Structural Topology Optimization with Local Finite-Life Fatigue Constraints

Xiaoyan Teng, Can Wang, Xudong Jiang () and Xiangyang Chen
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Xiaoyan Teng: College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China
Can Wang: Nanjing Research Institute of Electronics Technology, Nanjing 210039, China
Xudong Jiang: Mechanical Power and Engineering College, Harbin University of Science and Technology, Harbin 150080, China
Xiangyang Chen: College of Mechanical and Electrical Engineering, Harbin Engineering University, Harbin 150001, China

Mathematics, 2023, vol. 11, issue 5, 1-17

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.

Keywords: topology optimization; aggregation-free approach; local finite-life fatigue constraints; augmented Lagrangian method; polygonal finite element meshes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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