Three-dimensional analytical solution for a transversely isotropic functionally graded piezoelectric circular plate subject to a uniform electric potential difference  

作　　者：LI XiangYu DING HaoJiang CHEN WeiQiu 

机构地区：[1]Department of Civil Engineering,Zhejiang University,Hangzhou 310027,China

出　　处：《Science China(Physics,Mechanics & Astronomy)》2008年第8期1116-1125,共10页中国科学：物理学、力学、天文学（英文版）

基　　金：the National Natural Science Foundation of China (Grant Nos. 10472102 and 10432030) ;the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20060335107)

摘　　要：This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms,five differential equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form,which still involve four undetermined integral constants,through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence,three-dimen sional analytical solutions for electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness,and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis,and the effect of material inhomogeneity on the elastic and electric fields is discussed.This paper studies the problem of a functionally graded piezoelectric circular plate subjected to a uniform electric potential difference between the upper and lower surfaces. By assuming the generalized displacements in appropriate forms, five differential equations governing the generalized displacement functions are derived from the equilibrium equations. These displacement functions are then obtained in an explicit form, which still involve four undetermined integral constants, through a step-by-step integration which properly incorporates the boundary conditions at the upper and lower surfaces. The boundary conditions at the cylindrical surface are then used to determine the integral constants. Hence, three-dimensional analytical solutions for electrically loaded functionally graded piezoelectric circular plates with free or simply-supported edge are completely determined. These solutions can account for an arbitrary material variation along the thickness, and thus can be readily degenerated into those for a homogenous plate. A numerical example is finally given to show the validity of the analysis, and the effect of material inhomogeneity on the elastic and electric fields is discussed.

关 键 词：functionally graded MATERIAL PIEZOELECTRIC MATERIAL circular plates UNIFORM electric potential direct displacement method 

分 类 号：O441.1[理学—电磁学]