带隙特性计算的等效梁元法与等效平面应变法  

An equivalent beam and equivalent plane strain method for bang gap analysis of metamaterials

作　　者：毛翔 杨德庆[1,2] 李清[1] MAO Xiang;YANG Deqing;LI Qing(Collaborative Innovation Center for Advanced Ship and Deep-sea Exploration,State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University,Shanghai 200240,China;Yazhou Bay Institute of Deepsea Science and Technology,Shanghai Jiao Tong University,Sanya 572024,China)

机构地区：[1]上海交通大学海洋工程国家重点实验室高新船舶与深海开发装备协同创新中心,上海200240 [2]上海交通大学三亚崖州湾深海科技研究院,海南三亚572024

出　　处：《振动与冲击》2023年第8期319-325,共7页Journal of Vibration and Shock

基　　金：海南省三亚崖州湾科技城管理局深海科技先导创新项目(SKJC-KJ-2019KY07)。

摘　　要：针对可简化为平面应变类力学问题的超材料,根据矩形薄板筒形弯曲理论,提出该类超材料带隙特性计算的等效梁元法。应用等效梁元法和常规等效平面应变法对负泊松比超材料的多种典型构型(内六角、星形、箭形和旋转三角形)的带隙特性进行数值计算,比较两种方法在带隙计算精度、计算效率及拓扑优化中适用性等方面的差异,并经试验测试结果进行验证。研究表明,等效梁元法和等效平面应变法的带隙计算精度均较高,与实测值误差在7%以内。等效梁元法在带隙计算效率上比等效平面应变法高约50%,但拓扑优化基结构模型的规模较大,适用于杆件类超材料结构拓扑优化。等效平面应变法带隙计算效率较低,拓扑优化基结构模型的规模较小,适用于连续体类及骨架类超材料结构的拓扑优化。该研究可为带隙超材料的拓扑优化设计提供参考。Based on the barrel bending theory of rectangular thin plates,an equivalent beam element method was proposed for the calculation of bandgap properties of metamaterials that can be simplified as a plane strain mechanical problem.The equivalent beam element method and the conventional equivalent plane strain method were applied to numerically calculate the bandgap characteristics of various typical configurations of negative Poisson’s ratio metamaterials(re-entrant hexagonal,star-shaped,double arrowhead,and rotating triangle).The differences between the two methods in terms of bandgap calculation accuracy,calculation efficiency and applicability in topology optimization were compared and verified by experimental test results.It was shown that both the equivalent beam element method and the equivalent plane strain method have a high bandgap calculation accuracy,within 7%of the experimental measurements.The equivalent beam element method is about 50%more efficient than the equivalent plane strain method in bandgap calculation,but the scale of the topology optimization base structure model is larger and suitable for topology optimization of rod-like metamaterial structures.The equivalent plane strain method is less efficient in bandgap calculation and the size of the base structure model is smaller for topology optimization of continuum and skeleton metamaterials.This study can provide a reference for the design of bandgap topology optimization of metamaterials.

关 键 词：超材料 带隙特性 有限元分析 平面应变 薄板理论 

分 类 号：TH212[机械工程—机械制造及自动化] TH213.3