On approaches for avoiding low-stiffness regions in variable thickness sheet and homogenization-based topology optimization

Variable thickness sheet and homogenization-based topology optimization often result in spread-out, non-well-defined solutions that are difficult to interpret or de-homogenize to sensible final designs. By extensive numerical investigations, we demonstrate that such solutions are due to non-uniqueness of solutions or at least very flat minima. Much clearer and better-defined solutions may be obtained by adding a measure of non-void space to the objective function with little if any increase in structural compliance. We discuss various alternatives for cleaning up solutions and propose two efficient approaches which both introduce an auxiliary field to control non-void space: one approach based on a cut element based auxiliary field (hybrid approach) and another approach based on an auxiliary element based field (density approach). At the end, we demonstrate significant qualitative and quantitative improvements in variable thickness sheet and de-homogenization designs resulting from the proposed cleaning schemes.

Automated summary

This study explores the issue of non-unique or very flat minima solutions in variable thickness sheet and homogenization-based topology optimization. By adding a measure of non-void space to the objective function, clearer and better-defined solutions can be obtained without significantly increasing structural compliance. Various alternatives for cleaning up solutions are discussed, and two efficient approaches involving introducing an auxiliary field to control non-void space are proposed, leading to significant qualitative and quantitative improvements in designs.