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

doi:10.1007/s10483-023-3024-6

摘要/Abstract

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.

关键词: negative Poisson's ratio (NPR), negative thermal expansion (NTE), sandwich plate, vibration, buckling

Abstract: 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.

Key words: negative Poisson's ratio (NPR), negative thermal expansion (NTE), sandwich plate, vibration, buckling

中图分类号:

74H45

Qiao ZHANG, Yuxin SUN. Statics, vibration, and buckling of sandwich plates with metamaterial cores characterized by negative thermal expansion and negative Poisson's ratio[J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1457-1486.

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