A novel hr-adaptive mesh refinement scheme for stress-constrained shape and topology optimization using level-set-based trimmed meshes

This paper presents a new computational strategy for stress-constrained shape and topology optimization with adaptive mesh refinement using level-set-based trimmed meshes. An octree-based h-adaptive mesh refinement using a stress-based criterion is performed to dynamically refine or coarsen an initial uniform background hexahedral mesh during the optimization process. In order to estimate stresses and shape sensitivities accurately on the domain boundaries, an r-adaptive boundary-conforming trimmed hexahedral mesh is generated by cutting the background octree mesh with the zero-isosurface of a level-set function. The numerical results show that the proposed hr-adaptive mesh refinement scheme greatly reduces the computational cost and achieves a clear and explicit representation of desired optimal designs of structures with stress constraints.