摘要
功能梯度材料制成的微纳结构元件的力学性能截然不同于常规材料制成的宏观结构.本文基于Kirchhoff板理论以及考虑剪切变形的Mindlin板理论,研究了表面效应影响下功能梯度夹层纳米板的屈曲和后屈曲行为.通过平衡分析导出了屈曲和后屈曲的控制方程,得到了单轴和双轴压缩下临界屈曲载荷的解析解.利用Galerkin方法,给出了加载边可动和不可动两种边界条件下临界后屈曲载荷解答.数值结果表明,表面效应对功能梯度纳米层合板稳定性的影响与组成板的材料的体积分数有关,也与结构表面积与体积的比值有关.考虑剪切变形会减小功能梯度纳米层合板的屈曲和后屈曲的临界载荷;对于较薄纳米层合板可以忽略剪切变形的影响.
Nanoplate structures are widely used in nanoelectromechanical systems because of their excellent mechanical properties.At the same volume,the specific surface area of the nano-laminates is much larger than that of the single-layer nanomaterials,and the surface effect is more significant.The influence of the surface effect on nanostructures can be regarded as the combination of surface elasticity and surface residual stress.The classical plate-shell theory does not consider the surface effect and is no longer suitable for describing nanostructures such as nanoplate-shells.As a new type of composite materials,functionally graded materials have received more and more attention from researchers.The mechanical properties of micro/nano structural components made of functionally graded materials are completely different from the macroscopic structures made of conventional materials.Plate structure is a basic component in nanoelectromechanical systems,so it is necessary to study the mechanical properties of plates made of functionally graded materials.In this paper,based on Kirchhoff plate theory and Mindlin plate theory considering shear deformation,the buckling and post-buckling behaviors of functionally graded sandwich nanoplates with surface effect are studied.Based on the force balance analysis,the governing equations of buckling and post-buckling are obtained.The analytical solutions of critical buckling loads under uniaxial and biaxial compression are given.By using the Galerkin method,the approximate solutions of critical post-buckling loads under movable and immovable boundary conditions are given.Numerical results show that the influence of surface effects on the stability of functionally graded nano-laminated plates is related to the volume fraction of the materials that make up the plates,as well as to the ratio of structural surface area to volume.Considering that shear deformation will reduce the critical load for buckling and post-buckling of functionally graded nano-laminated plates,the influence of shear deformation can be ignored for thinner nano-laminated plates.
作者
肖俊华
王杰
Junhua Xiao;Jie Wang(Department of Engineering Mechanics,Yanshan University,Qinhuangdao,066004;Hebei Key Laboratory of Mechanics Reliability for Heavy Equipment and Large Structures,Yanshan University,Qinhuangdao,066004;State Key Laboratory of Nonlinear Mechanics(LNM),Institute of Mechanics,ChineseAcademyof Sciences,Beijing,100190;School of Engineering Science,University of Chinese Academy of Sciences,Beijing,100049)
出处
《固体力学学报》
北大核心
2025年第2期177-191,共15页
Chinese Journal of Solid Mechanics
基金
河北省自然科学基金项目(A2022203025)资助。
关键词
表面效应
功能梯度材料
矩形层合板
屈曲
后屈曲
surface effect
functionally graded material
rectangular laminate
buckling
post-buckling
