Statics of FGM circular plate with magneto-electro-elastic coupling:axisymmetric solutions and their relations with those for corresponding rectangular beam  

作　　者：Yanzheng WANG Weiqiu CHEN Xiangyu LI 

机构地区：[1]Department of Engineering Mechanics, Zhejiang University [2]State Key Laboratory of CAD & CG, Zhejiang University [3]School of Mechanics and Engineering, Southwest Jiaotong University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第5期581-598,共18页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11321202 and11272281);the Specialized Research Fund for the Doctoral Program of Higher Education(No.20130101110120);the Program for New Century Excellent Talents in University of Ministry of Education of China(No.NCET-13-0973);the Program for Sichuan Provincial Youth Science and Technology Innovation Team(No.2013-TD-0004);the Scientific Research Foundation for Returned Scholars(Ministry of Education of China)

摘　　要：This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic（MEE） materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately（in the Saint Venant sense）. The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material（FGM） with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic（FGMEE） circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.This paper investigates the static behavior of a functionally graded circular plate made of magneto-electro-elastic（MEE） materials under tension and bending.The analysis is directly based on the three-dimensional governing equations for magnetoelectro-elasticity, with the boundary conditions on the upper and lower surfaces satisfied exactly and those on the cylindrical surface satisfied approximately（in the Saint Venant sense）. The analytical solutions, derived with a direct displacement method, are valid for any functionally graded material（FGM） with its properties varying independently in a continuous manner along the thickness direction. For homogeneous materials, these solutions are degenerated to the ones available in the literature. Interesting relations are also found between the solutions for a functionally graded magneto-electro-elastic（FGMEE） circular plate and those for an FGMEE rectangular beam, and even those for a functionally graded elastic beam when only the elastic displacements are considered. The beam solutions are also derived using a direct displacement method. Numerical examples are presented to verify the present analytical solutions, show the effects of material heterogeneity and multi-field coupling, and indicate the correspondence between the plate solutions and beam solutions.

关 键 词：functionally graded circular rectangular magneto correspondence elasticity heterogeneity exactly piezoelectric 

分 类 号：TH133.4[机械工程—机械制造及自动化]