Three-dimensional elastostatic solutions for transversely isotropic functionally graded material plates containing elastic inclusion  

作　　者：Bo YANG Weiqiu CHEN Hao jiang DING 

机构地区：[1]Department of Civil Engineering, Zhejiang Sci-Tech University [2]Department of Engineering Mechanics, Zhejiang University [3]Department of Civil Engineering, Zhejiang University

出　　处：《Applied Mathematics and Mechanics(English Edition)》2015年第4期417-426,共10页应用数学和力学（英文版）

基　　金：Project supported by the National Natural Science Foundation of China(Nos.11202188,11321202,and 11172263)

摘　　要：Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α（ζ）, β（ζ）, φ（ζ）, and ψ（ζ） when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func- tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional （3D） elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.Based on the generalized England-Spencer plate theory, the equilibrium of a transversely isotropic functionally graded plate containing an elastic inclusion is studied. The general solutions of the governing equations are expressed by four analytic functions α（ζ）, β（ζ）, φ（ζ）, and ψ（ζ） when no transverse forces are acting on the surfaces of the plate. Axisymmetric problems of a functionally graded circular plate and an infinite func- tionally graded plate containing a circular hole subject to loads applied on the cylindrical boundaries of the plate are firstly investigated. On this basis, the three-dimensional （3D） elasticity solutions are then obtained for a functionally graded infinite plate containing an elastic circular inclusion. When the material is degenerated into the homogeneous one, the present elasticity solutions are exactly the same as the ones obtained based on the plane stress elasticity, thus validating the present analysis in a certain sense.

关 键 词：functionally graded plate elastic circular inclusion elasticity solution 

分 类 号：O343[理学—固体力学]