Aggregation-free fatigue constrained topology optimization using the constrained natural element method

Abstract

Fatigue resistance is one of the most important design criteria to ensure the safety of mechanical structures. In this paper, a topology optimization methodology for volume minimization under local fatigue constraints based on the augmented Lagrangian method and the constrained natural element method is proposed. The Sines fatigue criteria is used to define the equivalent alternating and average stresses to address fatigue resistance of additive manufactured Ti-6Al-4V alloy structure for infinite life. Since the fatigue criteria under consideration is based on stress invariants, the fatigue-driven problem has the same difficulties as the stress-based topology optimization problem, so that similar strategies can be used to circumvent the problem of stress singularity and the need for a large number of evaluation points. Although a large number of constraints are required to maintain the local nature of stress, the formulation presented requires only one adjoint vector, which leads to an efficient sensitivity assessment. Several numerical examples are presented to demonstrate the effectiveness of the proposed method.