基于功能基元拓扑优化法的任意正泊松比超材料结构设计

doi:10.16183/j.cnki.jsjtu.2019.07.008

上海交通大学学报 ›› 2019, Vol. 53 ›› Issue (7): 819-829.doi: 10.16183/j.cnki.jsjtu.2019.07.008

基于功能基元拓扑优化法的任意正泊松比超材料结构设计

杨德庆,秦浩星

上海交通大学高新船舶与深海开发装备协同创新中心; 海洋工程国家重点实验室，上海 200240

出版日期:2019-07-28 发布日期:2019-08-02
作者简介:杨德庆（1968-），男，辽宁省海城市人，教授，博士生导师，主要研究方向为船舶结构优化设计和振动噪声控制.
基金资助:
国家自然科学基金(51479115)资助项目

Metamaterials Design with Arbitrary Poisson’s Ratio by Functional Element Topology Optimization

YANG Deqing，QIN Haoxing

Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration; State Key Laboratory of Ocean Engineering, Shanghai Jiao Tong University, Shanghai 200240, China

Online:2019-07-28 Published:2019-08-02

摘要/Abstract

摘要： 采用功能基元拓扑优化设计方法，以超材料结构的承载能力为目标，选取功能基元结构刚度最大化为目标函数，以指定泊松比值作为约束条件，建立了任意正泊松比超材料结构拓扑优化设计模型并求解.提取拓扑优化得到的功能基元最优构型，建立有限元模型，验算了功能基元的泊松比值.计算了基于功能基元周期性序构形成的超材料结构的面内、面外结构承载性能.结果表明，设计的超材料结构与传统多孔材料结构相比，具有更好的承载能力，具备轻量化优势.

关键词: 超材料; 泊松比; 功能基元; 拓扑优化; 结构刚度

Abstract: Based on functional element topology optimization design method, taking the bearing capacity of the metamaterials structure as the objective, that is, the structural stiffness of the functional element is maximized as the objective function, with the specified Poisson’s ratio as constraints, then the optimization model is established and solved. The optimized structure of the functional primitives is deduced to construct the finite element model for checking the Poisson’s ratio of functional element. The functional element are distributed in a periodic order to form a metamaterials structure, and the in-plane and out-plane structural bearing properties of the metamaterials are calculated and analyzed. Analysis shows that the optimal metamaterial structure has better structural bearing capacity than the traditional honeycomb structure, and the proposed functional element topology optimization method provides a feasible method for the design of new metamaterial structures.

中图分类号:

TB 330

杨德庆,秦浩星. 基于功能基元拓扑优化法的任意正泊松比超材料结构设计[J]. 上海交通大学学报, 2019, 53(7): 819-829.

YANG Deqing，QIN Haoxing. Metamaterials Design with Arbitrary Poisson’s Ratio by Functional Element Topology Optimization[J]. Journal of Shanghai Jiaotong University, 2019, 53(7): 819-829.

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基于功能基元拓扑优化法的任意正泊松比超材料结构设计

Metamaterials Design with Arbitrary Poisson’s Ratio by Functional Element Topology Optimization

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