Polytope Mesh Generation and Finite Element Analysis Methods for Problems in Solid Mechanics

• Applicant: Professor Dr. Bert Jüttler
• Subject Area: Applied Mechanics, Statics and Dynamics ; Mathematics
• Term: since 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 495926269

The project, which is part of Research Unit "Polytope Mesh Generation and Finite Element Analysis Methods for Problems in Solid Mechanics" aims to establish Weakly Star-Shaped Spline Elements - abbreviated as WS3Es - for numerical simulation via Scaled Boundary Isogeometric Analysis (SBIGA). We will work towards achieving the following three specific objectives: 1) We plan to establish techniques for the segmentation of the computational domain into WS3Es. 2) These results will be complemented by methods for parameterization of the WS3Es in order to obtain discretizations. 3) We plan to investigate methods for adaptive discretization and efficient assembly, focusing on representations and discretizations with varying level of detail. The contribution of this project to the goals of the research unit consists in the geometric technology needed for numerical simulations via scaled boundary isogeometric analysis. It is expected that the proposed representations of domains via WS3Es represent a useful compromise between ease of generation/conversion on the one hand, and the availability of high level structural information that facilitates data exchange with CAD systems and their use in downstream applications (such as design optimization) on the other. Thus, they will represent a major step towards the friction-free integration of design and analysis and the creation of "digital twins" of man-made and natural objects and environments. It requires the joint effort of a research unit like this to bring about these benefits. On the one hand, the geometry-oriented participants (such as the PI of this project) will use their expertise to inform the simulation- and analysis-oriented community about the possibilities and also the limitations of the available representations of the domain. On the other hand, it is fundamental for them to learn from their simulation-oriented partners in the project about the requirements and constraints imposed by the analysis process, and this is expected to drive the creation of new types of representations with associated computational tools for the discretization of partial differential equations. There are several connections to the other projects: With P3 (Birk), we plan to explore the potential of using the WS3Es developed this project in the classical SBFEM framework, and we will investigate the potential of spline level set surfaces. The work on parameterization and highly regular discretizations will benefit from the interaction with the NURBS-based shell formulations and the related numerical simulation studied in P4 (Klinkel). The cooperation with P6 (Simeon) will focus on the polar structure of the parameterizations and the effect of the resulting singularity, and we expect to extend our previous work on adaptive spline refinement. Finally, the interface creation and parameterization problem will benefit from using machine learning, jointly with P7 (Chasapi).

• DFG Programme: Research Units
• Subproject of: FOR 5492: Polytope Mesh Generation and Finite Element Analysis Methods for Problems in Solid Mechanics
• International Connection: Austria
• Partner Organisation: Fonds zur Förderung der wissenschaftlichen Forschung (FWF)