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A holistic topology and shape optimization approach with an application to steel profiles


This paper addresses the problem of combining topology and shape optimization approaches by exploiting suitable methods from both discrete as well as nonlinear optimization. The topology decisions are made iteratively within the general optimization process by a branch-and-bound algorithm. In every node of the branch-and-bound tree a sequence of nonlinear subproblems which consist of a shape and topology optimization component are solved by using sequential quadratic programming (SQP). The topology component follows the solid isotropic material with penalization (SIMP) idea. One important application of the here presented approach in engineering consists of assisting the product development process in early stages. Here, we consider the design of multi-chambered sheet metal profiles. This work deals with the construction of the branch-and-bound tree and how effective node selection rules can be obtained, as well as with the resulting nonlinear subproblems and the applied SQP method. Finally, numerical results for different load scenarios and topology constraints are presented.

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This work was supported by the Deutsche Forschungsgemeinschaft (DFG) Collaborative Research Centre 666 “Integral Sheet Metal Design with Higher Order Bifurcations – Development, Production, Evaluation”.

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Correspondence to Benjamin M. Horn.

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Günther, U., Hess, W., Horn, B.M. et al. A holistic topology and shape optimization approach with an application to steel profiles. Struct Multidisc Optim 57, 1267–1281 (2018).

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  • Topology optimization
  • Geometry optimization
  • Shape optimization
  • Branch-and-bound
  • PDE-constrained optimization