Stress relaxation in topology optimization

Jenny_Koeckritz

Hi,

Does OptiStruct apply a stress relaxation for elements of a lower density in order to avoid highly stressed elements which don´t contribute much to the structural response? This is of interest for example when stress or strain constraints are applied or if my objective is to minimize the maximum stresses.

I can not find any documentation on this and would appreciate any input :) Thank you,

Jenny

SouravDas0306

Hi Jenny,

Yes, OptiStruct does apply a form of stress relaxation for low-density elements during topology optimization, particularly in stress- or strain-constrained problems. This is necessary because, in density based methods such as SIMP, stresses can become artificially high in elements with very low density since stiffness decreases much faster than the stress field itself. Without relaxation, the optimizer would tend to preserve many nearly void elements simply because they appear numerically highly stressed, even though they contribute very little to the actual structural response. To avoid this issue, OptiStruct internally uses stress interpolation and relaxation techniques for intermediate and low-density elements, often referred to in topology optimization literature as epsilon relaxation or stress penalization. In simple terms, stresses in near-void regions are scaled or regularized so that these elements do not dominate the optimization process. This is especially important when minimizing maximum stress or applying stress, strain, or fatigue constraints, where otherwise the optimization would suffer from stress singularities and poor convergence. Although the exact implementation details are not fully exposed in the documentation, this type of relaxation is a standard and necessary part of practical stress-constrained topology optimization.

Regards,

Sourav