Level set methods for the fully-coupled topology optimization of flexible multibody systems
The method of flexible multibody systems is used to model technical systems, whose components undergo both large rigid body motions and deformations. If the deformations are small and linear elastic, the floating frame of reference approach is often the most efficient way to model the flexible bodies. That is because the deformations are here approximated by a set of global shape functions. Next to the analysis of dynamical loads on the bodies, multibody simulations can also be used to develop control designs or perform simulation-based optimization, such as structural optimization. The latter is often applied to find optimal design of the flexible bodies with regard to the dynamical loads in order to prevent vibrations of undesired deformations. Topology optimization methods, such as the SIMP approach or level set methods, offer usually the biggest influence on the design. There are already some results for the optimization of flexible multibody systems using the SIMP approach. However, they confine to simple and mostly academic application examples, since the solution of these nonlinear large-scale optimization problems and, in particular, the gradient evaluation is highly complex and time consuming. The number of design variables is therefore limited. In this research project the potential of level set methods in the topology optimization of flexible multibody systems shall be used to solve more realistic and, thus, more complex optimization problems. In contrast to the SIMP approach using level set methods the design is described by an implicit level set function. Constructional details, which evolve along the optimization, can partially be described more efficiently using less design variables. At the same time the number of design variables in the topology optimization shall be significantly increased compared to the existing SIMP optimizations. In order to provide the gradient information for this high-dimensional optimization problem in reasonable times a parallelized adjoint variable method has to be developed. By combination of an efficient parameterization and a parallelized gradient computation the enormous computing and memory costs in the optimization can be managed and methods for the computer-aided design of dynamical loaded bodies with complex geometries can be provided.