WIAS Preprint No. 3026, (2023)

On a two-scale phasefield model for topology optimization


Authors

  • Ebeling-Rump, Moritz
  • Hömberg, Dietmar
    ORCID: 0000-0001-9460-5729
  • Lasarzik, Robert
    ORCID: 0000-0002-1677-6925

2020 Mathematics Subject Classification

  • 35K61 35M33 35Q93 49Q10 74P05 74P10

Keywords

  • Topology optimization, linear elasticity, phase field method, Allen--Cahn equation, existence, weak solutions

DOI

10.20347/WIAS.PREPRINT.3026

Abstract

In this article, we consider a gradient flow stemming from a problem in two-scale topology optimization. We use the phase-field method, where a Ginzburg--Landau term with obstacle potential is added to the cost functional, which contains the usual compliance but also an additional contribution including a local volume constraint in a penalty term. The minimization of such an energy by its gradient-flow is analyzed in this paper. We use an regularization and discretization of the associated state-variable to show the existence of weak solutions to the considered system.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. S, 17 (2024), pp. 326--361 (published online on 26.11.2023), DOI 10.3934/dcdss.2023206 .

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