横观各向同性功能梯度板的热弹性Navier解

Thermoplastic Navier Solutions of Transversely Isotropic Functionally Graded Rectangular Plates

本文利用推广后的Main和Spencer功能梯度板理论,研究了横观各向同性功能梯度简支矩形板在温度场作用下的热弹性响应。材料常数沿板厚可以任意连续变化,温度场为在板厚度方向上热传导产生的稳态温度场。将板的中面位移用双重三角级数展开并代入控制方程,利用板的柱面边界条件确定含有的待定常数。最终获得了横观各向同性功能梯度板在温度场作用下的热弹性Navier解。通过数值算例分析,讨论了板的几何尺寸变化、材料的梯度变化程度和不同表面温度等因素对功能梯度板热弹性响应的影响.

In this paper,thermoplastic problem of rectangular plates with transverse isotropic and functionally graded materials under temperature fields is studied by using the generalized Main and Spencer plate theory.The material can vary along the thickness direction of the plate in an arbitrary and continuous manner.Steady temperature field caused by heat conduction is considered in the thickness direction of the plate.The mid-plane displacements of the plate are expanded by double triangular series and involved undetermined constants are determined by using cylindrical boundary conditions of the plates.Finally,thermoplastic Navier solutions of functionally graded plates under temperature fields are obtained.Through numerical examples,the influences of the geometric size of the plate,the degree of gradient variation and different temperatures on the thermo-elastic response of functionally graded rectangular plates are also discussed.