Solving Stress and Compliance Constrained Volume Minimization using Anisotropic Mesh Adaptation, the Method of Moving Asymptotes and a Global p-norm

TL;DR

This paper combines anisotropic mesh adaptation, the method of moving asymptotes, and a global p-norm to effectively address stress and compliance constrained volume minimization problems, focusing on small length scales and mesh dependence.

Contribution

It introduces a novel integration of anisotropic mesh adaptation with the method of moving asymptotes for stress-constrained topology optimization using a p-norm.

Findings

Successful application to portal and L-bracket problems with p=10

Demonstrated mesh dependence investigation

Proposed relaxation of L-bracket problem with rounded corners

Abstract

The p-norm often used in stress constrained topology optimisation supposedly mimics a delta function and it is thus characterised by a small length scale and ideally one would also prefer to have the solid-void transition occur over a small length scale, since the material in this transition does not have a clear physical interpretation. We propose to resolve these small length scales using anisotropic mesh adaptation. We use the method of moving asymptotes with interpolation of sensitivities, asymptotes and design variables between iterations. We demonstrate this combination for the portal and L-bracket problems with p=10, and we are able to investigate mesh dependence. Finally, we suggest relaxing the L-bracket problem statement by introducing a rounded corner.