Topology optimization for infinite fatigue life of cyclic symmetric structures subjected to non-proportional loading

This paper presents a density based topology optimization method for infinite fatigue life constraints of non-proportional load cases, with a specific focus on parts with cyclic symmetry. Considering non-proportional loads in topology optimization significantly broadens the types of design problems that can be handled. The method estimates the local variation in Signed von Mises stress using a smooth min/max function and constrains the resulting stress amplitude using established stress based topology optimization methods. Accounting for non-proportionality of loading significantly increases the computation cost with respect to existing proportional methods, as the time-varying stress field needs to be computed. Inertia effects are neglected in the structural analysis. Therefore, a quasi-static analysis is used to obtain the stress history. To reduce the computational cost, advantage is taken of cyclic symmetric properties to reduce the number of necessary time steps to evaluate. This reduces the computational cost roughly proportional to the number of unique load time steps present in the repeated segments as opposed to a standard implementation. The method is tested on numerical examples in 2D and 3D for both proportional and non-proportional loads and was found to be locally accurate up to the accuracy of the constraint aggregation.