Analytical solutions for plane problem of functionally graded magnetoelectric cantilever beam  

作　　者：Yanmei YUE Xiaofen YE Kaiyu XU 

机构地区：[1]Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Key Laboratory of Mechanics in Energy Engineering,Department of Mechanics,Shanghai University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第7期955-970,共16页应用数学和力学（英文版）

基　　金：supported by the National Natural Science Foundation of China(Nos.10772106 and11072138);the Shanghai Leading Academic Discipline Project(No.S30106);the Research Fund for the Doctoral Program of Higher Education of China(No.20113108110005);the Natural Science Foundation Project of Shanghai(No.15ZR1416100)

摘　　要：In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic （FGMEE） cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.In this paper, an exact analytical solution is presented for a transversely isotropic functionally graded magnetomelectro-elastic （FGMEE） cantilever beam, which is subjected to a uniform load on its upper surface, as well as the concentrated force and moment at the free end. This solution can be applied for any form of gradient distribution. For the basic equations of plane problem, all the partial differential equations governing the stress field, electric, and magnetic potentials are derived. Then, the expressions of Airy stress, electric, and magnetic potential functions are assumed as quadratic polynomials of the longitudinal coordinate. Based on all the boundary conditions, the exact expressions of the three functions can be determined. As numerical examples, the material parameters are set as exponential and linear distributions in the thickness direction. The effects of the material parameters on the mechanical, electric, and magnetic fields of the cantilever beam are analyzed in detail.

关 键 词：functionally graded material （FGM） analytical solution magnetoelectrie（ME） material cantilever beam plane stress problem 

分 类 号：O344.1[理学—固体力学]