基于导重法的结构类周期性布局优化方法研究  

Study of Structural Periodic-like Layout Optimization Based on Guide-weight Method

作　　者：焦洪宇 李英 胡顺安 左克生 林玲 姜正义 于照鹏 JIAO Hongyu;LI Ying;HU Shunan;ZUO Kesheng;LIN Ling;JIANG Zhengyi;YU Zhaopeng(School of Automotive Engineering,Changshu Institute of Technology,Suzhou 215500;School of Mechanical,Material,Mechatronics and Biomedical Engineering,University of Wollongong,Wollongong,Australia 2519)

机构地区：[1]常熟理工学院汽车工程学院,苏州215500 [2]伍伦贡大学机械材料机械电子和生物医学工程学院,澳大利亚伍伦贡2519

出　　处：《机械工程学报》2020年第13期218-230,共13页Journal of Mechanical Engineering

基　　金：国家自然科学基金(51605046);江苏省自然科学基金(BK20181036);江苏政府留学奖学金(JS-2017-188)资助项目。

摘　　要：受外形尺寸限制,一些结构的优化区域无法划分为均匀一致的有限元网格。由此产生的单元体积依赖性,常规周期性拓扑优化无法求解。提出一种基于导重法的结构类周期性布局优化方法。以最小柔度为目标函数,结构质量为约束条件,构建结构类周期性布局优化的数学模型。利用导重法推导出结构类周期性布局优化的迭代准则,解释其物理意义并给出其优化流程。以单元应变能密度为基础,提出一种改进的过滤方案以解决结构类周期性布局优化中单元体积依赖性问题。利用所提出的方法,对循环对称结构、二维汽车轮毂结构和梯形结构进行结构类周期性布局优化研究。研究结果表明,子域数目不同时均可以得到具有类周期性布局的最优拓扑形式。通过性能指标和相对应变能两个指标来评价三个算例的最优拓扑形式,验证了利用导重法求解结构类周期性布局优化的可行性和有效性。Limited by boundary dimension, optimization area of some structures cannot be divided into finite element meshes uniformly. This results in element volume dependency, which cannot be solved by conventional periodic topology optimization. A periodic-like layout optimization method is proposed based on the guide-weight method. With the minimum compliance as the objective function and the structural mass as the constraint condition, a mathematical model for the periodic-like layout optimization is constructed. The iterative criterion for periodic-like layout optimization is derived using the guide-weight method, and its physical meaning is explained and its optimization process is given. Based on the element strain energy density, an improved filtering scheme is proposed to solve the problem of element volume dependence in structural periodic-like layout optimization. The structural periodic-like layout optimization of cyclic symmetry structure, two-dimensional automobile hub structure and trapezoidal structure are researched using the proposed method. The research results show that the optimal topological form with periodic-like layout can be obtained when the number of subdomains is different. The optimal topological forms of three examples are evaluated by two evaluation indicators:performance index and relative strain energy. The feasibility and effectiveness of using the guide-weight method to solve the periodic-like layout optimization are verified.

关 键 词：类周期性 布局优化 导重法 迭代准则 单元体积依赖性 

分 类 号：TH11[机械工程—机械设计及理论]