Effect of design parameterization and relaxation on model responses in topology optimization with stress constraints

Extensive research has been done on the handling of stress constraints in topology optimization. One of the main difficulties when dealing with stress constraints is the so-called singularity phenomenon. Constraint relaxation techniques are commonly applied to avoid the presence of singular optima. In this paper, we focus on the handling of stress constraints for density-based topology optimization, where the design is parameterized by the well-known SIMP model. We investigate the nature of the stress response and the effect of design parameterization, stress
relaxation and analysis discretization on the model response. For this purpose, an elementary numerical example is presented which represents a situation as may occur in density-based continuum topology optimization. The results show clearly the intrinsic difficulties that may be encountered when dealing with stress constraints in density-based topology optimization. We find that artificial local optima may arise and
that penalization increases non-convexity, causing optimizers to converge to suboptimal designs. Finally, it is shown that the global solution of the relaxed problem may not converge to the global solution of the original problem, which agrees with the results reported in truss optimization. The results give an insight in the limitations and difficulties of the present ways of dealing with stress constraints in density-based
topology optimization.