基于多分辨率-多边形单元建模策略的多材料结构动刚度拓扑优化方法  

TOPOLOGY OPTIMIZATION OF MULTI-MATERIAL STRUCTURES FOR DYNAMIC STIFFNESS USING POLYGONAL MULTIRESOLUTION SCHEME

作　　者：江旭东[1] 马佳琪 熊志 滕晓艳[2] 王亚萍[1] JIANG Xu-dong;MA Jia-qi;XIONG Zhi;TENG Xiao-yan;WANG Ya-ping(School of Mechanical and Power Engineering,Harbin University of Science and Technology,Harbin 150080,China;School of Mechanical and Electrical Engineering,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：《工程力学》2024年第2期222-235,共14页Engineering Mechanics

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

摘　　要：利用多边形有限单元的高精度求解优势,融合多分辨率拓扑优化方法,实现粗糙位移网格条件下的高分辨率构型设计,由此提出多材料结构动刚度问题的拓扑优化方法。将多边形单元(位移场求解单元)劈分为精细的小单元,构造设计变量与密度变量的重叠网格,形成多分辨率-多边形单元的优化建模策略;以平均动柔度最小化为目标和多材料的体积占比为约束,建立多材料结构的动力学拓扑优化模型,通过HHT-α方法求解结构动响应,采用伴随变量法推导目标函数和约束的灵敏度表达式,利用基于敏度分离技术的ZPR设计变量更新方案构建多区域体积约束问题的优化迭代格式;通过典型数值算例分析优化方法的可行性和动态载荷作用时间对优化结果的影响机制。Polygonal elements with high precision are used in finite element modeling along with a multiresolution scheme for topology optimization to achieve high resolution design with a coarse finite element mesh.A polygonal multiresolution scheme is proposed to perform a topology optimization of multi-material structures for dynamic stiffness.This combined modelling strategy of polygonal finite element with higher resolution density and design discretization is extended to optimal multi-material structural design problem,which is based on the concept that a polygonal element for dynamic analysis is split into fine design variable elements for optimization and overlapped density variable elements for representation of material distribution.To minimize the mean dynamic compliance subjected to the volume fraction constraints of each candidate material,a topology optimization model of multi-material structure is established.The HHT-αmethod is adopted to solve the structural dynamic problem.Following the sensitivity analysis of objective function and constraints by the adjoint variable method,the ZPR design variable update scheme is employed to solve highly nonlinear and non-convex optimization problem with multiple regional volume constraints.Several benchmark numerical examples are presented to analyze the feasibility of the proposed algorithm,and the influence of the duration time of dynamic load on the optimized results is analyzed.

关 键 词：拓扑优化 多材料 多分辨率 多边形单元 动刚度优化 

分 类 号：TU311[建筑科学—结构工程]