Dipl.-Ing. Tino Bog Wissenschaftlicher Mitarbeiter Email: Diese E-Mail-Adresse ist vor Spambots geschützt! Zur Anzeige muss JavaScript eingeschaltet sein!

Forschung

• Simulation in Applied Mechanics

Publications

Journal Papers (peer-reviewed)



• 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
  
  
  
  
  
  
  
• 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.
  
  
  
• 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.
  
  
  
• 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
  
  
  
  
  
  
  
• 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
  
  
  
  
  
  
  
• 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.
  
  
  
• 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.
  
  
  
• 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
  
  
  
  
  
  
  
• 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
  
  
  
  
  
  
  

Conference Talks

• Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Weak imposition of contact constraints on automatically recovered high order embedded interfaces
  In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016
  
  
  
  
  
  
  
• Zander, N.; D'Angella, D.; Bog, T.; Kollmannsberger, S.; Ruess, M.; Rank, E. Multi-level hp-FEM: dynamic discretizations with arbitrary hanging nodes for solid mechanics
  In: European Congress on Computational Methods in Applied Sciences and Engineering, Crete Island, Greece, 2016
  
  
  
  
  
  
  
• Rank, E.; Bog, T.; Elhaddad, M.; Kollmannsberger, S.; L., Kudela; Zander, N. Show abstract The Finite Cell Method: Some Principles and Recent Progress
  In: 13th U.S. National Congress on Computational Mechanics, San Diego, California, USA, 2015
  
  
  
  The finite cell method (FCM) is a combination of a fictitious domain approach with finite elements of high order. The physical domain is embedded into an easy to mesh bigger computational domain. Finite cell meshes are then generated ignoring boundaries of the physical domain and result in rectangular ‘cells’ as support for the higher order shape functions. The geometry of the problem is only considered during the integration of the cell matrices. To this end an indicator function is introduced being equal to 1 inside the physical domain. Outside it is set (in order to avoid conditioning problems) to a very small value. The contribution of the fictitious domain is thus penalized, shifting the effort of meshing towards the numerical integration of the cell matrices. Combining these ingredients, an exponential rate of convergence can be observed for smooth problems, when performing a p-extension. Since the quality and efficiency of the finite cell approximation strongly depends on the numerical integration scheme, this presentation will first discuss a new algorithmic subdivision approach, extending the conventional octree-based integration with the ability of resolving ‘kinks’ or corners of the physical domain. In combination with the blending function method, this algorithm yields a nearly exact decomposition of the cut cells. Our approach is able to resolve close-to-degenerate cases, but remains algorithmically simple at the same time. Several further recent developments of the FCM will be discussed. A new two- and three-dimensional hierarchical refinement strategy yields exponential rate of convergence in energy norm even for singular problems, and its simple algorithmic structure allows an easy extension to transient problems with local refinement and de-refinement. Finally, a re-interpretation of the fictitious domain in the sense of a ‘third material’ opens the way for a modified contact formulation without the necessity of contact search.
  
  
  
• Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. Small and large deformation contact simulation using the finite cell method
  In: European Solid Mechanics Conference 2015 (ESMC2015), Madrid, Spain, 2015
  
  
  
  
  
  
  
• Zander, Nils; Tino, Bog; Kollmannsberger, Stefan; Ruess, Martin; Schillinger, Dominik; Rank, Ernst Multi-level hp-adaptivity for transient discretizations of complex domains
  In: Engineering Mechanics Institute Conference, Stanford, USA, 2015
  
  
  
  
  
  
  
• Zander, N.; Bog, T..; Kollmannsberger, S.; Schillinger, D.; Rank, E. High-Order hp-FEM: High Order Mesh Adaptivity without the difficulties of Hanging Nodes
  In: 11th. World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain, 2014
  
  
  
  
  
  
  
• Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst A contact formulation based on high order fictitious domain methods
  In: 11th. World Congress on Computational Mechanics (WCCM XI), Barcelona, Spain, 2014
  
  
  
  
  
  
  
• Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. The Finite Cell Method for Contact Problems in Solid Mechanics
  In: 3rd International Conference on Computational Contact Mechanics (ICCCM 2013), Lecce, Italy, 2013
  
  
  
  
  
  
  
• Bog, T.; Zander, N.; Kollmannsberger, S.; Rank, E. The Finite Cell Method for Contact Problems in Solid Mechanics
  In: 6th EUROPEAN CONGRESS ON COMPUTATIONAL METHODS IN APPLIED SCIENCES AND ENGINEERING (ECCOMAS), 2012
  
  
  
  
  
  
  

Poster

• Bog, Tino; Zander, Nils; Kollmannsberger, Stefan; Rank, Ernst A formulation for frictionless contact using a material model and high order finite elements
  In: Sixth International Workshop on High-Order Finite Element and Isogeometric Methods, Frauenchiemsee Island, Germany, 2014
  
  
  
  
  
  
  
• Zander, Nils; Bog, Tino; Kollmannsberger, Stefan; Schillinger, Dominik; Rank, Ernst Multi-Level hp-Adaptivity: High-Order Mesh Adaptivity without the Difficulties of Constraining Hanging Nodes
  In: Sixth International Workshop on High-Order Finite Element and Isogeometric Methods, Frauenchiemsee Island, Germany, 2014
  
  
  
  
  
  
  

Theses

• Tino Bog
  Analysis of a Two-Axis Ion Thruster Orientation Mechanism by Finite Elements
  Diplomarbeit, Oerlikon Space AG Zürich, Schweiz, 2011
• Tino Bog
  A locking-free Mindlin-Reissner plate element for arbitrary cracks with smoothed curvatures
  Studienarbeit, University of Canterbury, Christchurch, Neuseeland, 2007

Lehre

• Organisation
  Software Lab
  Sommer Semester 2016, Master Programm Computational Mechanics COME@TUM
• Organisation
  Software Lab
  Sommer Semester 2015, Master Programm Computational Mechanics COME@TUM
• Organisation
  Software Lab
  Sommer Semester 2014, Master Programm Computational Mechanics COME@TUM
• Organisation
  Software Lab
  Sommer Semester 2013, Master Programm Computational Mechanics COME@TUM
• Übung
  Computerorientierte Methoden im Ingenieurwesen
  Winter Semester 2012/2013, Bachelor Programm Bau- und Umweltingenieurwesen@TUM
• Übung
  Computerorientierte Methoden im Ingenieurwesen
  Winter Semester 2011/2012, Bachelor Programm Bau- und Umweltingenieurwesen@TUM

Betreute Studienarbeiten

• Carraturo, M. Weakly enforced constraints the Finite Cell Method (FCM) using Lagrange Multipliers
  Honours project, Technische Universität München, 2015
  
  
  
  
  
  
  
• Coradello, L. Contact mechanics using a fictitious material approach and the Finite Cell Method (FCM)
  Honours project, Technische Universität München, 2015
  
  
  
  
  
  
  
• Elhaddad, M. Level-set Geometry Description for the Finite Cell Method
  Honours project, Technische Universität München, 2013
  
  
  
  
  
  
  

• Barzanooni, Reza Modeling of Flexible Wirings and Contact Interactions in Industrial Robots Using Geometrically Exact Beam Formulation
  Master's thesis, Technische Universität München, 2019
  
  
  
  
  
  
  
• Breu, T. Numerical Stabilization of badly cut cells for the Finite Cells Method using Gradient Jump Penalization
  Bachelor's thesis, Technische Universität München, 2016
  
  
  
  
  
  
  
• Mongeau, Alexandre Large deformation two- and three- dimensional contact on embedded interfaces using the Finite Cell Method
  Master's thesis, Technische Universität München, 2015
  
  
  
  
  
  
  
• Teschemacher, T. Analysis of slender structures using coupled oriented bounding boxes with the finite cell method
  Bachelor's thesis, Technische Universität München, 2014
  
  
  
  
  
  
  
• Buckel, Sebastian Dynamic Substructuring using the Finite Cell Method
  Bachelor's thesis, Technische Universität München, 2014
  
  
  
  
  
  
  
• Ruchti, Martin Show abstract Model Simplification via Super Elements using the Finite Cell Method
  Bachelor's thesis, Technische Universität München, 2013
  
  
  
  In this bachelor’s thesis, the theory and the application of the super element approach in the Finite Cell Method is given. Furthermore, an implementation in the FCM framework AdhoC++, which was developped by the chair of Computation in Engineering of the Technische Universität München is introduced. For simplicity, linear elasticity, static analysis and two-dimensionality are assumed. For generating super elements, weak constraints are used. The program developped as part of this thesis is analyzed by several tests, comparing results from a classical mesh patch test with results from a super element, obtained by patching meshes involving a reduced mesh.
  
  
  
• von Danwitz, Max Automated application of Dirichlet boundary conditions in voxel based analyses using the Finite Cell Method
  Bachelor's thesis, Technische Universität München, 2013
  
  
  
  
  
  
  

Betreute Software Labs

• Implementation of the Finite Cell Method in ANSYS
  Sommer Semester 2016
• Implementation of different Error estimators in Python
  Sommer Semester 2014
• Implementation of a Discontinuous Galerkin method in Python
  Sommer Semester 2014
• Design and Implementation of an object-oriented Matlab Toolbox for the Finite Cell Method
  Sommer Semester 2012