Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio

作     者：Qiao ZHANG Yuxin SUN Qiao ZHANG;Yuxin SUN

作者机构：National Key Laboratory of Strength and Structural IntegritySchool of Aeronautic Science and EngineeringBeihang UniversityBeijing 100191China 

出 版 物：《Applied Mathematics and Mechanics(English Edition)》 (应用数学和力学（英文版）)

年 卷 期：2023年第44卷第9期

页      面：1457-1486页

核心收录：

学科分类：08[工学] 080101[工学-一般力学与力学基础] 0701[理学-数学] 0801[工学-力学（可授工学、理学学位）] 080102[工学-固体力学] 

基　　金：Project supported by the National Natural Science Foundation of China(No.11872098)。 

主　　题：negative Poisson's ratio(NPR) negative thermal expansion(NTE) sand-wich plate vibration buckling 

摘      要：This paper proposes a three-dimensional(3D)Maltese cross metamaterial with negative Poisson’s ratio(NPR)and negative thermal expansion(NTE)adopted as the core layers in sandwich plates,and aims to explore the relations between the mechanical responses of sandwich composites and the NPR or NTE of the metamaterial.First,the NPR and NTE of the metamaterial are derived analytically based on energy conservation.The effective elastic modulus and mass density of the 3D metamaterial are obtained and validated by the finite element method(FEM).Subsequently,the general governing equation of the 3D sandwich plate under thermal environments is established based on Hamilton’s principle with the consideration of the von Kármán nonlinearity.The differential quadrature(DQ)FEM(DQFEM)is utilized to obtain the numerical solutions.It is shown that NPR and NTE can enhance the global stiffness of sandwich structures.The geometric parameters of the Maltese cross metamaterial significantly affect the responses of the thermal stress,natural frequency,and critical buckling load.