Structural Topology Optimization with Local Finite-Life Fatigue Constraints

Abstract

To improve the fatigue resistance of engineering structures, topology optimization has always been an effective design strategy. The direct calculation of large-scale local fatigue constraints remains a challenge due to high computational cost. In the past, the constraint aggregation techniques, such as the P-norm method, were often applied to aggregate local fatigue constraints into a global constraint, whereas the resultant optimal solution was not consistent with the original problem. In order to meet the local fatigue constraints accurately and reduce the number of constraints, the augmented Lagrangian scheme is employed to transform the original problem into the unconstrained problem. To evaluate the fatigue strength at every material point of structures under the proportional load with variable amplitude, we adopt the Sines fatigue criterion based on the Palmgren–Miner linear damage assumption. In addition, we solve the fatigue-constrained topology optimization problem on the unstructured polygonal meshes, which are not sensitive to numerical instabilities, such as checkerboard patterns, compared with lower-order triangular and bilateral meshes. We provide some numerical examples to validate the potential of the presented method to solve the fatigue-constrained topology optimization problem. Numerical results demonstrate that the optimized designs considering local fatigue constraints have a higher ratio of fatigue resistance to material consumption than those obtained through the traditional P-norm method. Therefore, the proposed approach retaining the local nature of fatigue constraints is more beneficial for realizing the efficient material utilization in structural topology.