The lecture gives insight into current research topics for the solution of structural mechanics problems. Following the interpolation of curves in CAD programs, approach functions are used in FEM, which describe the geometry exactly and allow higher continuity between the integration cells. Among other things, isogeometric analysis is a promising tool for use in the phase field method, which is used here for topology finding. Furthermore, a heuristic method for the optimization of structures is treated, which is based on the evolution strategy. The variable height of members (haunches) is treated theoretically and used for the optimization of structures in the context of the evolution strategy.
- Isogeometric analysis
- Introduction and basics
- Implementation in FEM programs
- Advantages and disadvantages of the method
- Phase field method
- Allen-Cahn and Cahn-Hilliard problems
- Topology finding by means of phases
- Evolution strategy for optimization of structures
- Bars of variable height (haunches) for the optimization of the structure
The numerical implementation of the theory is done with the program MATLAB. The exercises take place in the computer pool of the Faculty of Architecture and Civil Engineering (August-Schmidt-Str. 8, room 335).
The lecture material will be made available in the Moodle workroom BMSD-EMS.
Notes on the lecture
The exercises to the lecture will take place in the lecture hall or in the computer pool by arrangement.
The course is intended for students of the master programs Bauingenieurwesen (civil engineering), Maschinenbau (mechanical engineering), Technomathematik (Technomathematics), Computational Mechanics and other comparable programs of the UAR universities.
The number of credits that can be taken depends on the workload of the individual program of study.