Work

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

Year: 2024

Type: article

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: $$W^{1,p}$$ W 1 , p -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.

Source: Numerische Mathematik

DOI: 10.1007/s00211-024-01438-3

Author: Ioannis P. A. Papadopoulos

Institution: Weierstrass Institute for Applied Analysis and Stochastics

Language: English

Topic: Topology Optimization in Engineering

Subfield: Civil and Structural Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090

Funders: Leverhulme Trust, Deutsche Forschungsgemeinschaft, Engineering and Physical Sciences Research Council