Mesh generation for mixed structures

 

Project team leader Dr.-Ing. Stefan Kollmannsberger
PhD students Benjamin Wassermann, MSc, Dr.-Ing. Christian Sorger MSc
Principal investigators Prof. Dr. rer. nat. Ernst Rank
Prof. Dr.-Ing. Casimir Katz (SOFiSTiK AG)
Project partners SOFiSTiK AG

Project description

The Finite Element Method (FEM) is a numerical technique for finding approximate solutions of partial differential equations (PDE) as well as integral equations as they arise in many problem formulations in fluid and in solid mechanics. The basic idea of the FEM is to discretize complex structural domains by a surface or volume mesh consisting of a finite number of triangular, quadrilateral, tetrahedral, pentahedral and hexahedral elements and to render the governing PDEs into an approximating system of ordinary differential equations, which are then solved using numerical integration and solution techniques.

In the h-version of the FEM complex domains are discretized by introducing a large number of linear finite elements sharing the same boundary nodes to ensure conformity. All physical quantities are defined in the nodes of an element; the distribution of the physical quantity inside the elements is determined by linear interpolation. In the h-version of the FEM the results of the simulation and the geometry of the structure are exactly described in the nodes, an improvement of the accuracy is achieved by locally or globally refining the mesh.

The idea of the p-version of the FEM is to increase the accuracy of the solution by increasing the polynomial degree of the solution space locally defined on each single finite element. By this it is possible to compute accurate solutions for large and complex domain with only a few numbers of finite elements. In case of complex and curved structural domains therefore it is necessary that the single elements describe the geometry of the original structure exactly. This can be achieved either by coupling the geometric description of the original domain with the geometric description of each element, or by approximating the original structure with curved finite elements using polynomial formulations.

In terms of surface meshing the research fields have been widely exploited and also the generation of tetrahedral elements is mostly solved by many different efficient and powerful algorithms. Nevertheless, the generally valid computation of qualitatively good hexahedral elements is still afflicted with difficulties and lots of research projects have been investigated in finding a general solution.

In modern civil engineering there exists a growing number of mixed models containig surfaces (e.g. walls and plates) to be meshed with 2D-elements and containing thin walled structures (e.g. shells and plates) and solid volumes (e.g. foundations and spheres) to be meshed with 3D-elements. The mesh generation for this kind of mixed structures is still an unsolved field in research and there exists no algorithm, that is able to automatically mesh those problems by using a combination of different meshing techniques.

 

 

mesh

Mesh example of a multistory building

 

In this project, a number of different meshing techniques are investigated and coupled in order to create a generally valid meshing algorithm for mixed structures. Therefore, the geometry of the whole domain has to be divided into regions that have to be meshed by surface meshing techniques and regions that need to be discretized by one of the different volume meshing algorithms. After the mesh generation of the different domain sections the joint mesh of the whole domain is generated by merging the different meshes.



Publications


Contact: Benjamin Wassermann, M.Sc.

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