基于复杂约束拓扑优化的负泊松比超材料设计  

Negative Poisson’s Ratio Metamaterial Design Based on TopologyOptimization with Complex Constraints

作　　者：孟军辉 刘清洋 金泽华 MENG Junhui;LIU Qingyang;JIN Zehua(School of Aerospace Engineering,Beijing Institute of Technology,Beijing 100081,China;Beijing Institute of Technology Chongqing Innovation Center,Chongqing 401135,China)

机构地区：[1]北京理工大学宇航学院,北京100081 [2]北京理工大学重庆创新中心,重庆401135

出　　处：《北京理工大学学报》2023年第8期852-862,共11页Transactions of Beijing Institute of Technology

基　　金：国家自然科学基金资助项目(11902029)。

摘　　要：针对现阶段超材料拓扑优化设计在飞行器设计领域存在的微观尺度上难以制造和宏观尺度上不具有周期性的问题,提出了一种宏观尺度下的超材料拓扑优化设计方法,分别应用优化准则法和移动渐近线法进行了指定泊松比约束的超材料拓扑优化设计,得到了在横向、纵向两个方向上的泊松比都满足约束的负泊松比超材料,并对两种优化算法的设计结果进行了对比分析.针对拓扑优化得到的胞元构型,建立了理论模型和有限元模型,对拓扑优化结果的力学性能进行验证.经理论模型和有限元模型计算,拓扑优化设计结果的泊松比满足设计要求,证明了宏观尺度拓扑优化方法设计负泊松比超材料的有效性.To solve the problems of metamaterial topology optimization design in aircraft design—being diffi-cult to manufacture on the micro scale and non-periodic on the macro scale,a macro scale metamaterial topo-logy optimization design method was proposed.The topological optimization design of metamaterials with pre-scribed Poisson’s ratio was carried out using optimality criteria and the method of moving asymptotes respect-ively.The negative Poisson’s ratio metamaterials satisfying the constraints in both transverse and longitudinal directions were obtained,and the design results of the two optimization algorithms were compared and analyzed.For the cell configuration obtained by topology optimization,the theoretical model and the finite element model were established,and the mechanical properties of the topology optimization results were verified.According to the calculation of the theoretical model and the finite element model,the Poisson’s ratio of the design results of topology optimization meets the design requirements.It proves the effectiveness of the macro scale topology op-timization method in designing metamaterials with prescribed Poisson’s ratio.

关 键 词：负泊松比超材料 结构优化 宏观尺度拓扑优化法 优化准则法 移动渐近线法 

分 类 号：TB330.1[一般工业技术—材料科学与工程]