局部有限寿命疲劳约束条件下的结构拓扑优化方法  

Structural topology optimization with local finite-life fatigue constraints

作　　者：江旭东[1] 武子旺 滕晓艳[2] JIANG Xudong;WU Ziwang;TENG Xiaoyan(Mechanical and Power Engineering College,Harbin University of Science and Technology,Harbin 150080,China;Mechanical and Electrical Engineering College,Harbin Engineering University,Harbin 150001,China)

机构地区：[1]哈尔滨理工大学机械动力工程学院,哈尔滨150080 [2]哈尔滨工程大学机电工程学院,哈尔滨150001

出　　处：《振动与冲击》2023年第16期110-119,共10页Journal of Vibration and Shock

基　　金：国家自然科学基金(52175502;51675144);黑龙江省自然科学基金联合引导项目(LH2020E064)。

摘　　要：拓扑优化方法为工程结构抗疲劳性能的改善提供了有效的设计策略,为了减少大规模局部疲劳约束引起的计算代价,往往采用P范数方法将其凝聚成全局约束,但是,满足这类弱约束的最优解与原问题的最优解存在间隙。为了精确满足局部疲劳约束和降低约束数量,采用增广拉格朗日方法将原问题处理为无约束问题,提出局部有限寿命疲劳约束条件下的结构拓扑优化方法。考虑变幅值的比例载荷作用,采用Palmgren-Miner线性损伤假设和Sines疲劳准则评价材料点的疲劳强度,以局部疲劳性能为约束条件,建立结构的轻量化设计模型,采用全局收敛移动渐近线算法求解局部疲劳约束下的结构拓扑优化问题。另外,将非结构化多边形网格技术融入到拓扑优化模型,实现复杂几何边界结构的抗疲劳轻量化设计。数值算例结果表明,与P范数方法的优化结果相比,局部疲劳约束条件下的优化结构具有更优的抗疲劳性能和更少的材料用量,因而考虑局部疲劳约束有益于材料的充分利用和结构抗疲劳性能的改善。A 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 constraints,a global fatigue damage measure based on the P-norm method was traditionally introduced in current literatures.However there exists a gap at the optimal solution subjected to the weak constraints compared with accurate local fatigue constraints.To solve the fatigue-constrained problem,a scheme based on the augmented Lagrangian method was 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 the Sines fatigue criterion was employed to evaluate the fatigue strength at every material point.In the augmented Lagrangian,the lightweight design model with satisfying the fatigue constraints locally was established and then was solved by a globally convergent method of moving asymptotes.Moreover,a general topology optimization framework using unstructured polygonal finite element meshes was 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.

关 键 词：拓扑优化 非凝聚方法 局部有限寿命疲劳约束 增广拉格朗日方法 多边形有限元网格 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3