Adaptive P-norm Method in Stress-Based StructuralOptimization

This study aims to propose and discuss an adaptive P-norm method for stress-based structural optimization problems. When stress is considered in the optimal design process, one of the main challenges is the large number of constraints owing to the local quantity of stress. The problem is more important in stress-constrained topology optimization where the number of design variables is huge and also the number of stress constraints is at least equal to the number of elements in finite element discretization. To overcome this drawback, a popular and efficient method is the P-norm method. The P-norm relation approximates the maximum stress in structure and is more accurate when the P value is large enough. However, assigning a very large number for the P value causes instabilities in the optimization process. In this study, utilizing an adaptive value for P is investigated. It has been shown that employing the adaptive value for the P-norm usually leads to better-optimized solutions in structural optimization when stress is considered as a constraint or objective function. The reason is discussed in this study by using a simple truss problem. Moreover, the method is investigated in a continuum topology optimization problem