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Akronym
LSM_TEMBS
Projekt Titel
Level set methods for the fully-coupled topology optimization of flexible multibody systems II
Förderkennzeichen
HE 8261/2-3
Funding code
945.03-029
Startdatum
December 1, 2025
Enddatum
November 30, 2028
Gepris ID
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The project's overall goal is to develop efficient level set methods for fully coupled topology optimization of flexible multibody systems. For the modeling of flexible multibody systems, it is assumed that the deformations of the flexible bodies are small and linear-elastic. This assumption is valid for the vast majority of mechanical systems. Therefore, the kinematics of the flexible bodies is described using the floating frame of reference formulation. In the first phase of the project, weakly and fully coupled level set-based topology optimizations were established, an approach to reduce the computational effort during adjoint sensitivity analysis was developed, and optimization results were presented for the example of a flexible slider-crank mechanism. In the project's second phase, the focus will be on aspects of the level set methods that have proven to be particularly advantageous compared to the Solid Isotropic Material with Penalization (SIMP) approach that has been frequently used to date. Among other things, it could be shown in the first project phase that the computational effort in the sensitivity analysis is significantly lower than the computational effort of comparable SIMP optimizations. This is because the gradient information is no longer required in the entire design domain but only along the body's boundaries and interior. In addition, it is possible to interpolate the gradient in the interior from selected support points without preventing the formation of new holes. This advantage is to be further investigated and developed in the project's second phase. For this purpose, the heuristic sampling used so far to determine the interpolation support points in the interior and along the edges of the body is to be replaced by an error-based method. By improving the interpolation process, the number of necessary samples in the design domain and, thus, the computational effort for the determination of the gradient shall be further significantly reduced. In level set-based optimization, local constraints can be considered more efficiently in the optimization, since the boundary and, thus, the topology is implicitly known. Therefore, unlike in the SIMP approach, local constraints do not have to be taken into account in the entire design domain, but only for the subdomain that is part of the current design. As a consequence, among others, the gradient calculation is greatly simplified. In the second project phase, the potential of level set methods for the consideration of stress constraints in the fully coupled topology optimization of flexible multi-body systems using the augmented Lagrange method will therefore be intensively investigated.