of the ventilation facility, and the energy conservation ratio of the heat pump increases with temperature of supplying fresh air. Detailed correlations of heat recovery ventilation and heat pump energy conservation have been presented. This research illuminated that enhancement of classroom air quality and reduction of school building energy consumption could be simultaneously achieved with the appropriate operation of heat recovery heat pump and ventilation system.

Borrmann, A.; Flurl, M.; Jubierre, J.R.; Mundani, R.-P.; Rank, E. Synchronous collaborative tunnel design based on consistency-preserving multi-scale models
Advanced Engineering Informatics, 2014 - Status: Verlagsversion / published

Steuer, H.; Donaubauer, A.; Kolbe, T.H.; Flurl, M.; Mundani, R.-P.; Rank, E. Collaborative Planning of Inner-City-Railway-Tracks: A Generic Description of the Geographic Context and Its Dynamic Integration in a Collaborative Multi-Scale Geometry Modelling Environment
Advanced Engineering Informatics, 2014 - Status: Verlagsversion / published

Borrmann, A.; Kolbe, T.H.; Donaubauer, A.; Steuer, H.; Jubierre, J.R.; Flurl, M. Multi-scale geometric-semantic modeling of shield tunnels for GIS and BIM applications
Computer-Aided Civil and Infrastructure Engineering, 2014 - Status: Verlagsversion / published

Ruess, Martin; Schillinger, Dominik; Özcan, Ali I.; Rank, Ernst Weak coupling for isogeometric analysis of non-matching and trimmed multi-patch geometries
Computer Methods in Applied Mechanics and Engineering 269, pp. 46--71, 2014
DOI: 10.1016/j.cma.2013.10.009

Ranjbar, M.; Mashayekhi, M.; Parvizian, J.; Düster, A.; Rank, E. Show abstract Using the finite cell method to predict crack initiation in ductile materials
Computational Materials Science 82, pp. 427 - 434, 2014
DOI: 10.1016/j.commatsci.2013.10.012



In this paper, the Finite Cell Method (FCM) is used to predict the crack evolution in ductile materials under small strains and nonlinear isotropic hardening conditions. The FCM is the result of combining the p-version finite element and fictitious domain methods, and has been shown to be effective in solving problems with complicated geometries for which the meshing procedure can be quite expensive. The crack evolution is introduced to the constitutive equations by using the simplified Lemaitre ductile damage model. The performance of the method is verified by means of two numerical examples in both 2D and 3D problems.

Frisch, Jerome; Mundani, Ralf-Peter; Rank, Ernst Show abstract Adaptive Multi-Grid Methods for Parallel CFD Applications
Scalable Computing: Practice and Experience 15 (1), pp. 33--48, 2014
DOI: 10.12694/scpe.v15i1.964



Computational fluid dynamic (CFD) computations are memory and time intensive and need to be executed in parallel for larger computational domains. In order to produce physical accurate solutions, adaptive grid setups have to be chosen as the memory and computing time would otherwise be too high, and results would not be obtained in a reasonable amount of time. This paper describes the usage of a multi-grid based approach for solving the pressure Poisson equation, arising during every time step of the Navier-Stokes equations. It will then highlight an analysis of errors introduced due to an adaptive setup of the domain, and show performance measurements for uniform and adaptive grid setups. Last but not least, a CFD benchmark example based on the von Kàrmàn vortex street will be presented, and the results will be discussed.

Sorger, C.; Frischmann, F.; Kollmannsberger, S.; Rank, E. Show abstract TUM.GeoFrame: Automated high-order hexahedral mesh generation for shell-like structures
Engineering with Computers 30 (1), pp. 41-56, 2014
DOI: 10.1007/s00366-012-0284-8



This paper presents a fully automated high-order hexahedral mesh generation algorithm for shell-like structures based on enhanced sweeping methods. Traditional sweeping techniques create all-hexahedral element meshes for solid structures by projecting an initial single surface mesh along a specified trajectory to a specified target surface. The work reported here enhances the traditional method for thin solids by creating conforming high-order allhexahedral finite element meshes on an enhanced surface model with surfaces intersecting in parallel, perpendicular and skew-angled directions. The new algorithm is based on cheap projection rules separating the original surface model into a set of disjoint single surfaces and a so-called interface skeleton. The core of this process is reshaping the boundary representations of the initial surfaces, generating new sweeping templates along the intersection curves and joining the single swept hex meshes in an independently generated interface mesh.

Cai, Quanji; Kollmannsberger, Stefan; Sala, Esther; Antonio, Huerta; Rank, Ernst On the natural stabilization of convection dominated problems using high order Bubnov-Galerkin Finite Elements
Computers & Mathematics with Applications 66 (12), pp. 2545-2558, 2014
DOI: 10.1016/j.camwa.2013.09.009 - Status: Verlagsversion / published

Rabold, A.; Schanda, U.; Kollmannsberger, S.; Rank, E. Schallschutz im mehrgeschossigen Holzbau - Luft- und Trittschalldämmung von Trenndecken -
Bauingenieur 89, 2014 - Status: Verlagsversion / published

Zander, N.; Bog, T; Elhaddad, M.; Espinoza, R.; Hu, H.; Joly, A.F.; Wu, C.; Zerbe, P.; Düster, A.; Kollmannsberger, S.; Parvizian, J.; Ruess, M.; Schillinger, D.; Rank, E. FCMLab: A Finite Cell Research Toolbox for MATLAB
Advances in Engineering Software 74, pp. 49-63, 2014
DOI: 10.1016/j.advengsoft.2014.04.004 - Status: Verlagsversion / published

Abedian1, A.; Parvizian, J.; Düster, A.; Rank, E. Show abstract The FCM compared to the h-version FEM for elasto-plastic problems
Applied Mathematics and Mechanics, 2014
DOI: 10.1007/s10483-014-1861-9 - Status: Verlagsversion / published



The Finite Cell Method (FCM) combines the high-order finite element method and the fictitious domain approach for the purpose of simple meshing. In the present study, the FCM is applied to the Prandtl-Reuss flow theory of plasticity and the results are compared with an h-version Finite Element Method (h-FEM). The numerical results show that the FCM is more efficient compared to h-FEMfor elasto-plastic problems, although the mesh does not conform to the boundary. It is also demonstrated that the FCM performs well for elasto-plastic loading and unloading.

Horger, T.; Kollmannsberger, S.; Frischmann, F.; Rank, E.; Wohlmuth, B. A new mortar formulation for modeling elastically bedded structures in vibro-acoustics in 3D
Advanced Modeling And Simulation In Engineering Sciences 1 (18), 2014 - Status: Postprint / reviewed

Ruess, M.; Schillinger, D.; Bazilevs, Y.; Varduhn, V.; Rank, E. Weakly enforced essential boundary conditions for NURBS-embedded and trimmed NURBS geometries on the basis of the finite cell method
International Journal for Numerical Methods in Engineering 95 (10), pp. 811-846, 2013

Abedian, Alireza; Parvizian, Jamshid; Düster, Alexander; Rank, Ernst The finite cell method for the J2 flow theory of plasticity
Finite Elements in Analysis and Design 69, pp. 37–47, 2013
DOI: 10.1016/j.finel.2013.01.006

Abedian, Alireza; Parvizian, Jamshid; Düster, Alexander; Khademyzadeh, Hassan; Rank, Ernst Performance of Different Integration Schemes in Facing Discontinuities in the Finite Cell Method
International Journal of Computational Methods 10 (03), pp. 1350002, 2013
DOI: 10.1142/S0219876213500023

Hernandez, H.; Knezevic, J.; Fogal, T.; Sherman, T.; Jevremovic, T. Show abstract Visual Numerical Steering in 3D AGENT Code System for Advanced Nuclear Reactor Modeling and Design
Annals of Nuclear Energy, 2013



The AGENT simulation system is used for detailed three-dimensional modeling of neutron transport and corresponding properties of nuclear reactors of any design. Numerical solution to the neutron transport equation in the AGENT system is based on the Method of Characteristics (MOCs) and the theory of R-functions. The latter of which is used for accurately describing current and future heterogeneous lattices of reactor core configurations. The AGENT code has been extensively verified to assure a high degree of accuracy for predicting neutron three-dimensional point-wise flux spatial distributions, power peaking factors, reaction rates, and eigenvalues. In this paper, a new AGENT code feature, a computational steering, is presented. This new feature provides a novel way for using deterministic codes for fast evaluation of reactor core parameters, at no loss to accuracy. The computational steering framework as developed at the Technische Universität München is smoothly integrated into the AGENT solver. This framework allows for an arbitrary interruption of AGENT simulation, allowing the solver to restart with updated parameters. One possible use of this is to accelerate the convergence of the final values resulting in significantly reduced simulation times. Using this computational steering in the AGENT system, coarse MOC resolution parameters can initially be selected and later update them – while the simulation is actively running – into fine resolution parameters. The utility of the steering framework is demonstrated using the geometry of a research reactor at the University of Utah: this new approach provides a savings in CPU time on the order of 50

Schillinger, D.; Stefanov, D.; Stavrev, A. Show abstract The method of separation for evolutionary spectral density estimation of multi-variate and multi-dimensional non-stationary stochastic processes
Probabilistic Engineering Mechanics, 2013



The method of separation can be used as a non-parametric estimation technique, especially suitable for evolutionary spectral density functions of uniformly modulated and strongly narrow-band stochastic processes. The paper at hand provides a consistent derivation of method of separation based spectrum estimation for the general multi-variate and multi-dimensional case. The validity of the method is demonstrated by benchmark tests with uniformly modulated spectra, for which convergence to the analytical solution is demonstrated. The key advantage of the method of separation is the minimization of spectral dispersion due to optimum time- or space-frequency localization. This is illustrated by the calibration of multi-dimensional and multi-variate geometric imperfection models from strongly narrow-band measurements in I-beams and cylindrical shells. Finally, the application of the method of separation based estimates for the stochastic buckling analysis of the example structures is briefly discussed.

Liu, D.; Zhao, F.-Y.; Wang, H.-Q.; Rank, E. Show abstract History source identification of airborne pollutant dispersions in a slot ventilated building enclosure
International Journal of Thermal Sciences 64 (2), pp. 81-92, 2013
DOI: 10.1016/j.ijthermalsci.2012.08.005 - Status: Verlagsversion / published



The backward time modeling of diffusion–convection pollutant dispersions has been developed with quasi-reversibility method in this work. The procedure is applied to the backward time identification of the contaminant release history and source location in a three-dimensional slot ventilated building enclosure. Spatial distributions of pollutant concentrations are known in priori. The effects of supplying air velocity, pollutant source location, pollutant diffusivity property, and pollutant release time on the accuracy of the pollutant dispersion history recovery have been investigated. Numerical results demonstrate that the accuracy of the pollutant dispersion history recovery can be enhanced with different approaches and measures, including the promotion of room ventilation rate, the shrinkage of distance between the pollutant source and supplying air port, and the reduction of pollutant diffusivity. The facilitated implementations of boundary conditions and the improved generality of quasi-reversibility methods make the pollutant source history identifications of less computational efforts. Particularly, the good agreement of the backward time identified source location with the true situation fully shows that quasi-reversibility method is more competitive in the engineering applications involving with convective fluid flows.

Liu, Di; Zhao, Fu-Yun; Wang, Hang-Quing; Rank, Ernst Show abstract Turbulent transport of airborne pollutants in a residential room with a novel air conditioning unit
International Journal of Refrigeration, 2012



Modeling on indoor air quality is performed considering the effect of a new window-type air conditioner, which is a promising way toward compromising energy consumption and residential air environment. Sensitivity analysis of the actual operating situations has been implemented, including the total fresh air supply and the full room air recirculation. The effects of supplying air flow rate, pollutant filtration efficiency, and indoor thermal buoyancy on the airborne pollutant transports are also illustrated. The numerical results demonstrate that the reduction of indoor pollutant levels can be accomplished either by increasing the fresh air ratio, or by increasing filtered removal efficiency, or by increasing the supplying airflow rate, or by decreasing the strength of indoor heating source. The indoor contaminant concentration asymptotically approaches to a small value for the situation of full fresh air supply, which agrees well with the analytical solutions of indoor contaminant concentration under the extreme operations.

Liu, Di; Zhao, Fu-Yun; Wang, Hang-Quing; Rank, Ernst; Kou, Guang-Xiao Show abstract Inverse determination of building heating profiles from the knowledge of measurements within the turbulent slot-vented enclosure
International Journal of Heat and Mass Transfer, 2012



Slot ventilated enclosure flows have been simulated, respectively in displacement ventilation and mixed ventilation covering from the forced convection dominated flow to the natural convection dominated flow. Direct convection simulation together with the turbulent streamlines and turbulent heatlines demonstrate that the enclosure flow pattern, indoor thermal level and heat transfer potential will depend on the interactions of external forced flow and thermal buoyancy driven flows, i.e., Reynolds number and Grashof number. In subsequent inverse convection modeling, the inverse determination of enclosure wall heat flux profiles was conducted by the use of adjoint methodology, in which the direct, sensitivity and adjoint problems are formulated and solved by finite volume method. The effects of the supplying air flow rate, thermal source strength, ventilation mode, flux functional forms, and the measurement errors on the accuracy of inverse turbulent convection estimation have been investigated. The inverse solutions of turbulent convections are of low level accuracy as the flow becomes thermal-driven turbulent flows, and they deteriorate as the noise levels increase. This work is of fundamental importance for the room air flow design and measurements involving the turbulent thermal convections.

Stavrev, A.; Stefanov, D.; Schillinger, D.; Rank, E. Show abstract Comparison of Eigenmode based and random field based imperfection modeling for the stochastic buckling analysis of I-section beam-columns
International Journal of Structural Stability and Dynamics, 2012



The uncertainty of geometric imperfections in a series of nominally equal I-beams leads to a variability of corresponding buckling loads. Its analysis requires a stochastic im- perfection model, which can be derived either by the simple variation of the critical Eigenmode with a scalar random variable, or with the help of the more advanced theory of random fields. The present paper first provides a concise review of the two different modeling approaches, covering theoretical background, assumptions and calibration, and illustrates their integration into commercial finite element software to conduct stochastic buckling analyses with the Monte Carlo method. The stochastic buckling behavior of an example beam is then simulated with both stochastic models, calibrated from corre- sponding imperfection measurements. The simulation results show that for different load cases, the response statistics of the buckling load obtained with the Eigenmode based and the random field based models agree very well. A comparison of our simulation results with corresponding Eurocode 3 limit loads indicates that the design standard is very conservative for compression dominated load cases.

Schillinger, D.; Dedè, L.; Scott, M.A.; Evans, J.A.; Borden, M.J.; Rank, E.; Hughes, T.J.R. Show abstract An Isogeometric Design-through-analysis Methodology based on Adaptive Hierarchical Refinement of NURBS, Immersed Boundary Methods, and T-spline CAD Surfaces
Computer Methods in Applied Mechanics and Engineering (HOFEIM special issue), 2012
DOI: 10.1016/j.cma.2012.03.017



We explore hierarchical refinement of NURBS as a basis for adaptive isogeometric and immersed boundary analysis. We use the principle of B-spline subdivision to derive a local refinement procedure, which combines full analysis suitability of the basis with straightforward implementation in tree data structures and simple generalization to higher dimensions. We test hierarchical refinement of NURBS for some elementary fluid and structural analysis problems in two and three dimensions and attain good results in all cases. Using the B-spline version of the finite cell method, we illustrate the potential of immersed boundary methods as a seamless isogeometric design-through-analysis procedure for complex engineering parts defined by T-spline CAD surfaces, specifically a ship propeller and an automobile wheel. We show that hierarchical refinement considerably increases the flexibility of this approach by adaptively resolving local features.

Düster, Alexander; Sehlhorst, Hans-Georg; Rank, Ernst Numerical homogenization of heterogeneous and cellular materials utilizing the finite cell method
Computational Mechanics 50 (4), pp. 413--431, 2012
DOI: 10.1007/s00466-012-0681-2

Schillinger, Dominik; Ruess, Martin; Zander, Nils; Bazilevs, Yuri; Düster, Alexander; Rank, Ernst Show abstract Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method
Computational Mechanics 50 (4), pp. 445-478, Springer-Verlag, 2012
DOI: 10.1007/s00466-012-0684-z



The Finite Cell Method (FCM) is an embedded domain method, which combines the fictitious domain approach with high-order finite elements, adaptive integration, and weak imposition of unfitted Dirichlet boundary conditions. For smooth problems, FCM has been shown to achieve exponential rates of convergence in energy norm, while its structured cell grid guarantees simple mesh generation irrespective of the geometric complexity involved. The present contribution first unhinges the FCM concept from a special high-order basis. Several benchmarks of linear elasticity and a complex proximal femur bone with inhomogeneous material demonstrate that for small deformation analysis, FCM works equally well with basis functions of the p-version of the finite element method or high-order B-splines. Turning to large deformation analysis, it is then illustrated that a straightforward geometrically nonlinear FCM formulation leads to the loss of uniqueness of the deformation map in the fictitious domain. Therefore, a modified FCM formulation is introduced, based on repeated deformation resetting, which assumes for the fictitious domain the deformation-free reference configuration after each Newton iteration. Numerical experiments show that this intervention allows for stable nonlinear FCM analysis, preserving the full range of advantages of linear elastic FCM, in particular exponential rates of convergence. Finally, the weak imposition of unfitted Dirichlet boundary conditions via the penalty method, the robustness of FCM under severe mesh distortion, and the large deformation analysis of a complex voxel-based metal foam are addressed.

Wille, H.; Rank, E.; Yosibash, Z. Show abstract Prediction of the mechanical response of the femur with uncertain elastic properties
Journal of Biomechanics 45 (7), pp. 1140-1148, 2012



A mandatory requirement for any reliable prediction of the mechanical response of bones, based on quantitative computer tomography, is an accurate relationship between material properties (usually Young's modulus E) and bone density ?. Many such E-? relationships are available based on different experiments on femur specimens with a large spread due to uncertainties. The first goal of this study is to pool and analyze the relevant available experimental data and develop a stochastic E-? relationship. This analysis highlights that there is no experimental data available to cover the entire density range of the human femur and that some ``popular'' E-? relationships are based on data that contains extreme scatter, while others are based on a very limited amount of information. The second goal is to use the newly developed stochastic E-? relationship in high-order finite element analyses (FEAs) for the computation of strains and displacements in two human proximal femurs, mimicking in vitro experiments. When compared with the experimental observations, the FEA predictions using the median of the stochastic E-? relationship follow the underlying distribution of the stochastic E-? relationship. Thus, most deviations of the FEA predictions from experimental observations can possibly be explained by uncertain elastic properties of the femur.

Zhao, F.-Y.; Rank, E.; Liu, D.; Wang, H.-Q.; Ding, Y.-L. Show abstract Dual steady transports of heat and moisture in a vent enclosure with all round states of ambient air
International Journal of of Heat and Mass Transfer 55 (11), pp. 6979-6993, 2012
DOI: DOI:10.1016/j.ijheatmasstransfer.2012.07.011 - Status: Verlagsversion / published



Combined natural convective heat and moisture transports in a moist-air-filled enclosure with four free vent ports are numerically investigated. Four situations of ambient air states, hot and humid (I), hot and arid (II), cold and arid (III), and cold and humid (IV), are taken into consideration. Convective transports of semi-enclosed air, heat and moisture are respectively analyzed using the contours of streamfunction, heatfunction and massfunction, in addition to the isotherms and iso-concentrations. Overall convective heat transfer rate (Nu) and moisture transfer rate (Sh) of the internal concentrated heat and moisture source have been correlated with the thermal Rayleigh number respectively within the domain of the heat transfer driven flows and that of moisture transfer driven flows. When different initial convective flow conditions were imposed in the cases (I) and (IV), dual steady flow states of semi-enclosed heat and moisture convection are observed, and heat and moisture transport potentials can be enhanced or inhibited depending on the flow solution branches. These results can be adopted to guide the design of natural ventilation in the humid regions.

Yang, Z.; Ruess, M.; Kollmannsberger, S.; Düster, A.; Rank, E. An efficient integration technique for the voxel-based finite cell method
International Journal for Numerical Methods in Engineering 91 (5), pp. 457--471, John Wiley & Sons, Ltd, 2012
DOI: 10.1002/nme.4269

Zander, N.; Kollmannsberger, S.; Ruess, M.; Yosibash, Z.; Rank, E. Show abstract The Finite Cell Method for linear thermoelasticity
Computers & Mathematics with Applications 64 (11), pp. 3527 - 3541, 2012
DOI: 10.1016/j.camwa.2012.09.002



The recently introduced Finite Cell Method (FCM) combines the fictitious domain idea with the benefits of high-order Finite Elements. While previous publications concentrated on single-field applications, this paper demonstrates that the advantages of the method carry over to the multi-physical context of linear thermoelasticity. The ability of the method to converge with exponential rates is illustrated in detail with a benchmark problem. A second example shows that the Finite Cell Method correctly captures the thermoelastic state of a complex problem from engineering practice. Both examples additionally verify that, also for two-field problems, Dirichlet boundary conditions can be weakly imposed on non-conforming meshes by the proposed extension of Nitsche's Method. The recently introduced Finite Cell Method (FCM) combines the fictitious domain idea with the benefits of high-order Finite Elements. While previous publications concentrated on single-field applications, this paper demonstrates that the advantages of the method carry over to the multi-physical context of linear thermoelasticity. The ability of the method to converge with exponential rates is illustrated in detail with a benchmark problem. A second example shows that the Finite Cell Method correctly captures the thermoelastic state of a complex problem from engineering practice. Both examples additionally verify that, also for two-field problems, Dirichlet boundary conditions can be weakly imposed on non-conforming meshes by the proposed extension of Nitsche's Method.

Rank, E.; Ruess, M.; Kollmannsberger, S.; Schillinger, D.; Düster, A. Geometric modeling, isogeometric analysis and the finite cell method
Computer Methods in Applied Mechanics and Engineering 249-252 (0), pp. 104 - 115, 2012
DOI: 10.1016/j.cma.2012.05.022

Ruess, M.; Yosibash, Z.; Rank, E. Show abstract Application of the Finite Cell Method to patient-specific femur simulations
In: GAMM, 2011



Standard methods for predicting the mechanical response of a human femur bone from quantitative computer-tomography (qCT) scans are classically based on the h-version of the finite element method. These methods are often limited in accuracy and efficiency due to the need for segmentation and the slow convergence rate. With the Finite Cell Method (FCM) a high-order fictitious domain method has been developed that overcomes the aforementioned problems and provides accurate results when compared to high-order finite element methods and experimental results. Herein the FCM applied to the analysis of a patient-specific femur is presented. The femur model is determined based on qCT-scans and the elastic response under compression is presented in terms of strains and displacements. The results are compared with a p-FE analysis and validated by results from an in-vitro test of the modeled femur.

Sehlhorst, H.-G.; Düster, A.; Jänicke, R.; Diebels, S.; Rank, E. Show abstract Extraction of effective material parameters with application to sandwich structures
Proceedings in Applied Mathematics and Mechanics, 2011



In this contribution we present a first-order numerical homogenization approach which allows for extracting effective linear elastic properties of heterogeneous materials. The approach is based on the window or self consistency method where a representative microscopic subdomain is embedded into a window of effective properties. Since these properties are not known in advance they have to be determined iteratively. For the discretization of the micro structures we use the Finite Cell Method, which is a fictitious domain method of higher-order. It is very well suited for efficiently discretizing complicated geometries stemming, for example, from tomography (CT-scans). In the numerical examples we will investigate a bending test of a sandwich plate which is composed of a polymeric core with thin faceplates made of Aluminum. Firstly, effective properties of the core are extracted and then applied to a macroscopic numerical model. The numerical results are validated by experiments.

Parvizian, J.; Duester, A.; Rank, E. Show abstract Topology optimization using the finite cell method
Optimization and Engineering, 2011



Huge effort has been spent over the past decades to develop efficient numerical methods for topology optimization of mechanical structures. Most recent investigations have focused on increasing the efficiency and robustness, improving the optimization schemes and extending them to multidisciplinary objective functions. The vast majority of available methods is based on low order finite elements, assuming one element as the smallest entity which can be assigned material in the optimization process. Whereas the present paper uses only a very simple, heuristic optimization procedure, it investigates in detail the feasibility of high order elements for topology optimization. The Finite Cell Method, an extension of the p-version of FEM is used, which completely separates between the description of the geometry of a structure and cells, where the high order shape functions are defined. Whereas geometry is defined on a (very) fine mesh, the material grid, shape functions live on a much coarser grid of elements, the finite cells. The method takes advantage of the ability of high order elements to accurately approximate even strongly inhomogeneous material distribution within one element and thus boundaries between material and void which pass through the interior of the coarse cells. Very attractive properties of the proposed method can be observed: Due to the high order approach the stress field in the optimized structure is approximated very accurately, no checkerboarding is observed, the iteratively found boundary of the structure is very smooth and the observed number of iterations is in general very small.

Ruess, M.; Tal, D.; Trabelsi, N.; Yosibash, Z.; Rank, E. Show abstract The finite cell method for bone simulations: Verification and validation
Biomechanics and Modeling in Mechanobiology, 2011



Standard methods for predicting bone's mechanical response from quantitative computer tomography (qCT) scans are mainly based on classical h-version finite element methods (FEMs). Due to the low-order polynomial approximation, the need for segmentation and the simplified approach to assign a constant material property to each element in h-FE models, these often compromise the accuracy and efficiency of h-FE solutions. Herein, a non-standard method, the finite cell method (FCM), is proposed for predicting the mechanical response of the human femur. The FCM is free of the above limitations associated with h-FEMs and is orders of magnitude more efficient, allowing its use in the setting of computational steering. This non-standard method applies a fictitious domain approach to simplify the modeling of a complex bone geometry obtained directly from a qCT scan and takes into consideration easily the heterogeneous material distribution of the various bone regions of the femur. The fundamental principles and properties of the FCM are briefly described in relation to bone analysis, providing a theoretical basis for the comparison with the p-FEM as a reference analysis and simulation method of high quality. Both p-FEM and FCM results are validated by comparison with an in vitro experiment on a fresh-frozen femur.

Schillinger, D.; Düster, A.; Rank, E. Show abstract The hp-d adaptive Finite Cell Method for geometrically nonlinear problems of solid mechanics
International Journal for Numerical Methods in Engineering doi:10.1002/nme.3289, 2011



The Finite Cell Method (FCM) combines the fictitious domain approach with the p-version of the finite element method and adaptive integration. For problems of linear elasticity, it offers high convergence rates and simple mesh generation irrespective of the geometric complexity involved. The present article presents the integration of the Finite Cell Method into the framework of nonlinear finite element technology. However, the penalty parameter of the fictitious domain is restricted to few orders of magnitude in order to maintain local stability of the deformation gradient. As a consequence of the weak penalization, nonlinear strain measures provoke excessive stress oscillations in the cells cut by geometric boundaries, leading to a low algebraic rate of convergence. Therefore, the FCM approach is complemented by a local overlay of linear hierarchical basis functions in the sense of the hp-d method, which synergetically use the h-adaptivity of the integration scheme. Numerical experiments show that the hp-d overlay effectively reduces oscillations and permits stronger penalization of the fictitious domain by stabilizing the deformation gradient. The hp-d adaptive Finite Cell Method is thus able to restore high convergence rates for the geometrically nonlinear case, while preserving the easy meshing property of the original FCM. Accuracy and performance of the present scheme are demonstrated by several benchmark problems in 1, 2 and 3 dimensions, and the nonlinear simulation of a complex foam sample.

Franke, D.; Duester, A.; Rank, E. Show abstract Computational contact mechanics based on the rp-version of the Finite Element Method
International Journal of Computational Methods 8 (3), 2011



In this paper we present an rp-adaptive discretization strategy to perform unilateral two-dimensional mechanical contact simulations by combining the r and p-version of the finite element method (FEM). The p-version leaves the finite element mesh unchanged and increases the shape function's polynomial degree in order to obtain convergence towards the exact solution of the underlying mathematical model. The r-method relocates nodes of an existing FE-mesh to improve the discretization of a given problem without introducing additional degrees of freedom, therefore keeping the problem size fixed. The rp-version, which is a combination of the two aforementioned methods, is used in our study to move a node of the FE-mesh to the end of the contact zone to account for the loss of regularity which arises due to the change from contact to non-contact along the edge. It will be shown that highly accurate results can be obtained by using highorder (p) finite elements in combination with the penalty method and a relocation (r) of element nodes.

Schillinger, D.; Rank, E. Show abstract An unfitted hp-adaptive finite element method based on hierarchical B-splines for interface problems of complex geometry
Computer Methods in Applied Mechanics and Engineering 200 (47-48), pp. 3358-3380, 2011



Generating finite element discretizations with direct interface parameterizations constitutes a considerable computational expense in case of complex interface geometries. The paper at hand introduces a B-spline finite elementmethod, which circumvents parameterization of interfaces and offers fast and easy meshing irrespective of the geometric complexity involved. Its core idea is the adaptive approximation of discontinuities by hierarchical grid refinement, which adds several levels of local basis functions in the close vicinity of interfaces, but unfitted to their exact location, so that a simple regular grid of knot span elements can be maintained. Numerical experiments show that an hp-refinement strategy, which simultaneously increases the polynomial degree of the B-spline basis and the levels of refinement around interfaces, achieves exponential rates of convergence despite the presence of discontinuities. It is also demonstrated that the hierarchical B-spline FEM can be used to transfer the recently introduced Finite Cell concept to geometrically nonlinear problems. Its computational performance, imposition of unfitted boundary conditions and fast hierarchical grid generation are illustrated for a set of benchmark problems in one, two and three dimensions, and the advantages of the regular grid approach for complex geometries are demonstrated by the geometrically nonlinear simulation of a voxel based foam composite.

Varduhn, V.; Mundani, R.-P.; Rank, E. Show abstract Real Time Processing of Large Data Sets from Built Infrastructure
Journal of Systemics, Cybernetics and Informatics 9 (3), pp. 63-67, 2011



In this paper, we present a framework that gives the user a tool at hand to explore large data sets from built infrastructure. In a first step we describe the integration of fully detailed product models of constructions delivering the geometric and auxiliary information we build up our data exploration from. The main part of this paper follows by presenting the application of a hierarchical data structure, an octree, that is capable of holding building information for a whole region or even a country and the development of complexity reduction algorithms that allow the visualisation of those data. To exploit the full performance of modern hardware platforms, the application of parallelisation techniques is inevitable and we present the implementation of these techniques to the data processing steps performed in the framework. After introducing the framework, we show possible applications to various disciplines such as environmental and civil engineering, architecture, or disaster management.

Knezevic, J.; Frisch, J.; Mundani, R.-P.; Rank, E. Show abstract Interactive Computing Framework for Engineering Applications
Journal of Computer Science 7 (5), pp. 591-599, 2011



Problem statement: Even though the computational steering state-of-the-art environments allow users to embed their simulation codes as a module for an interactive steering without the necessity for their own expertise in high-performance computing and visualisation, e.g., these environments are limited in their possible applications and mostly entail heavy code changes in order to integrate the existing code. Approach: In this study, we introduce an integration framework for engineering applications that supports distributed computations as well as visualization on-the-fly in order to reduce latency and enable a high degree of interactivity with only minor code alterations involved. Moreover, we tackle the problem of long communication delays in the case of huge data advent, which occur due to rigid coupling of simulation back-ends with visualization front-ends and handicap a user in exploring intuitively the relation of cause and effect. Results: The results for the first test cases are encouraging, both showing that we obtain excellent speedup in parallel scenarios and proving that the overhead introduced by the framework itself is negligible. Conclusion/Recommendations: Testing the case involving massively parallel simulation, as well as the integration of the framework into several parallel engineering applications are part of our imminent research.

Knezevic, J.; Mundani, R.-P.; Rank, E. Show abstract Interactive Computing - Virtual Planning of Hip Joint Surgeries with Real-Time Structure Simulations
International Journal of Modeling and Optimization 1 (4), pp. 308-313, 2011



Current interactive computing state-of-the-art environments, libraries, and frameworks open the door for engineers to run their simulation codes in an interactive mode, i. e. allowing for estimations of the state and tendency, as well as modifications, during a simulation program runtime without the necessity for their own expertise in efficient algorithms and data structures, high-performance computing, and visualisation. Nevertheless, when it comes to the real-time response of the simulation to this interaction - namely, keeping the connection between the user's change and its effect intuitive or at least observable - these environments are still limited in their possible application and, furthermore, often entail heavy code changes in order to be coupled to existing codes. Therefore, we introduce an integration framework applicable to different engineering applications, which with only minor code modifications involved supports distributed simulations as well as visualisation on-the-fly and enables real time interactive computational steering. Furthermore, we present its integration into a previously existing pre-operative planning environment for joint replacement surgery, which makes possible an interactive patient-specific selection of the optimal implant design, size, and position. The environment is supposed to enable the real-time surgeon's interplay with virtual models of bones and implants in 3D, thus, simultaneous computation and visualisation of the load transfer between the bone and the implant. Moreover, we tackle the problem of long communication delays which occur in the case of rigid coupling of simulation back-ends with visualisation front-ends and handicap a surgeon in observing which of his modifications leads to which outcome.

Schorr, M.; Borrmann, A.; Obergrießer, M.; Ji, Y.; Günthner, W.; Rank, E. Show abstract Using Product Data Management Systems for Civil Engineering Projects - Potentials and Obstacles
Journal of Computing in Civil Engineering 25 (6), pp. 430-441, 2011



Product data management (PDM) systems are well-established in the manufacturing industry. They form the standard solution for the central storage of all data relating to a product and the processes involved in its manufacture. Particularly, the consistent management of computer-aided design (CAD) models, including sophisticated versioning techniques, access rights management, and the integrated workflow management, are attractive features for using PDM systems for civil engineering projects. This paper investigates the technical concepts behind PDM systems and compares their suitability as a data management solution in civil engineering projects with that of document management systems and product model servers. Alongside a comparative study of the major PDM systems available on the market, we also present a case study involving a PDM system that has been employed for a concrete civil engineering project.

Yang, Zhengxiong; Kollmannsberger, Stefan; Düster, Alexander; Ruess, Martin; Garcia, Eduardo Grande; Burgkart, Rainer; Rank, Ernst Show abstract Non-standard bone simulation: interactive numerical analysis by computational steering
Computing and Visualization in Science 14 (5), pp. 207–216, Springer-Verlag, 2011
DOI: 10.1007/s00791-012-0175-y



Numerous numerical methods have been developed in an effort to accurately predict stresses in bones. The largest group are variants of the h-version of the finite element method (h-FEM), where low order Ansatz functions are used. By contrast, we3 investigate a combination of high order FEM and a fictitious domain approach, the finite cell method (FCM). While the FCM has been verified and validated in previous publications, this article proposes methods on how the FCM can be made computationally efficient to the extent that it can be used for patient specific, interactive bone simulations. This approach is called computational steering and allows to change input parameters like the position of an implant, material or loads and leads to an almost instantaneous change in the output (stress lines, deformations). This direct feedback gives the user an immediate impression of the impact of his actions to an extent which, otherwise, is hard to obtain by the use of classical non interactive computations. Specifically, we investigate an application to pre-surgical planning of a total hip replacement where it is desirable to select an optimal implant for a specific patient. Herein, optimal is meant in the sense that the expected post-operative stress distribution in the bone closely resembles that before the operation.

Rank, E.; Kollmannsberger, S.; Sorger, Ch.; Düster, A. Shell Finite Cell Method: A high order fictitious domain approach for thin-walled structures
Computer Methods in Applied Mechanics and Engineering 200 (45-46), pp. 3200 - 3209, 2011
DOI: 10.1016/j.cma.2011.06.005

van Treeck, Christoph; Frisch, Jérôme; Rao Bolineni, Sandeep; Stratbücker, Sebastian; Holm, Andreas Scale-Adaptive Indoor Thermal Comfort Analysis
In: Proc. of the 1st International Conference on Multiphysics Simulation - Advanced Methods for Industrial Engineering, 2010

Schillinger, D.; V.Papadopoulos; Bischoff, M.; Papadrakakis, M. Show abstract Buckling Analysis of Imperfect I-Section Beam- Columns with Stochastic Shell Finite Elements
Computational Mechanics, 2010



Buckling loads of thin-walled I-section beam-columns exhibit a wide stochastic scattering due to the uncertainty of imperfections. The present paper proposes a finite element based methodology for the stochastic buckling simulation of I-sections, which uses random fields to accurately describe the fluctuating size and spatial correlation of imperfections. The stochastic buckling behaviour is evaluated by crude Monte-Carlo simulation, based on a large number of I-section samples, which are generated by spectral representation and subsequently analyzed by non-linear shell finite elements. The application to an example I-section beam-column demonstrates that the simulated buckling response is in good agreement with experiments and follows key concepts of imperfection triggered buckling. The derivation of the buckling load variability and the stochastic interaction curve for combined compression and major axis bending as well as stochastic sensitivity studies for thickness and geometric imperfections illustrate potential benefits of the proposed methodology in buckling related research and applications.

Schillinger, D.; Papadopoulos, V. Show abstract Accurate estimation of evolutionary power spectra for strongly narrow-band random fields
Computer Methods in Applied Mechanics and Engineering 17-20 (199), pp. 947-960, 2010



One of the most widely used techniques for the simulation of non-homogeneous random fields is the spectral representation method. Its key quantity is the power spectrum, which characterizes the random field in terms of frequency content and spatial evolution in a mean square sense. The paper at hand proposes a method for the estimation of separable power spectra from a series of samples, which combines accurate spectrum resolution in space with an optimum localization in frequency. For non-separable power spectra, it can be complemented by a joint strategy, which is based on the partitioning of the space-frequency domain into several sub-spectra that have to be separable only within themselves. Characteristics and accuracy of the proposed method are demonstrated for analytical benchmark spectra, whose estimates are compared to corresponding results of established techniques based on the shorttime Fourier, the harmonic wavelet and the Wigner - Ville transforms. It is then shown by a practical example from stochastic imperfection modeling in structures that in the presence of strong narrowbandedness in frequency, the proposed method for separable random fields leads to a considerable improvement of estimation results in comparison to the established techniques.

Rabold, A.; Buchschmid, M.; Düster, A.; Müller, G.; Rank, E. Show abstract Modelling the excitation force of a standard tapping machine on lightweight floor structures
Building Acoustics 17 (3), pp. 175-197, 2010



Up to now the research and development in the field of building acoustics is based mainly on measurements. In consequence the development and optimization of a new building component is a very tedious and expensive task. A considerable reduction of these costs could be achieved, if the optimization relying on measurements would be replaced - at least to some extent - by a computational prediction model. For these models it is necessary to represent not only the component and the adjacent rooms but also the excitation in a suitable way. This paper gives an overview of models for the excitation generated by a standard tapping machine taking into account the interaction between the impacting steel cylinders of the tapping machine and the vibrating surface of the floor.

Wu, I-C.; Borrmann, A.; Beissert, U.; König, M.; Rank, E. Show abstract Bridge Construction Schedule Generation with Pattern-based Construction Models and Constraint-based Simulation
Advanced Engineering Informatics 24 (4), pp. 379-388, 2010



This paper presents a novel methodology which assists in automating the generation of time schedules for bridge construction projects. The method is based on a simulation of construction works, taking into account the available resources and the interdependencies between individual tasks. The simulation is realized by means of a discrete-event simulation software originally created for plant layout in the manufacturing industry. Due to the fact that the fixed process chains provided are too rigid to model the spontaneous construction task sequences, a constraint module that dynamically selects the following task has been incorporated. Constraint module input data is formed by activity packages comprising of the affected building element, the required material, machine and manpower resources, as well as the technological pre-requisites of the activity to be performed. Since manual creation of the large set of activity packages is laborious and error-prone, a 3D model-based application has been developed which allows the interactive assignment of construction methods to individual building elements. To facilitate this process, a level-of-detail approach has been implemented which allows the user to successively refine both the process model and the corresponding product model. The discrete-event simulation system uses all the given information to create a proposal for the construction schedule automatically, which may then be refined using standard scheduling software.

Franke, D.; Duester, A.; Nuebel, V.; Rank, E. Show abstract A comparison of the h-, p-, hp-, and rp-version of the FEM for the solution of the 2D Hertzian contact problem (R)
Computational Mechanics 45 (5), pp. 513, 2010



Even after more than three decades of intensive research in the field of contact mechanics, there is still a great need for improving the numerical methods. Recent investigations on the 2D Hertzian contact problem clearly showed significantly varying results for different finite element versions. In this paper we will compare the analytical solution of the 2D Hertzian contact problem with the numerical results of the classical h-version with uniform and locally refined meshes, as well as with the p-, the hp-, and the rp-version of the FEM. The penalty method is used to incorporate the contact constraints.

Ledentsov, Dmitry; Düster, Alexander; Volk, Wolfram; Wagner, Marcus; Heinle, Ingo; Rank, Ernst Model adaptivity for industrial application of sheet metal forming simulation
Finite Elements in Analysis and Design 46 (7), pp. 585--600, 2010
DOI: 10.1016/j.finel.2010.02.006

Bordas, Stéphane P.A.; Rabczuk, Timon; Hung, Nguyen-Xuan; Nguyen, Vinh Phu; Natarajan, Sundararajan; Bog, Tino; Quan, Do Minh; Hiep, Nguyen Vinh Strain smoothing in FEM and XFEM
Computers & Structures 88 (23–24), pp. 1419 - 1443, 2010
DOI: 10.1016/j.compstruc.2008.07.006

Rank, E.; Kollmannsberger, S.; Düster, A. High Order Finite Elements: Principles, Achievements, Open Questions
In: Topping, B.H.V.; Adam, J.M.; Pallares, F.J.; Bru, R.; Romero, M.L. (Eds): Computational Technology Reviews, SAXE-COBURG Publications, 2010

Geller, S.; Kollmannsberger, S.; Bettah, M.El; Krafczyk, M.; Scholz, D.; Düster, A.; Rank, E. An Explicit Model for Three-Dimensional Fluid-Structure Interaction using LBM and p-FEM
In: Bungartz, Hans-Joachim; Mehl, Miriam; Schäfer, Michael (Eds.), Fluid Structure Interaction II, 73, Springer Berlin Heidelberg, 2010, pp. 285-325

Borrmann, A. Notitle
ITcon 14, pp. 705-723, 2009

van Treeck, C.; Frisch, J.; Pfaffinger, M.; Rank, E.; Paulke, S.; Schweinfurth, I.; Schwab, R.; Hellwig, R.; Holm, A. Show abstract Integrated thermal comfort analysis using a parametric manikin model for interactive real-time simulation
Journal for Building Performance Simulation in press, 2009



Following the work of Fiala we developed and tested a parametric multi-segment manikin model as the interface between Fiala's human thermoregulation model and other computational codes for studying transient and local effects of thermal sensation and comfort perception. The model allows for motion control by transforming body parts according to an armature model which relates topological dependencies. The position of joints and decomposition into segments is chosen in terms of the settings of Fiala's model. Several faceted geometric models are available such as the NASA MSIS Standard or predefined NASTRAN geometries. The developed thermoregulation interface provides means to computational steering, i.e. to interact with an ongoing simulation. The boundary conditions, the type of clothing, or the activity level can be modified online, results are updated on a real time scale during the simulation. The visualization on the artificial skin of the manikin includes the surface/skintemperatures and the local thermal sensation votes (LTSV); likewise the predicted mean vote (PMV) and the dynamic thermal sensation (DTS) are output. The LTSV data are based on experimental data which were obtained in a test chamber involving 24 test subjects for three levels of clothing insulation and a light level of activity.

Hegger, J.; Dreßen, T.; Schießl, P.; Gehlen, C.; Zintel, M.; Mayer, T. F.; Kessler, S.; Rank, E.; Lukas, K.; Borrmann, A.; Hauer, B.; Wiens, U. Beton - Nachhaltiges Bauen im Lebenszyklus
Bauingenieur 84, 2009

Rabold, A.; Hamm, P. Schall- und schwingungsoptimierte Holzdecken
Bauen mit Holz, 2009

Ruess, M.; Pahl, P. Show abstract An extended QR-solver for large profiled matrices
International Journal for Numerical Methods in Engineering, 2009



A new method for the solution of the standard eigenvalue problem with large symmetric profile matrices is presented. The method is based on the well-known QR-method for dense matrices. A new, flexible and reliable extension of the method is developed that is highly suited for the independent computation of any set of eigenvalues. In order to analyze the weak convergence of the method in the presence of clustered eigenvalues, the QR-method is studied. Two effective, stable and numerically cheap extensions are introduced to overcome the troublesome stagnation of the convergence. A repeated preconditioning process in combination with Jacobi rotations in the parts of the matrix with the strongest convergence is developed to significantly improve both local and global convergence. The extensions preserve the profile structure of the matrix. The efficiency of the new method is demonstrated with several examples.

Borrmann, A.; Rank, E. Show abstract Topological analysis of 3D Building Models using a Spatial Query Language
Advanced Engineering Informatics 23 (4), pp. 370-385, 2009



The paper presents parts of the development of a spatial query language for building information models. Such a query language enables the spatial analysis of building information models and the extraction of partial models that fulfill certain spatial constraints. Among other features, it includes topological operators, i.e. operators that reflect the topological relationships between 3D spatial objects. The paper presents definitions of the semantics of the topological operators within, contain, touch, overlap, disjoint and equal in 3D space by using the 9-intersection model. It further describes a possible implementation of the topological operators by means of an octree-based algorithm. The recursive algorithm presented in this article relies on a breadth-first traversal of the operands' octree representations and the application of rules that are based on the color of the octants under examination. Because it successively increases the discrete resolution of the spatial objects employed, the algorithm enables the user on the one hand to handle topological relationships in a fuzzy manner and on the other hand to trade-off between computational effort and the required accuracy. The article also presents detailed investigations on the runtime performance of the developed algorithm.

Borrmann, A.; Rank, E. Show abstract Specification and implementation of directional operators in a 3D spatial query language for building information models
Advanced Engineering Informatics 23 (1), pp. 32-44, 2009



A spatial query language enables the spatial analysis of building information models and the extraction of partial models that fulfill certain spatial constraints. Among other features, the developed spatial query language includes directional operators, i.e., operators that reflect the directional relationships between 3D spatial objects, such as northOf, southOf, eastOf, westOf, above and below. The paper presents in-depth definitions of the semantics of two new directional models for extended 3D objects, the projection-based and the halfspace-based model, by using point-set theory notation. It further describes the possible implementation of directional operators using a newly developed space-partitioning data structure called slot-tree, which is derived from the objects' octree representation. The slot-tree allows for the application of recursive algorithms that successively increase the discrete resolution of the spatial objects employed and thereby enables the user to trade-off between computational effort and the required accuracy. The article also introduces detailed investigations on the runtime performance of the developed algorithms.

Borrmann, A.; Schraufstetter, S.; Rank, E. Show abstract Implementing metric operators of a Spatial Query Language for 3D Building Models: Octree and B-Rep approaches
Journal of Computing in Civil Engineering 23 (1), pp. 34-46, 2009



A spatial query language for building information models enables the spatial analysis of buildings and the extraction of partial models that fulfill certain spatial constraints. Among other features, the developed spatial query language includes metric operators, i.e., operators that reflect distance relationships between spatial objects, such as mindist, maxdist, isCloser and isFarther. The paper presents formal definitions of the semantics of these operators by using point set theory notation. It further describes two possible implementation methods: the first one is based on a discrete representation of the operands’ geometry by means of the hierarchical, space-partitioning data structure octree. The octree allows for the application of recursive algorithms that successively increase the discrete resolution of the spatial objects employed and thereby enables the user to trade off between computational effort and the required accuracy. By contrast, the second approach uses the exact boundary representation (B-Rep) of both spatial objects resulting in precise distance measurements. Here, the bounding facets of each operand are indexed by a so-called axis-aligned bounding boxes tree (AABB tree). The algorithm uses the AABB-tree structure to identify candidate pairs of facets, for which an exact but expensive distance algorithm is employed. The article compares both approaches by means of detailed investigations on the runtime performance of the developed algorithms.

Paul, N.; Borrmann, A. Show abstract Geometrical and topological approaches in building information modelling
ITCon 14, pp. 705-723, 2009



This paper presents concepts for dealing with topological information in building informa¬tion models. On the one hand, it shows how to derive topological relationships from “traditional” building models consisting of unconnected B-Rep bodies by means of geometric processing algorithms. On the other hand, it discusses the capabilities of building modelling based on topological concepts. This approach combines relational database design principles with algebraic and point set topology and shows how complexes—in particular cw-complexes—and topological spaces can be stored in relational databases. To make complexes suitable for building modelling it is necessary to extend them by geometric properties. Finally, the paper depicts an advantageous application of cell-complex-based modelling: the separation of the building model into an abstract specification of building entities (sketch), a collection of possible concrete realizations of such sketch entities (details), and a specification of the details used by sketch entities. Then a working drawing results from the spatial version of the relational operator inner equi-join, the so-called fibre product. The first section of this paper introduces into the problem and into current modelling concepts. Section 2 discusses geometry-based modelling whereas the following sections present the topological approach. First, Section 3 takes a topological view on buildings and then Section 4 discusses the corresponding data models. At Section 5 geometry is re-introduced. Section 6 presents the above mentioned application and, together with the subsequent conclusion, advocates the topological viewpoint.

Schleinkofer, M.; Rank, E. Show abstract Ein Ansatz zur automatischen Erstellung eines 3D-Modells für den Baubestand
Bauingenieur, 2009



Modellbasierte Planung gestattet die Durchführung einer Vielzahl von Planungsaufgaben in einer ganzheitlichen Sicht auf das Bauobjekt. Im Bereich der Umbau und Sanierungsplanung findet sie jedoch nur sehr geringen Zuspruch, da ein räumliches Bauwerksmodell bislang nur unter großem manuellen Einsatz zu erstellen ist. Der vorliegende Aufsatz stellt hierfür einen weitgehend automatisierten Weg vor. Aus dem wirtschaftlich effizienten Messablauf terrestrischer Laserscanner resultieren Punktwolken mit einer in der Regel sehr großen Anzahl an Einzelpunkten. Stufenweise wird daraus ein Oberflächenmodell entwickelt, wobei die räumliche Triangulierung der Punkte das zentrale Element darstellt. Aus dem Oberflächenmodell abgeleitete Volumenkörper werden dann mittels eines künstlichen neuronalen Netzes in Bauteilklassen kategorisiert. Gemäß dieser Klassifizierung entsteht schließlich, entsprechend der aufgemessenen Geometrie, ein Bauwerksdatenmodell.

Sehlhorst, H. -G.; Jänicke, R.; Düster, A.; Rank, E.; Steeb, H.; Diebels, S. Numerical investigations of foam-like materials by nested high-order finite element methods
Computational Mechanics 45 (1), pp. 45--59, 2009
DOI: 10.1007/s00466-009-0414-3

Kollmannsberger, S.; Geller, S.; Düster, A.; Tölke, J.; Sorger, C.; Krafczyk, M.; Rank, E. Fixed-grid fluid-structure interaction in two dimensions based on a partitioned Lattice Boltzmann and p-FEM approach
International Journal for Numerical Methods in Engineering 79 (7), pp. 817-845, John Wiley & Sons, Ltd., 2009
DOI: 10.1002/nme.2581

Sehlhorst, H.; Jänicke, R.; Duester, A.; Rank, E.; Steeb, H.; Diebels, S. Numerical homogenization techniques applying higher-order finite elements
submitted to Computational Mechanics, 2008

Duester, A.; Parvizian, J.; Yang, Z.; Rank, E. Show abstract The Finite Cell Method for three-dimensional problems of solid mechanics
Computer Methods in Applied Mechanics and Engineering, 2008



This article presents a generalization of the recently proposed finite cell method to three-dimensional problems of linear elasticity. The finite cell method combines ideas from embedding or fictitious domain methods with the p-version of the finite element method. Besides supporting a fast, simple generation of meshes it also provides high convergence rates. Mesh generation for a boundary representation of solids and for voxel-based data obtained from CT scans is addressed in detail. In addition, the implementation of non-homogeneous Neumann boundary conditions and the computation of cell matrices based on a composed integration is presented. The performance of the proposed method is demonstrated by three numerical examples, including the elastostatic computation of a human bone biopsy.

Heisserer, U.; Hartmann, S.; Duester, A.; Bier, W.; Yosibash, Z. Show abstract p-FEM for finite deformation powder compaction
Computer Methods in Applied Mechanics and Engineering 197, pp. 727-740, 2008



The simulation of powder compaction problems (die-compaction and cold isostatic pressing) is considered herein by an implicit highorder (p-version) finite element method. In this class of problems use is made of a finite strain viscoplasticity model with evolution equations for internal variables developed for the highly compressible behavior in powder compaction processes. The classical approach of implicit finite elements applies the combination of Backward-Euler integration scheme and the Multilevel-Newton algorithm to solve the system of differential-algebraic equations resulting from the space-discretized weak formulation by means of p-version finite elements. This approach requires on Gauss-point level a robust stress-algorithm. The challenging investigations are the incorporation of the applied highly non-linear viscoplasticity model into a p-version finite element formulation using follower load applications. Several axisymmetric numerical examples show the feasibility and good performance of this p-version approach.

Borrmann, Andre; Rank, Ernst Show abstract Topological operators in a 3D Spatial Query Language for Building Information Models
In: Proc. of the 12th Int. Conf. on Computing in Civil and Building Engineering (ICCCBE-XII)., 2008 - Status: Erstveröffentlichung



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van Treeck, C.; Wenisch, P.; Pfaffinger, M.; Egger, M.; Scheck, L.; Rank, E. Show abstract Interactive Indoor Thermal Comfort Evaluation
High Performance Computing in Science and Engineering, 2007



This report briefly summarizes the current state of the HLRB II project h005y which focuses on the interactive simulation and local assessment of indoor thermal comfort. The research group therefore develops a Computational Steering Environment (CSE) which consists of a parallel CFD kernel, a fast 3D mesh generator and a virtual reality-based visualization and steering component. The numerical method is based on a lattice Boltzmann algorithm with extensions for simulations of turbulent convective flows. Utilizing high-performance supercomputing facilities, the CSE allows for modifying both the geometric model and the boundary conditions during runtime coupled with the immediate update of results. This is made possible by a space-tree based partitioning algorithm that facilitates the meshing of arbitrarily shaped, complex facet models in a matter of just a few seconds computing time. Ongoing developments address the integration of a radiation solver, a human thermoregulation model and a local thermal comfort model.

Parvizian, J.; Duester, A.; Rank, E. Finite Cell Method, h- and p- extension for embedded domain problems in solid mechanics
Computational Mechanics 41, pp. 121-133, 2007

Heisserer, U.; Hartmann, S.; Yosibash, Z.; Duester, A. Show abstract On volumetric locking-free behavior of p-version finite elements under finite deformations.
Communications in Numerical Methods in Engineering., 2007



We demonstrate the locking-free properties of the displacement formulation of p-finite elements when applied to nearly incompressible Neo-Hookean material under finite deformations. For an axisymmetric model problem we provide semi-analytical solutions for a nearly incompressible Neo-Hookean material exploited to investigate the robustness of p-FEM with respect to volumetric locking. An analytical solution for the incompressible case is also derived to demonstrate the convergence of the compressible numerical solution towards the incompressible case when the compression modulus is increased.

van Treeck, C. Show abstract Energieeffizienz von Gebäuden und Behaglichkeit in Räumen
Editorial, Bauphysik 29, pp. 1, 2007



Die Begeisterung war vielen Teilnehmern anzusehen und in den fachlichen Diskussionen spürbar, offensichtlich hatte man auf eine Veranstaltung dieser speziellen Art gewartet, um die “Simulationsgemeinschaft” im deutschsprachigen Raum zusammenzuführen: Unter dem Leitthema “Energieeffizienz von Gebäuden und Behaglichkeit in Räumen” fand im Oktober 2006 an der Technischen Universität München die erste deutsch-österreichische IBPSA-Konferenz BauSIM2006 statt. Begleitend wurde eine industrielle Fachausstellung durchgeführt, die das Programm im Sinne einer intensiven Vernetzung mit der Industrie abrundete. Vorliegende Ausgabe der BAUPHYSIK enthält im Hauptteil die erweiterten Artikel einer vom wissenschaftlichen Gremium der Konferenz getroffenen Auswahl aus den rund 90 Tagungsbeiträgen. IBPSA steht für International Building Performance Simulation Association und ist ein internationales Forum für Anwender, Forscher und Entwickler im Bereich der thermisch-energetischen, ökologischen und anlagentechnischen Simulation von Gebäuden. IBPSA-Germany wurde 2004 als regionale Dependance gegründet und besteht derzeit aus rund 80 aktiven Mitgliedern aus Industrie, Forschungseinrichtungen und Universitäten aus dem deutschsprachigen Raum. Die Konferenz BauSIM wird künftig alle zwei Jahre angeboten. Sie soll dabei keine der zahlreichen kleineren etablierten Veranstaltungen ersetzen, sondern die Vielfalt der Fachthemen entsprechend der Ausrichtung der internationalen IBPSA-Tagungen vereinen. Seit Anfang 2007 ist die vollständig überarbeitete Homepage www.ibpsa-germany.org verfügbar, die den Mitgliedern der IBPSA-Gemeinschaft (Mitgliedschaft kostenfrei) Zugriff auf die Tagungsbeiträge der lokalen Konferenzen gestattet. Weiterhin wird gegenwärtig unter anderem an einem Simulationsratgeber nach dem konzeptionellen Vorbild eines offenen Wiki-Media-Systems gearbeitet. Ihr fachlicher Beitrag ist dabei herzlich willkommen!

van Treeck, C.; Egger, M.; Pueltz, G. Simupedia – the new IBPSA-Germany MediaWiki
IBPSA News 17 (1), pp. 45-46, 2007

Wenisch, P.; van Treeck, C.; Scheck, L.; Rank, E. Computational Steering: Interactive Flow Simulation in Civil Engineering
inSiDE 5 (2), pp. 18-21, 2007

Nuebel, V.; Duester, A.; Rank, E. Show abstract An rp-adaptive finite element method for the deformation theory of plasticity
Computational Mechanics (submitted) 39, pp. 557-574, 2007



In this paper we present an rp-discretization strategy for physically non-linear problems based on a high order finite element formulation. In order to achieve convergence, the p-version leaves the mesh unchanged and increases the polynomial degree of the shape functions locally or globally,whereas the r-method moves nodes and edges of an existing FE-mesh. The basic idea of our rp-version approach is to adjust the finite element mesh to the shape of the elastic-plastic interface in order to take into account the loss of regularity which arises along the curve of the plastic front. Numerical examples will demonstrate that this approach leads to an exponential rate of convergence and highly accurate results.

van Treeck, C.; Rank, E. Show abstract Dimensional reduction of 3D building models using graph theory and its application in building energy simulation
Engineering with Computers, 2007



Since the various people involved in the design process for a building project tend to hold conflicting views, this inevitably leads to a range of disparate models for planning and calculation purposes. In order to interpret the relevant geometrical, topological and semantical data for any given building model, we identify a structural component graph, a graph of room faces, a room graph and a relational object graph as aids and explain algorithms to derive these relations. We start with a building model by transferring its geometrical, topological and semantical data into a volume model, decomposing the latter into a so-called connection model and then extracting all air volume bodies and hulls of the model by means of further decomposition into elementary cyclic connection components. The technique is demonstrated within the scope of building energy simulation by deriving both a dimensionally reduced object model required for setting up a thermal multizone model and a geometrical model for defining single or multiple computational fluid dynamic domains in a building together with incidence matrices correlating these models. The algorithm is basically applicable to any building energy simulation tool.

van Treeck, C.; Wenisch, P.; Borrmann, A.; Pfaffinger, M.; Wenisch, O.; Rank, E. Show abstract ComfSim – Interaktive Simulation des thermischen Komforts in Innenräumen auf Höchstleistungsrechnern
Bauphysik 29. Heft 1, pp. 1-7, 2007



Der Beitrag gibt eine Übersicht über den gegenwärtigen Stand der Entwicklungen eines “Computational Steering” Werkzeuges zur interaktiven Simulation und Bewertung des thermischen Komforts in Innenräumen. Das System besteht aus einem parallelen CFD Rechenkern, einem schnellen 3D Gittergenerator und einer integrierten VR-basierten Visualisierungskomponente. Das numerische Verfahren basiert auf einem hybriden thermischen Gitter-Boltzmann-Verfahren mit Erweiterungen zur Simulation turbulenter konvektiver Raumluftströmungen. Die Nutzung von Techniken des wissenschaftlichen Höchstleistungsrechnens ermöglicht dabei interaktive Veränderungen am geometrischen Modell und an den Randbedingungen zur Laufzeit bei gleichzeitiger Neuberechnung und Darstellung von Ergebnissen. Das Modell wird gegenwärtig um ein Strahlenmodell und ein lokales thermisches Komfortmodell erweitert, das gemeinsam mit Projektpartnern entwickelt wird. Die Anwendung wird anhand der Strömungssimulation des Großraumabteils eines Zuges demonstriert.

Wenisch, P.; van Treeck, C.; Borrmann, A.; Rank, E.; Wenisch, O. Show abstract Computational Steering on Distributed Systems: Indoor Comfort Simulations as a Case Study of Interactive CFD on Supercomputers
Int. Journal of Parallel, Emergent and Distributed Systems 22 (4), pp. 275 – 291, 2007



This paper presents the current state of a computational steering system for interactive computational fluid dynamics (CFD) simulations, allowing engineers to simulate interactively indoor climate and to evaluate human comfort. The tools presented support cooperative planning and design by providing means for interactively adding, removing and modifying geometry and boundary conditions online during a CFD simulation. To ensure interactivity and short-latency updates even for high-resolution runs the parallel Lattice-Boltzmann-based simulation kernel is optimized for high-performance computing systems. Emphasis is placed on the computational steering architecture, connecting a supercomputer with one or more visualization workstations. In particular, we show how a high-performance communication between simulation and visualization or steering front-end can be achieved together with preserving a flexible mechanism of on-the-fly attachment of multiple cooperation clients.

Duester, A.; Niggl, A.; Rank, E. Show abstract Applying the hp-d version of the FEM to locally enhance dimensionally reduced models
Computer Methods in Applied Mechanics and Engineering 196, pp. 3524-3533, 2007



A modification of the hp–d method is presented, which allows to locally enhance a dimensionally reduced finite element approximation with an Ansatz based on a more accurate, i.e. dimensionally higher, model. The procedure is based on a hierarchical domain decomposition which is applied to couple discretizations of different types of mechanical models, like beams, plates and solids. Thereby, the error of the underlying mathematical model can be reduced in critical regions by introducing locally a physically more sophisticated model. Two examples are given to demonstrate the basic properties of the proposed method. In the first example the solution of a one-dimensional beam model is improved locally by a two-dimensional finite element computation. In the second example the local enhancement of a Reissner–Mindlin plate by a fully three-dimensional continuum approach is considered, yielding a significant reduction of the model error.

Duester, A.; Scholz, D.; Rank, E. Show abstract pq-Adaptive solid finite elements for three-dimensional plates and shells
Computer Methods in Applied Mechanics and Engineering 197, pp. 243-254, 2007



This article presents a pq-adaptive finite element procedure for three-dimensional computation of thin-walled structures like plates and shells. The approach is based on a hexahedral element with high-order shape functions. The polynomial degree of the shape functions in the three spatial directions of the element is adjusted by means of an adaptive procedure. To this end, a hierarchical error indicator is applied to automatically control the polynomial degree q in thickness and p in the in-plane direction of plate- and shell-like structures. The efficiency and reliability of the proposed adaptive method is demonstrated using two numerical examples.

Yosibash, Z.; Hartmann, S.; Heisserer, U.; Duester, A.; Rank, E.; Szanto, M. Show abstract Axisymmetric pressure boundary loading for finite deformation analysis using p-fem
Computer Methods in Applied Mechanics and Engineering 196 (7), pp. 1261 -- 1277, 2007



Follower loads, i.e. loads which depend on the boundary displacements by definition, frequently occur in finite deformation boundary-value problems. Restricting to axisymmetrical applications, we provide analytical and numerical solutions for a set of problems in compressible Neo-Hookean materials so to serve as benchmark problems for verifying the accuracy and efficiency of various FE methods for follower load applications. Thereafter, the weak formulation for the follower-load in 3-D domain is reduced to an axisymmetrical setting, and, subsequently, consistently linearized in the framework of p-FEMs, exploiting the blending function mapping techniques. The set of axisymmetric benchmark solutions is compared to numerical experiments, in which the results obtained by a p-FEM code are compared to these obtained by a state-of-the-art commercial h-FEM code and to the “exact” results. These demonstrate the efficiency and accuracy of p-FEMs when applied to problems in finite deformations with follower loads.

Heisserer, U. Back to the roots and beyond – A personal account on the tracks of Abraham from the Iron Age to metallurgy of the future.
GIF in Brief, 2006

van Treeck, C.; Rank, E. ComfSim – Interaktive Strömungssimulation und lokale Komfortanalyse in Innenräumen
Jahresbericht 2005, 2006

van Treeck, C.; Rank, E. SIMFAS – Thermische Gebäudesimulation
Jahresbericht 2005, 2006

Zechbauer, U.; van Treeck, C. Show abstract An Kopf und Fuß angenehme Turbulenzen, Klimatisierung: Superrechner erlaubt erstmals Strömungssimulation in Echtzeit
VDI Nachrichten, 2006



Heißer Kopf, kalte Füße. Der Dummy in der Flugzeugkabine schwitzt und friert gleichzeitig. Aus den Belüftungsdüsen strömt viel zu warme Luft direkt in sein Gesicht. Dafür herrscht an seinen Füßen Eiszeit, deshalb auch die warmen Socken. "Die Klimatisierung von Innenräumen ist eine Kunst für sich", sagt Dr. Christoph van Treeck von der TU München.

Wassouf, Z.; Egger, M.; Neuberg, F.; van Treeck, C.; Rank, E. Show abstract Produktmodell basierte Simulation des Ressourcenbedarfs von Bauwerken
Bauingenieur 81, 2006



Eine ganzheitliche Bewertung der ökologischen Auswirkungen eines Bauwerks beruht neben der primärenergetischen Betrachtungsweise während der Nutzungsphase auf der Berücksichtigung emittierter Schadstoffe während der Erstellung, der Instandhaltung und des Abrisses des Gebäudes. Um in frühen Planungsphasen die ökologischen Kosten praxisgerecht abschätzen zu können, sind rechnergestützte Verfahren zu entwickeln, die sich reibungslos in den Planungsablauf integrieren lassen. Dazu wurde ein Produktmodell basierter Ansatz verwendet, der in Bezug auf Emissionskennwerte einzelner Bauteile einen zentral verwalteten Typenkatalog mit massenbezogenen Schadstoffemissionen verwendet. Zur Kalkulation der während des Betriebs auftretenden ökologischen Belastungen wurde ein Informationsmodell als Kombination der Gebäudehülle und der technischen Gebäudeausstattung entwickelt, das es dem Nutzer erlaubt, dynamische Kenngrößen direkt abzulesen und die Anlagentechnik daraufhin zu optimieren.

Zechbauer, U.; van Treeck, C. Show abstract Angenehme Turbulenzen, Klima in Innenräumen – in Echtzeit und interaktiv
Mitteilungen der Technischen Universität München, 2006



Mit der Technischen Universität München und anderen Partnern entwickelt Siemens ein weltweit einzigartiges Modell: Es simuliert das Klima in Innenräumen – in Echtzeit und interaktiv.

Borrmann, A.; Wenisch, P.; van Treeck, C.; Rank, E. Show abstract Collaborative Computational Steering: Principles and Application in HVAC Layout
Integrated Computer-Aided Engineering 13 (4), pp. 361-376, 2006



In this article, we present the Collaborative Computational Steering platform CoCoS.It enables geographically distributed engineers to use steerable simulation and analysis facilities during a collaborative design session. The environment is based on a distributed component architecture composed of a central Collaboration Server, an arbitrary number of Simulation Servers and an arbitrary number of clients. The Collaboration Server manages the shared model consisting of a three-dimensional geometric model and additional semantic data like boundary conditions for a certain simulation. The Simulation Servers provide simulation and analysis data for the engineer's front-end application and can be connected to the platform on demand. By using the explicitly available meta-model, the shared model can be dynamically adapted to the needs of simulation facilities that are not known a-priori. Exemplarily, the utilization of the CoCoS platform for the collaborative layout of a Heating Bentilation Air-Conditioning (HVAC) system is shown. In this context, the implementation of an interactively steerable fluid simulatior based on the lattice-Boltzmann method is discussed. This simulator allows obstacles to be inserted into the fluid domain, relocated, and removed from it during the simulation process and the impact of these modifications on the fluid flow to be seen immediately.

Duester, A.; Demkowicz, L.; Rank, E. Show abstract High-order finite elements applied to the discrete Boltzmann equation
International Journal for Numerical Methods in Engineering 67, pp. 1094-1121, 2006



A discontinuous Galerkin approach for solving the discrete Boltzmann equation is presented, allowing to compute approximate solutions for fluid flow problems. Based on a two-dimensional high-order finite element and an explicit Euler time stepping scheme, the D2Q9 model is discretized and the results are compared to the exact solution of the Navier–Stokes equation. Four numerical examples are considered, including stationary and instationary problems with curved boundaries. It is demonstrated that the proposed method allows to obtain the desired, highly efficient exponential convergence.

van Treeck, C.; Rank, E.; Krafczyk, M.; Toelke, J.; Nachtwey, B. Show abstract Extension of a hybrid thermal LBE scheme for Large-Eddy simulations of turbulent convective flows
Elsevier Science (submitted to), 2006



Following the work of Lallemand and Luo [Phys. Rev. E 68, 036706 (2003)] we validate, apply and extend the hybrid thermal lattice Boltzmann scheme (HTLBE) by a large-eddy approach to simulate turbulent convective flows. For the mass and momentum equations, a multiple-relaxation-time LBE scheme is used while the heat equation is solved numerically by a finite difference scheme. We extend the hybrid model by a Smagorinsky subgrid scale model for both the fluid flow and the heat flux. Validation studies are presented for laminar and turbulent natural convection in a cavity at various Rayleigh numbers up to 5·1010 for

Muthler, A.; Duester, A.; Volk, W.; Wagner, M.; Rank, E. Show abstract High order thin-walled solid finite elements applied to elastic spring-back computations
Computer Methods in Applied Mechanics and Engineering 195 (41-43), pp. 5377-5389, 2006



In this paper we present a new approach for computing elastic spring-back based on a strictly three-dimensional, high order, solid, finite element formulation for curved, thin-walled structures allowing for an anisotropic discretization. In combination with appropriate mesh design, the p-version yields an exponential rate of convergence in the error in energy norm in contrast to low-order elements, which yield only an algebraic rate of convergence. Anisotropic Ansatz spaces based on high order elements lead to very efficient discretizations. The structural behavior of three-dimensional thin-walled continua can be predicted with a similar number of degrees of freedom as in the two-dimensional case, yet significantly more accurately because of the three-dimensional model. We also introduce an approach for the efficient computation of the relevant geometrically nonlinear problem. Furthermore the paper describes the necessary model conversion from a low-order deep drawing simulation to a spring-back computation based on the p-version of the FEM.

Scholz, Dominik; Kollmannsberger, Stefan; Düster, Alexander; Rank, Ernst Thin Solids for Fluid-Structure Interaction
In: Bungartz, Hans-Joachim; Schäfer, Michael (Eds.), Fluid-Structure Interaction, 53, Springer Berlin Heidelberg, 2006, pp. 294-335

van Treeck, C.; Rank, E.; Schrag, T.; Katz, C. Abschlußbericht zum Forschungsprojekt SIMFAS
Förderung: Bayerische Forschungsstiftung, 2005

Rank, E.; Wassouf, Z.; van Treeck, C. Show abstract Simulation des Ressourcenbedarfes von Bauwerken: Integration eines Produktmodells der technischen Gebäudeausstattung
Abschlußbericht zum Forschungsprojekt F235, 2005



Das Projekt F235 gliedert sich in den Arbeitsbereich ‚Modelle’ des Schwerpunktthemas ‚Stoffflussmanagement Bauwerke’ (F268) ein. Auf der Grundlage der Ergebnisse des bereits abgeschlossenen Projektes F219 „Internet basierte Simulation des Ressourcenbedarfs von Bauwerken“ soll das dort entwickelte Lösungskonzept (Produktmodell, Datenbanken, Internetanbindung und Software) um die Komponenten der technischen Gebäudeausstattung erweitert werden. Dazu werden Softwaremodule für eine detaillierte Energiesimulationen auf der Basis eines Produktmodells der Anlagentechnik entwickelt und damit die Wechselwirkung mit dem Produktmodell der Gebäudehülle analysiert. Weiterhin sind die Elemente der technischen Gebäudeausstattung mit Datenbanken zum Material- und Primärenergiebedarf von Baustoffen, Anlagenkomponenten und Energieträgern zu verbinden und durch numerische Simulation der Ressourcenbedarf während des gesamten Lebenszyklus abzuschätzen. Im Projekt F235 wird ein Computergestütztes Modell eines Bauwerks (z.B. Alter Hof – Lorenzistock) inklusive dessen Anlagentechnik und darauf integrierte Simulations-, Analyse- und Bewertungsmethoden (z.B. Sach- und Ökobilanzen, energetische und thermische Gebäudesimulationen) entwickelt. Damit kann der Planer bzw. Architekt bereits in frühen Phasen des Gebäudeentwurfs ganzheitliche Lebenszyklusanalysen durchführen und eine Abschätzung bzw. eine Optimierung des Ressourcenverbrauchs unter Berücksichtigung der Wechselwirkung zwischen Gebäudehülle und Anlagentechnik vornehmen. Die Durchführung erfolgt in enger Zusammenarbeit mit den Industriepartner COPLAN AG in Eggenfelden.

Berkhahn, V.; Tilleke, S.; Schleinkofer, M.; Rank, E. Re-Engineering im Konstrukiven Ingenieurbau. Von der Bauzeichnung zum Produktmodell
Bauingenieur (11/2005), 2005

Wenisch, P.; Wenisch, O.; Rank, E. Show abstract Optimizing an Interactive CFD Simulation on a Supercomputer for Computational Steering in a Virtual Reality Environment
High Performance Computing in Science and Engineering, Garching 2004, 2005



This article presents a computational steering research project coupling a supercomputer with a virtual reality (VR) environment to allow for interaction during a real-time CFD simulation using an immersive high-end visualization interface. Interaction comprises not only the changing of parameters, but also the modification of geometry, e.g. removing, adding and transforming objects in a virtual CAD-generated room during runtime. The underlying CFD computation and grid generation is processed on a high-performance computer (HPC) to enable a real-time simulation which instantly reacts to user manipulations. Based on the Lattice-Boltzmann method, the simulation kernel shows good parallel efficiency on the Hitachi SR8000 pseudo-vector supercomputer at the Leibniz Computing Center (LRZ) in Munich. For post-processing and steering in virtual reality a stereoscopic projection screen and a tracked wand input device is used. To achieve optimal immerson a head-tracked view is supported and complemented by a context-sensitive 3D VR menu.

Franke, D.; Lam, N.; Gad, E.; Chandler, A. Show abstract Seismically Induced Overturning of Objects and Filtering Effects of Buildings
Journal of Seismology and Earthquake Engineering Vol 7 (No. 2), 2005



The seismic performance of unrestrained objects is critically dependent on the displacement demand behaviour of the building floor. The risk of an object overturning can be estimated from the dual independent criteria of object width and height, as opposed to the usual single criterion of the object aspect ratio (or slenderness ratio) based on static analysis. An object is at risk from overturning if the displacement demand of the floor exceeds one-third of the width of the object. According to floor amplification clauses in earthquake codes of practice, the filtering effects of a building amplify ground motions up its height. However, the building may also behave as an isolation medium, which attenuates the transmitted motions. These two perceptions seem contradictory. This paper aims to resolve this significant dilemma and hence contribute to improving the fundamental understanding of the dynamical processes of damage to building contents. Floor spectra of buildings, as presented in the paper, demonstrate both amplification and isolation actions.

Rank, E.; Halfmann, A.; Scholz, D.; Glueck, M.; Breuer, M.; Durst, F.; Kaiser, U.; Bergmann, D.; Wagner, S. Show abstract Wind loads on lightweight structures: Numerical simulation and wind tunnel tests
Gamm-Mitteilungen 28 (1), pp. 73 - 89, 2005



In this paper basic principles of a numerical computation of fluid-structure interaction will be discussed. Starting point are standard software systems for the simulation of fluid dynamics and structural dynamics. These program systems are adequately extended and coupled in a partitioned solution approach. Results of the presented methods will be compared in detail with wind tunnel experiments for a lightweight membrane construction.

Rank, E.; Düster, A.; Nübel, V.; Preusch, K.; Bruhns, O.T. High order finite elements for shells
Computer Methods in Applied Mechanics and Engineering 194 (21-24), pp. 2494--2512, 2005
DOI: 10.1016/j.cma.2004.07.042

van Treeck, C.; Rank, E.; Schrag, T.; Katz, C. 2. Zwischenbericht zum Forschungsprojekt SIMFAS
Förderung: Bayerische Forschungsstiftung, 2004

Borrmann, A.; Wenisch, P.; van Treeck, C. Show abstract Eine verteilte Architektur für synchrones kooperatives Arbeiten mit einer interaktiven Strömungssimulation
J. Zimmermann, S. Geller (Hrsg.): Forum Bauinformatik 2004, 2004



Der Beitrag stellt eine CORBA-basierte Client-Server-Architektur für die synchrone Zusammenarbeit mehrerer verteilt arbeitender Ingenieure vor. Exemplarisch wird die Einsatz der entwickelten Architektur für ein Collaborative Virtual Environment (CVE) gezeigt, da sich gerade hier die Vorteile einer zentralen Verwaltung des abstrakten Geometriemodells in der damit verbundenen Möglichkeit zeigen, individuelle Views für jeden der Beteiligten anbieten zu können. Es wird die Integration eines Simulationsservers besprochen, der verteilte Fachapplikationen mit Daten einer Strömungssimulation versorgt, gleichzeitig aber auch Modifikationen am Geometriemodell als geänderte Randbedingungen an den CFD-Simulationskern weitergibt. Dadurch wird den Anwendern gemäß dem Computational-Steering-Paradigma ein interaktives Eingreifen in den Simulationsablauf ermöglicht.

Barthel, R.; Bletzinger, K.; Eckl, M.; Faulstich, M.; Heinz, D.; Jurecka, F.; Rank, E.; Schäfer, T.; Schießl, P.; Schleinkofer, M.; Schöpe, B.; Wassouf, Z.; Weber-Blaschke, G. Show abstract Bauwerke der Zukunft
Zukunft im Brennpunkt 3, pp. 41 - 46, 2004



Menschen planen, bauen und nutzen seit Jahrtausenden Bauwerke. Dennoch würde wohl niemand auf die Idee kommen, dass es sich bei der Bauwerkserrichtung um eine veraltete Technik handelt. Im Gegenteil: Wir gehen ganz selbstverständlich davon aus, dass bewährte Traditionen über Generationen weiterentwickelt und verbessert wurden. Ergebnis ist nicht nur ein höherer Wohnkomfort, sondern auch ein erheblicher Fortschritt in der Effizienz von Bauwerken, insbesondere in der Nutzungsphase. Man denke nur an die Entwicklung des Heizenergiebedarfes und der zugehörigen Standards beziehungsweise an Regelwerke von der Wärmeschutzver- ordnung über die Energieeinsparverordnung (EnEV) zum Passivhaus-Standard. Trotzdem: Die Bauwirtschaft muss sich neuen Anforderungen stellen. Bauwerke der Zukunft müssen funktional flexibel sein, Ressourcen schonen, die Umwelt nicht belasten und Baureststoffe vermeiden – eine große Herausforderung für Planung, Bau und Betrieb.

Kuehner, S.; Crouse, B.; Rank, E.; Toelke, J.; Krafczyk, M. Show abstract From a Product Model to Visualization: Simulation of Indoor Flows with Lattice-Boltzmann Methods
Computer-Aided Civil and Infrastructure Engineering 19, pp. 411-420, 2004



After a short discussion of different types of models being involved in the process of numerical simulation in civil engineering, we focus on the analysis of indoor air flow through complex geometries. All models are derived from a product data model based on Industry Foundation Classes. Concepts of the Lattice-Boltzmann method are described, being used as the numerical kernel of our simulation system. We take advantage of spacetrees as a central data structure for all geometry related objects. Finally, we describe some advanced postprocessing and visualization techniques allowing to efficiently analyze huge amounts of simulation data.

Rank, E.; van Treeck, C. Kopplung von dynamischer Gebäudesimulation und CFD-Methoden zur Untersuchung des Energiehaushalts und Komforts von Gebäuden basierend auf dem IFC-Produktmodellstandard (SIMFAS)
Jahresbericht 2002, 2003

Bungartz, H.-J.; Mundani, R.-P. Show abstract Simulation technology – the role of concepts and algorithms
Selcuk Journal of Applied Mathematics 4 (2), pp. 33-52, 2003



Since modern numerical simulation is a transdiscipli-nary field of research, the question often arises up to which extent this fact should be reflected by the content of single courses as well as by the structure of the whole respective study programs. Here, an issue that is disputed especially hotly is how and where to keep the balance between an application-oriented education on the one hand, trying to start from real-life problems, and a more concept-based one on the other hand, where the focus is on deriving and depicting general principles of algorithm development that may be fruitful for completely different problem classes. In this paper, we give two examples of such a general algorithmic framework -- octrees as an efficient interface of geometric modelling and numerical simulation, and sparse grids as an a priori optimised grid setting for tasks such as numerical quadrature or the numerical solution of PDE. Both are based upon a hierarchical approach, which turns out to be an advantageous strategy for a large variety of problems.

Düster, Alexander; Hartmann, Stefan; Rank, Ernst p-FEM applied to finite isotropic hyperelastic bodies
Computer Methods in Applied Mechanics and Engineering 192 (47-48), pp. 5147--5166, 2003
DOI: 10.1016/j.cma.2003.07.003

Glueck, M.; Breuer, M.; Durst, F.; Halfmann, A.; Rank, E. Computation of wind-induced vibrations of flexible shells and membranous structures
Journal of Fluids and Structures, 2002

Ekkerlein, C.; Neuberg, F.; Faulstich, M. Show abstract Internetbasierte Simulation des Ressourcenbedarfs von Gebäuden
VDI-Bericht 1668, Bauen mit Computern - Kooperation in IT-Netzwerken, Tagung Bonn, 2002



Due to the long life cycle of a building the expenses for usage and maintenance are very high compared to those for the construction, only. About 1/3 of the total energy demand in Germany is used for heating, air-conditioning and hot water supply in buildings. In addition the building wastes resulting for disposal represent a quantitatively enormous material flow. As the most significant decisions are made in early planning steps it is very important to enable planners to estimate the energy demand, resource requirement and ecological impact of different scenarios at this stage. Nowadays more and more architects and engineers use CAD software, like the Architectural Desktop from Autodesk, supporting the generation of three dimensional product models. One prominent model being now well established in the building industry is defined by the Industry Foundation Classes (IFC). This model is also the starting point of our resource oriented design system. To get a basis for a comparative assessment of different design variants it is first necessary to augment the product model with information on resource consumption of the used materials. Therefore a database server accessible via the Internet is developed within our research project providing a service for planners to extend their product model with information necessary for life cycle assessment (LCA) and building energy simulation (EnEV). The data exchange format for the property sets is ifcXML. In our presentation the general software concept together with first simulation tools will be discussed.

Neuberg, F.; Rank, E.; Ekkerlein, C. Show abstract Simulation von Energieströmen nach der Energieeinsparverordnung (EnEV) auf der Grundlage des IFC Produktmodells
VDI-Bericht 1668, Bauen mit Computern - Kooperation in IT-Netzwerken, Tagung Bonn, 2002



Die neue Energieeinsparverordnung (EnEV) fordert eine komplexere Analyse der energetischen Effizienz von Gebäuden als die bis Februar 2002 gültige Wärmeschutzverordnung von 1995. Das hier vorgestellte Softwarekonzept zeigt, wie auf der Grundlage eines Produktmodells (IFC) die Berechnungsverfahren nach der EnEV durchgeführt werden können. Die notwendigen Erweiterungen eines vorhandenen Gebäudemodells um z.B. bauphysikalische Eigenschaften kann der Anwender über einen internetbasierten Datenbankserver mit ifcXML Schnittstelle durchführen. Dieses Produktmodell bildet die Datenbasis für die anschließenden Analyse- und Nachweisverfahren der EnEV. Die implementierte Software wird anhand einer Beispielberechnung für ein Einfamilienhaus mit Wintergarten vorgestellt.

Düster, Alexander; Niggl, Andreas; Nübel, Vera; Rank, Ernst A numerical investigation of high-order finite elements for problems of elastoplasticity
Journal of scientific computing 17 (1-4), pp. 397–404, 2002

Duester, A.; Rank, E. Show abstract A p-version finite element approach for two- and three-dimensional problems of the J2 flow theory with non-linear isotropic hardening
International Journal for Numerical Methods in Engineering 53 (49-63), 2002



In this paper an implementation of a two- and three-dimensional p-version approach to the J2 4ow theory with non-linear isotropic hardening for small displacements and small strains is presented. Based on higher-order quadrilateral and hexahedral element formulations, a Newton–Raphson iteration scheme combined with a radial return algorithm is applied to )nd approximate solutions for the underlying physically non-linear model problem. Curved boundaries are taken care of with the blending function method, allowing an accurate representation of geometry with only a few p-elements. Numerical examples demonstrate, that the p-version supplies effcient and accurate approximations to this class of physically non-linear problems.

Crouse, B.; Kuehner, S.; Krafczyk, M.; Rank, E.; van Treeck, C. Show abstract Indoor air flow analysis based on lattice Boltzmann methods
Energy and Buildings 34 (9), pp. 941-949, 2002



The modeling of convective flows based on a 3D lattice Boltzmann approach for low Mach number flows with variable density combined with a large eddy turbulence model is presented. The ability to handle non-Boussinesq density variation problems is depicted for two-dimensional Rayleigh-Benard convection at a Rayleigh number Ra=800,000.A complex three-dimensional example shows the status of our work with respect to turbulent flow in and around a building, so far without consideration of the energy equation in the full scale 3D case. Integrated within a CAD environment, the spatial geometric model, based on an IFC building product data model, is discretized using a hierarchic data structure. Results are presented for a Reynolds number Re=75,000 computed on a high-performance parallel vector computer.State-of-the-art visualization techniques integrate the simulation results and the CAD model into a virtual reality environment. The VR environment allows also for an interactive analysis of thermal comfort criteria, being demonstrated for an indoor air flow simulation of an open-plan office.

Glueck, M.; Breuer, M.; Durst, F.; Halfmann, A.; Rank, E. Show abstract Computation of fluid-structure interaction on lightweight structures
Journal of Wind Engineering and Industrial Aerodynamics, Vol. 89, S. 1352-1368, 2001



In this paper a numerical approach of a time-dependent fluid-structure coupling for membrane and thin shell structures with large displacements is presented. The frame algorithm is partitioned, yet fully implicit because of a predictor-corrector scheme being applied to the structural displacements within each time step. In order to reach a high modularity, two powerful codes—one of them highly adapted to flow simulation and the other one to structural dynamics—run simultaneously and exchange fluid loads and displacements within each fluid-structure iteration. The finite volume based CFD code is able to compute three-dimensional, incompressible, turbulent flows. The structural simulations are performed using a finite element program including algorithms for geometrically and physically non-linear problems. In this paper the coupled algorithm will first be applied to some geometrically simple test cases to validate the interaction scheme. Then a real-life textile tent structure of glass-fibre synthetics with a complex shape is taken into account. This example was investigated under turbulent flow conditions at a high wind speed leading to a steady deformation state.

Rank, E.; Broeker, H.; Duester, A.; Ruecker, M. Show abstract Integrierte Modellierungs- und Berechnungssoftware für den konstruktiven Ingenieurbau: Die p-Version und geometrische Elemente
Bauingenieur 76, pp. 53-61, 2001



In einem vorangegangenen Aufsatz wurden die Systemarchitektur und Netzgenerierungstechniken für eine integrierte Modellierungs- und Berechnungssoftware im konstruktiven Ingenieurbau beschrieben. Teil dieses im Rahmen eines von der EU geförderten Forschungsprojekts entwickelten Softwaresystems ist die p-Version der Methode der Finiten Elelmente. Während dieses Berchnungsverfahren vor allem im Maschinenbau und in der Luft- und Raumfahrttechnik mit einigen kommerziell verfügbaren Programmsystemen bereits eine erhebliche Verbreitung gefunden hat, sind Anwendungen im Bauingenieurwesen noch recht spärlich. Die in diesem Aufsatz dargestellten Untersuchungen sollen zeigen, dass die Vorteile dieser Methode bei den im Bauwesen üblichen Berechnungen von Plattenstrukturen oder dünnwandigen räumlichen Tragwerken besonders deutlich zu Tage treten.

Duester, A.; Broeker, H.; Rank, E. Show abstract The p-version of the finite element method for three-dimensional curved thin walled structures
International Journal for Numerical Methods in Engineering 52, pp. 673-703, 2001



In this paper we present an implementation of a three-dimensional p-version for structural problems of solids with almost arbitrarily curved surfaces. Applying the blending function method, complex structures can often be modelled by a few p-elements, being the basis for a higher order approximation. Numerical examples will demonstrate, that the p-version with anisotropic Ansatz spaces allows to predict the structural behaviour of three-dimensional plates and shells with approximately the same amount of degrees of freedom as in the two-dimensional case, yet significantly more accurate due to the three-dimensional model. Furthermore, it is advantageous to compute complex structures exclusively with three-dimensional discretizations as no special elements are needed to model the transition from dimensionally reduced formulations like plates or shells to fully three-dimensional solid elements. Using the p-version with anisotropic Ansatz spaces the whole structure can be efficiently discretized with solid elements, even if the aspect ratio of the elements becomes very large.

Krafczyk, M.; Toelke, J.; Rank, E.; Schulz, M. Show abstract Two-dimensional of fluid-structure interaction using lattice-Boltzmann methods
Computers and Structures 79, pp. 2031-2037, 2001



The development of flow instabilities due to high Reynolds number flow in artificial heart-value geometries inducing high strain rates and stresses often leads to hemolysis and related highly undesired effects. Geometric and functional optimization of artificial heart valves is therefore mandatory. In addition to experimental work in this field it is meanwhile possible to obtain increasing insight into flow dynamics by computer simulation of refined model problems. Here we present two-dimensional simulation results of the coupled fluid–structure problem defined by a model geometry of an artificial heart value with moving leaflets exposed to a channel flow driven by transient boundary conditions representing a physiologically relevant regime. A modified lattice-Boltzmann approach is used to solve the coupled problem.

Rank, E.; Ruecker, M.; Duester, A.; Broeker, H. Show abstract The efficiency of the p-version finite element method in a distributed computing environment
International Journal for Numerical Methods in Engineering 52, pp. 589-609, 2001



The p-version of the finite element method is now commonly considered to be a very accurate discretization method for linear elliptic partial differential equations, but many researchers still doubt the efficiency of this method, when compared to the classical h-version and applied to more complex problems. This paper will first discuss some general considerations about the efficiency of a numerical method and then present results on an evaluation of the p-version. It will be shown, that there are many special techniques being applicable to the p-version, yielding a well-performing and robust method. This will be demonstrated on several examples, including non-linear problems and a parallel implementation on a workstation cluster. A client–server software structure for an efficient integration of CAD and FEA using a strict separation of geometric and non-geometric aspects will also be outlined.

Düster, Alexander; Rank, Ernst The p-version of the finite element method compared to an adaptive h-version for the deformation theory of plasticity
Computer Methods in Applied Mechanics and Engineering 190 (15-17), pp. 1925–1935, 2001
DOI: 10.1016/S0045-7825(00)00215-2

Krafczyk, M.; Lehmann, P.; Philippova, O.; Haenel, D.; Lantermann, U. Lattice Boltzmann Simulations of complex Multi-Phase Flows
Multifield Problems: State of the art, 2000

Halfmann, A.; Rank, E.; Ruecker, M.; Katz, C.; Gebhard, S. Show abstract Integrierte Modellierungs- und Berechnungssoftware für den konstruktiven Ingenieurbau: Systemarchitektur und Netzgenerierung
Bauingenieur, 2000



The present paper first presents some aspects of the system architecture of an integrated environment for modelling and computation in engineering design. Cooperation is supported by using a network-enabled relational project database. Whereas all engineering definitions of a load bearing system are performed completely independant of any computational mesh on a structural model, the following automatic mesh generation and transfer of all structural properties defines a fully consistent finite element model. This concept shows its strengths especially in situations, where a modification of the load bearing system can be investigated with a minimum of additional labour effort.

Doster, A.; Werner, H. Objektorientierte Modellierung einer wissensbasierten Benutzungsoberfläche im konstruktiven Ingenieurbau
KI-Forschung im Baubereich, 1999

Krafczyk, M.; Schmidhuber, C.; Rank, E.; Cerrolaza, M. Show abstract Analysis of 3D transient Blood Flow passing through an Artificial Aortic Valve by Lattice-Boltzmann Methods
Journal of Biomechanics, 1998



The development of flow instabilities due to high Reynolds number flow in artificial heart valve geometries inducing high strain rates and stresses often leads to hemolysis and related highly undesired effects. Geometric and functional optimization of artificial heart valves is therefore mandatory. In addition to experimental work in this field it is meanwhile possible to obtain increasing insight into flow dynamics by computer simulation of refined model problems. After giving an introductory overview we report the results of the simulation of three-dimensional transient physiological flows in fixed geometries similar to a CarboMedics bileaflet heart valve at different opening angles. The visualization of emerging complicated flow patterns gives detailed information about the transient history of the systems dynamical stability. Stress analysis indicates temporal shear stress peaks even far away from walls. The mathematical approach used is the Lattice Boltzmann method. We obtained reasonable results for velocity and shear stress fields. The code is implemented on parallel hardware in order to decrease computation time. Finally, we discuss problems, shortcomings and possible extensions of our approach.

Emmerich, H.; Rank, E. Show abstract An Improved Cellular Automaton Model for Traffic Flow Simulation
Published in Phisica A 234 (1997), 1996



Starting from a basic cellular automaton model (CA) for traffic flow on a freeway we study various modifications to its update procedure aiming at a quantitative improvement of the fundamental diagram obtained. The investigation results in the suggestion of an improved automaton, showing qualitative and quantitative coincidence of maximum flux with values taken from real traffic measurements.

Rank, E.; Ruecker, M. Technische Dokumentation im Datennetz
Bauingenieur 71 (2), pp. 57-67, 1996

Rank, E.; Krause, R. A-posteriori-Fehlerschätzung bei Multi-Skalen-Problemen
ZAMM 75 (1995) SI, 1995

Doster, A.; Christmann, A.; Werner, H. Show abstract Berechnung von Unterfangungen am PC
Bautechnik 72, pp. 101-106, 1995



Unterfangungen für Sanierung und Umbau von Gebäuden gewinnen durch die zunehmende Verdichtung in Ballungsräumen immer mehr an Bedeutung. Berechnung und Nachweis von Unterfangungen stellen hohe Anforderungen an den Bearbeiter. Die Berücksichtigung der schrägen Begrenzungen des Unterfangungskörpers für den Erddruck, die Berechnung des statischen Systems als geknickter Stabzug und die erdstatischen Nachweise wie Gleitsicherheit, Grundbruchsicherheit und Ankernachweis in den tiefer Gleitfuge erfordern einen hohen Arbeitsaufwand. Im Beitrag werden die speziellen Anforderungen für die Berechnung von Unterfangungen näher dargestellt. Am Beispiel eines Programms "DC-Unterfangung" wird die Unterstützung des Bearbeiters durch PC-Software erläutert.

Emmerich, H.; Rank, E. Show abstract Investigating Traffic Flow in the Presence of Hindrances by Cellular Automata
Physica A 216, pp. 435-444, 1995



Starting from a cellular automaton model (CA) for general conditions on a freeway we come up with a formulation of an automaton to include the case of hindrances on a road. Investigation of our model results in a phase diagram introducing a new phase between laminar and jammed traffic. This phase is characterized by the spatial coexistence of behaviour known from the original model.

Krafczyk, M.; Rank, E. Show abstract A parallelized lattice-gas solver for transient Navier-Stokes-flow: Implementation and simulation results
Int. J. for Numer. Meth. in Eng. 38 (8), pp. 1243-1258, 1995



The last decade has seen the development of Lattice-Gas (LG) schemes as a complementary if not alternative method for the simulation of moderate Reynolds-Number Navier–Stokes flow. After a short theoretical introduction we present a detailed discussion of implementation features for a specific 2D-LG algorithm, which runs in parallel on a workstation-cluster, discuss simulation results and compare one of them to experimental studies. Finally, we attempt to point out present problems and perspectives of these methods.

Rank, E.; Ruecker, M.; Schweingruber, M. Automatische Generierung von Finite-Element-Netzen
Bauingenieur 10, 1994

Paffrath, M.; Jacobs, W.; Klein, W.; Rank, E.; Steger, K.; Weinert, U.; Wever, U. Concepts and algorithms in process simulation
Surv. Math. Ind. 3, 1993

Mackert, M. Wissensbasierte Unterstützung der statischen Modellbildung und der numerischen Analyse im Tunnelbau
Fortschritt-Berichte 4 (116), 1992

Rank, E.; Weinert, U.; Klein, W. Numerical modelling in semiconductor process simulation
Video Journal of Engineering Research, 1992

Stark, M. Feature-basierter Ansatz zur Integration im Bauwesen am Beispiel der Tragwerksanalyse
Fortschritt-Berichte 4 (116), 1992

Rank, E. Show abstract Adaptive remeshing and h-p domain decomposition
Computer Methods in Applied Mechanics and Engineering 101, pp. 299-313, 1992



The h-p version of the finite element method combines local mesh refinement wiht an increase of the shape functions' polynomial degree. This paper presents a method which uses an h-p-approximation for a domain decomposition with fully overlapping domains, allowing C°- continuous approximation for geometrically incompatible mesh refinement to be obtained. The method is applied to a reaction-diffusion problem resulting from semiconductor process simulation. In numerical examples, it is demonstrated that this approach is well suited for problems with sharp interior layers or shock-like behaviour.

Werner, H.; Stark, M.; Holzer, S. Ansätze für die wissensbasierte Modellbildung mit finiten Elementen und Randelementen
Finite Elemente-Anwendungen in der Baupraxis, 1991

Rank, E. Finite-Element-Simulation of local oxidation in semiconductor processing
The Mathematics of Finite Elements and Applications VII, 1991

Weinert, U.; Rank, E. A simulation system for diffusive oxidation of silicon: One-dimensional analysis
Z. Naturforsch., 1991

Holzer, S.; Hausser, C. Verbesserung von Finite-Element-Berechnungen durch exakte Geometriemodellierung
Forschung im Ingenieurwesen 56 (3), pp. 65-70, 1990

Holzer, S.; Rank, E.; Werner, H. Show abstract An Implementation of the hp-Version of the Finite Element Method for Reissner-Mindlin Plate Problems
Intern. Journal for Numerical Methods in Engineering 30, pp. 459-471, 1990



Reissner-Mindlin plate theory is still a topic of research in finite element analysis. One reason for the continuous development of new plate elements is that it is still difficult to construct elements which are accurate and stable against the well-known shear locking effect. In this paper we suggest an approach which allows high order polynomial degrees of the shape functions for deflection and rotations. A balanced adaptive mesh-refinement and increase of the polynomial degree in an hp-version finite element program is presented and it is shown in numerical examples that the results are highly accurate and that high order elements show virtually no shear locking even for very small plate thickness.

Merten, K.; Rank, E. Das Innovationspotential der Numerischen Simulation
Siemens Review Special, R & D, F & E, 1989

Bellmann, J.; Rank, E. Die p- und hp-Version der Finite-Elemente-Methode oder: Lohnen sich höherwertige Ansatzfunktionen?
Bauingenieur, 1989

Rank, E. Local oxidation of silicon - A finite element approach
Mathematical Modelling and Simulation of Electrical Circuits, 1989

Rank, E. Show abstract Adaptive h-, p- and hp-versions for the boundary element methods
Int. J. for Numer. Meth. in Eng. 28, pp. 1335-1349, 1989



Recently very promising results in a so-called hp-version of the finite element method have been obtained. The basic idea is a balanced combination of mesh refinement and increase of the polynomial degree of the shape functions. This idea is applied to a boundary collocation method in this paper. The new method is compared with adaptive h- and p-versions and it is shown in numerical examples that even in the presence of singularities in the exact solution exponential convergence is obtained.

Rank, E. Adaptive Netzverfeinerung und Erhöhung des Ansatzgrades bei Finite-Element-Verfahren
ZAMM 4, pp. T243-T245, 1989

Doster, A.; Werner, H. Ingenieurgerechte Dateneingabe bei Berechnungsprogrammen
Bauingenieur 63 (3), pp. 105 - 111, 1988

Rank, E.; Roßmann, A. Fehlerschätzung und automatische Netzanpassung bei Finite-Element-Berechnungen
Bauingenieur 62 (10), 1987

Rank, E.; Zienkiewicz, O. Show abstract A simple error estimator in the finite element method
Communications in Applied Numerical Methods 3, pp. 243 - 249, 1987



Recently, a new class of error indicators and estimators for the finite element methods has been introduced which is particularly easy to implement into existing finite element codes. This paper proves that the new indicators are equivalent to those analysed earlier by Babuska, thus showing that the rigorous mathematical results for the well-known jump indicator apply also for the new ones.

Babuska, I.; Rank, E. Show abstract An expert system-like feedback approach in the hp-version of the finite element method
Finite Elements in Analysis and Design 3, pp. 127 - 147, 1987



It has been theoretically shown that exponential rate of convergence in the energy norm can be obtained by a proper combination of the h- and p- extension of the finite element method for essentially all engineering problems in plane elasticity, including those with singularities in the exact solution. In this paper we present an expert system frame, which guides the user to an optimal selection of the mesh and degree distribution. After a crude preliminary computation the expert system predicts the performance of various mesh and degree combinations and provides the analyst with rational support for his decisions about the mesh design. Numerical examples show that the suggested approach gives superior results with the minimum effort in human data preparation and computer time.

Rank, E.; Werner, H. Show abstract An adaptive finite element approach for the free surface seepage problem
International Journal for Numerical Methods in Engineering 23, pp. 1217 - 1228, 1986



A posteriori error estimates and adaptive mesh refinements are now on a rigorous mathematical foundation for linear, elliptic boundary-value problems of second order. Yet, for non-linear problems only a few results have been obtained till now. In this paper we consider as a non-linear model problem the two-dimensional fluid flow with free surface and show how results from linear a posteriori theory can be used to control the non-linear iteration and to refine the mesh adaptively. A numerical example shows that, similar to linear problems, considerable improvement of the accuracy is obtained by an adaptive mesh refinement and that the influence of singularities on the order of convergence disappears.

Hartmann, F.; Katz, C.; Protopsaltis, B. Show abstract Boundary elements and symmetry
Ingenieur-Archiv 55, pp. 440 - 449, 1985



This paper discusses the deficiencies of boundary element stiffness matrices, gives an account of the methods proposed to circumvent these defects and proposes a new procedure to obtain symmetric stiffness matrices.

Werner, H.; Kuehl, C.; Stieda, J.; v. Verschuer, T. Show abstract Das Softwarekonzept SYRAKUS - Eine Lösung zur Anpassung unterschiedlicher Entwurfsprogramme
Bauingenieur 59, pp. 455 - 460, 1984



Die an der Technischen Universitaet Muenchen entwickelte Arbeitsplatzloesung SYRAKUS hat mehrere Ziele: 1. Der Benutzer ist mit dem System im Gespraech ueber eine Dialogform, die unabhaengig von dem benutzten Programm ist. 2. Die Dialogform kann vom Benutzer nach seinen Vorstellungen und bisherigen Erfahrungen mit der Datenverarbeitung ausgewaehlt werden. Beim Uebergang auf andere oder neue Dialogstationen bleibt die Dialogform erhalten. 3. Bisherige Entwicklungen und Erfahrungen an bewaehrter Software werden mit minimalem Anpassungsaufwand genutzt. Die Methodenbank enthaelt Programme unterschiedlicher Hersteller, der Benutzer hat aber mit nur einer Dialogform zu tun. 4. Eingabe- und Ergebnisdaten werden in einer Form gehalten, die unabhaengig von den verwendeten Programmen ist. 5. Die Ausgabeform von Ergebnisdaten kann benutzerspezifisch gestaltet werden - weitgehend unabhaengig von den in der Methodenbank vorhandenen Programmen. Sowohl fuer alphanumerische als auch fuer graphische Ausgabe ist das System offen fuer unterschiedlichste und kuenftige Geraetearten (Bildschirm, Plotter, Rasterdrucker, etc.). 6. Neue Softwareentwicklungen koennen auf die angebotenen Werkzeuge zurueckgreifen. Das System wurde als Prototyp auf der Rechenanlage HP 1000L, einem 16-Bit-Prozessor mit dem Betriebssystem RTE-XL, das die parallele Bearbeitung mehrerer Auftraege (multitasking system) erlaubt, entwickelt. Als Datenbankverwaltungssystem stand das IMAGE/1000 zur Verfuegung und als Speicher eine Fest-Wechselplatte mit 10 MB.

Werner, H.; Stieda, J.; Katz, C.; v. Verschuer, T. Rechnereinsatz für Entwurfsaufgaben im konstruktiven Ingenieurbau
Bauingenieur 58, pp. 361 - 368, 1983

Rank, E.; Katz, C.; Werner, H. Show abstract On the Importance of the Discrete Maximum Principle in Transient Analysis Using Finite Element Methods
International Journal for Numerical Methods in Engineering 19, pp. 1771 - 1782, 1983



In transient analysis it is generally thought that small time steps can only improve the accuracy, because standard stability theorems limit the maximum time step for a given mesh size. In finite element approximations, however, small time steps may cause stability problems which lead to physically unreasonable results. It is shown that this is due to the violation of a discrete maximum principle. The influence of lumped and consistent mass matrices on a stable discretization of time and space is presented.

Fink, T.; Kreutz, J. Berechnungsverfahren nach Fließzonentheorie II. Ordnung für räumliche Rahmensysteme aus metallischen Werkstoffen
Bauingenieur 57, pp. 297 - 302, 1982

Schikora, K.; Fink, T. Berechnungsmethoden moderner, bergmännischer Bauweisen beim U-Bahn-Bau
Bauingenieur 57, pp. 193 - 198, 1982

Werner, H. Rechnergestützter Arbeitsplatz des konstruktiven Ingenieurbaus mit Mikrorechner und Methodenbank
Bauwirtschaft 36, pp. 1018 - 1022, 1982

Katz, C.; Werner, H. Implementation of Nonlinear Boundary Conditions in Finite Element Analysis
Computers & Structures 15 (3), pp. 299 - 304, 1982

Rank, E.; Werner, H. Show abstract A Graph-Theoretical Approach to a Plotter Pen Touring Problem
Computer Methods in Applied Mechanics and Engineering 30, pp. 95 - 102, 1982



A graph-theoretical approach to the problem of optimizing the sequence of plot commands is presented. The mesh to be drawn is described by a graph which is extended to an Euler graph. In the extended graph an Euler tour is found, which is associated with the tour of the pen. A typical application of the algorithm is that of plotting meshes as they appear in finite element problems.

Werner, H.; Katz, C.; Axhausen, K. Programmaufbau und Datenstrukturen in entwurfsunterstützenden Programmketten
Finite Elemente in der Baupraxis, 1978

Werner, H. Show abstract Rechnerorientierte Nachweise an schlanken Massivbauwerken
Beton- und Stahlbetonbau 73 (H. 11), pp. 263 - 268, 1978



Der Beitrag behandelt Grundlagen der statischen Berechnung räumlich beanspruchter Rahmentragwerke nach der Theorie II. Ordnung. Es wird ein Bemessungsalgorithmus und ein Iterationsverfahren für die Erfassung der Nichtlinearität des Werkstoffs beschrieben.

Werner, H. Show abstract Schiefe Biegung polygonal umrandeter Stahlbetonquerschnitte
Beton- und Stahlbetonbau 69, pp. 91 - 97, 1974



Es wird ein numerisch stabiles Iterationsverfahren zur Bemesung polygonal umrandeter Stahlbetonquerschnitte unter zweiachsiger Biegung und Normalkraft beschrieben.

Werner, H. Show abstract Rechnerorientierte Stahlbeton- und Spannbetonbemessung
Beton- und Stahlbetonbau 96, pp. 230 - 239, 1974



Für die Bemessung von Stahlbeton- und Spannbetonquerschnitten unter zweiachsiger Biegebeanspruchung mit Normalkraft, Querkraft und Torsion werden Algorithmen beschrieben, die für die Aufstellung von Rechenprogrammen geeignet sind.

Werner, H. Berechnung des räumlichen Stab-Platten-Tragwerkes mit Hilfe eines verallgemeinerten Kraftgrößenverfahrens
Der Stahlbau 40, pp. 201 - 209, 1971

Werner, H. Biegemomente elastisch eingespannter Pfähle
Beton- und Stahlbetonbau 65 (H. 2), 1970

Werner, H. Einfluß- und Schnittkraftflächen dünner, aufgeschlitzer Platten auf Einzelstützen
ZAMM 48, pp. T 177 - 178, 1969

Werner, H. Zustands- und Einflußflächen unendlich ausgedehnter Platten mit einem freien oder gehaltenen Schlitz und zusätzlichen punktförmigen Festhaltungen
Der Stahlbau 38 (H. 3), 1969

Werner, H.; Schikora, K. Der eingespannte Plattenstreifen mit einem freien Randstück unter Gleichlast
Bauingenieur 44, pp. 258 - 262, 1969

Euringer, T.; Werner, H. Konstruktion und Bemessung einer schiefwinkligen Zweifeldplatte mit unterschiedlicher Dicke
Beton- und Stahlbetonbau 62 (H. 7), 1967

Werner, H.; Peter, J. Beitrag zur Berechnung von Platten mit teilweiser Randeinspannung und teilweise einspannungsfreier Auflagerung
Der Stahlbau 35 (H. 4), 1966