3D thermoelasticity solutions for functionally graded thick plates  

作　　者：Ji YING Chao-feng LU C. W. LIM 

机构地区：[1]Department of Mechanical Engineering, Zhejiang University, Hangzhou 310027, China [2]Department of Civil Engineering, Zhejiang University, Hangzhou 310058, China [3]Department of Building and Construction, City University of Hong Kong, Hong Kong, China

出　　处：《Journal of Zhejiang University-Science A(Applied Physics & Engineering)》2009年第3期327-336,共10页浙江大学学报（英文版）A辑（应用物理与工程）

基　　金：supported by the National Natural Science Foundation of China (Nos. 10702061, 10725210, and 10832009);Zhejiang Provincial Natural Science Foundation of China (No. Y607116)

摘　　要：Thermal-mechanical behavior of functionally graded thick plates, with one pair of opposite edges simply supported, is investigated based on 3D thermoelasticity. As for the arbitrary boundary conditions, a semi-analytical solution is presented via a hybrid approach combining the state space method and the technique of differential quadrature. The temperature field in the plate is determined according to the steady-state 3D thermal conduction. The Mori-Tanaka method with a power-law volume fraction profile is used to predict the effective material properties including the bulk and shear moduli, while the effective coefficient of thermal expansion and the thermal conductivity are estimated using other micromechanics-based models. To facilitate the im-plementation of state space analysis through the thickness direction, the approximate laminate model is employed to reduce the inhomogeneous plate into a homogeneous laminate that delivers a state equation with constant coefficients. The present solutions are validated by comparisons with the exact ones for both thin and thick plates. Effects of gradient indices, volume fraction of ceramics, and boundary conditions on the thermomechanical behavior of functionally graded plates are discussed.Thermal-mechanical behavior of functionally graded thick plates, with one pair of opposite edges simply supported, is investigated based on 3D thermoelasticity. As for the arbitrary boundary conditions, a semi-analytical solution is presented via a hybrid approach combining the state space method and the technique of differential quadrature. The temperature field in the plate is determined according to the steady-state 3D thermal conduction. The Mori-Tanaka method with a power-law volume fraction profile is used to predict the effective material properties including the bulk and shear moduli, while the effective coefficient of thermal expansion and the thermal conductivity are estimated using other micromechanics-based models. To facilitate the implementation of state space analysis through the thickness direction, the approximate laminate model is employed to reduce the inhomogeneous plate into a homogeneous laminate that delivers a state equation with constant coefficients. The present solutions are validated by comparisons with the exact ones for both thin and thick plates. Effects of gradient indices, volume fraction of ceramics, and boundary conditions on the thermomechanical behavior of functionally graded plates are discussed.

关 键 词：Functionally graded plates Semi-analytical solutions 3D thermoelasticity Mori-Tanaka method 

分 类 号：O34[理学—固体力学]