Stress-Norm vs ALM

Mohan Parthasarathy

• Given any two converged, feasible designs, one could be considered better than the other purely from a mathematical point of view by comparing the objective function value and satisfaction of the constraints.
• But in the presence of stress singularity in the FE model, such a quantitative comparison may not be adequate.
• In the presence of stress singularity, mere satisfaction of a stress constraint may not be meaningful. If the mesh is refined, the stress increases at the area of stress singularity and hence the previously used stress constraint may be violated.
• From an engineering point of view, it is desirable that the stress singularity be eliminated.
• In the case of stress constrained topology optimization, the number of local stress constraints is very high. Hence a method that efficiently handles the stress constraints and at the same time eliminates the stress singularity is desirable.
• The stress-norm method, which has been available in OptiStruct since v14.0 has been shown to eliminate stress singularity in the optimized design (Altair knowledge base KB0115720 by Mohan Parthasarathy and references therein)
• An alternative method called ALM (Augmented Lagrangian Method) is available in OptiStruct since v2022 for stress constrained topology optimization.
• Two examples (L-Bracket and Control Arm) considered in the previous study (Altair knowledge base KB0115720) are revisited using ALM and the results are compared in this study. A third example called Portal Frame is also included in this study for the comparison.
• For details regarding the first two examples solved using the stress-norm method, the reader is referred to the previous study.