Relating Phase Field and Sharp Interface Approaches to Structural Topology Optimization

Luise Blank, Harald Garcke, Vaness Styles and Hassan Farshbaf-Shaker^*

A phase field approach for structural topology optimization which allows for topology changes and multiple materials is analyzed. First order optimality conditions are rigorously derived and it is shown via formally matched asymptotic expansions that these conditions converge to classical first order conditions obtained in the context of shape calculus. Finally, we present several numerical results for mean compliance problems and a cost involving the least square error to a target displacement.

Mathematics Subject Classification: 49Q10 74P10, 49Q20, 74P05, 65M60

Keywords: Structural topology optimization, linear elasticity, phase-field method, first order conditions, matched asymptotic expansions, shape calculus, numerical simulations

Minisymposion: Nonsmooth and Unilateral Problems - Modelling, Analysis and Optimization Methods