Structural topology optimization with local finite-life fatigue constraints
JIANG Xudong1,WU Ziwang1,TENG Xiaoyan2
1.Mechanical and Power Engineering College, Harbin University of Science and Technology, Harbin 150080, China;
2.Mechanical and Electrical Engineering College, Harbin Engineering University, Harbin 150001, China
Abstract:Topology optimization method is a feasible design strategy to improve fatigue-resistance performance of engineering structures. To reduce the computational cost due to numerous local fatigue constraint, a global fatigue damage measure based on P-norm method is traditionally introduced in current literatures. However there exists a gap at the optimal solution subjected to the weak constraints compared with accurate local fatigue constraint. To solve the fatigue-constrained problem, a scheme based on the augmented Lagrangian method is adopted to address the problem consistently with the local definition of fatigue damage without using traditional aggregation techniques. Under proportional loadings with various amplitude, the Palmgren-Miner linear damage hypothesis combined with Sines fatigue criterion is employed to evaluate the fatigue strength at every material point. In the augmented Lagrangian, the lightweight design model with satisfying the fatigue constraints locally is established and then is solved by globally convergent method of moving asymptotes. Moreover, a general topology optimization framework using unstructured polygonal finite element meshes is developed to realize the lightweight design of fatigue-resistance structures with complex geometrical boundary. The numerical results of several benchmark examples show that the optimal configuration obtained by local fatigue constraints provides a superior fatigue-resistance performance with less material usage to that by P-norm aggregative fatigue constraints. Therefore, topology optimization with local fatigue constraints contributes to effectiveness of material usage and enhancement of fatigue-resistance performance.
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