Stress-constrained shape and topology optimization with the level set method using trimmed hexahedral meshes

In this paper, we present a novel approach to solve stress-constrained shape and topology optimization problems based on the level set method using trimmed hexahedral meshes. A trimmed hexahedral mesh is generated at each optimization iteration by cutting a regular hexahedral background mesh with the zero-isosurface of a level set function to minimize a volume with stress constraints. A clear and explicit boundary-conforming mesh can be obtained by using trimmed hexahedral elements placed at the boundary of the solid domain, which leads to an accurate estimation of stresses and shape sensitivities. Since the void domain is not considered in the optimization process, the singularity phenomenon in stress-constrained optimization problems is essentially eliminated without using any relaxation technique. Numerical examples show that the proposed method is an efficient and effective approach to solve stress-constrained shape and topology optimization problems.