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

Abstract This work presents 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 derived from the P-norm — of the safety factor associated with an arbitrary static failure criterion, under a volume constraint. The formulation is examined for von Mises-Hencky and Drucker-Prager static failure theories, allowing the proposed approach to be applied to a wide range of ductile and brittle materials. Through selected numerical examples, it is demonstrated that the method successfully produces topologies with maximum stress magnitudes consistent with reference results for the von Mises-Hencky criterion. Moreover, it achieves topologies with reduced stress concentration and higher safety factors compared to the traditional mean-compliance-based approach when using the Drucker-Prager failure criterion.