Stress-constrained topology optimization with precise and explicit geometric boundaries

The solution of stress-constrained topology optimization problems is strongly affected by the accuracy of the computed stresses on the boundary of the evolving structure. In this paper, we address stress-constrained topology optimization using an explicit and precise representation of the boundaries. The geometrical model is a spline-based topology that evolves following the level set method. Untrimming techniques are used to construct the topology from the implicit boundaries defined by the level set function. Subsequently, a mechanical model that replicates the geometrical model precisely is constructed by mesh refinement. The governing state equations are solved using Iso Geometric Analysis (IGA). This leads to accurate stress computations and smooth stress fields, which are critical for constraining the stresses in regions that exhibit high concentrations. Consistent analytical sensitivity analysis is formulated for the entire procedure. Utilizing the smooth IGA solution, the stress is limited in the domain as well as in precise computation points on the boundaries. The applicability of the proposed approach, as well as its relative advantages compared to density-based approaches is demonstrated on several benchmark cases of stress-constrained topology optimization.