WIAS Preprint No. 3219, (2025)

Numerical analysis of the SIMP model for the topology optimization problem of minimizing compliance in linear elasticity


Authors

  • Papadopoulos, Ioannis
    ORCID: 0000-0003-3522-8761

2020 Mathematics Subject Classification

  • 65K10 65N30 74F99 90C26

Keywords

  • Topology optimization, linear elasticity, nonconvex variational problem, multiple local minimizers, finite element method

DOI

10.20347/WIAS.PREPRINT.3219

Abstract

We study the finite element approximation of the solid isotropic material with penalization method (SIMP) for the topology optimization problem of minimizing the compliance of a linearly elastic structure. To ensure the existence of a local minimizer to the infinite-dimensional problem, we consider two popular regularization methods: Sobolev-type penalty methods and density filtering. Previous results prove weak(-*) convergence in the space of the material distribution to a local minimizer of the infinite-dimensional problem. Notably, convergence was not guaranteed to all the isolated local minimizers. In this work, we show that, for every isolated local or global minimizer, there exists a sequence of finite element local minimizers that strongly converges to the minimizer in the appropriate space. As a by-product, this ensures that there exists a sequence of unfiltered discretized material distributions that does not exhibit checkerboarding.

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