Bidirectional Evolutionary Stress-Based Topology Optimization: Global P-Measure Approach for the von Mises-Hencky and Drucker-Prager Failure Criteria

Abstract

This work focuses on developing a methodology for stress-based topology optimization using the bidirectional evolutionary structural optimization method, considering static failure theories. The base problem is formulated in a general form as the maximization of the P-measure – an aggregation function based on the P-norm – of the safety factor associated with an arbitrary static failure theory, while the volume is constrained. The base problem is approached by considering two of the main static failure criteria, enabling the developed method to be applied to a wide range of materials. From selected examples, it was possible to verify that the proposed method was able to generate topologies with maximum stress magnitudes compatible with reference works for the von Mises-Hencky failure theory. Additionally, it was demonstrated that it can obtain topologies with lower stress concentration and a higher safety factor when compared to the approach based on the mean compliance for the Drucker-Prager failure criteria.