中文摘要：

基于非线性经典梁理论和物理中面的概念,推导面内热载荷作用下功能梯度梁过屈曲问题的基本方程.将两个非线性方程化简为一个关于横向挠度的四阶非线性积分-微分方程.该方程与相应的边界条件构成微分特征值问题.直接求解该问题,得到功能梯度梁热过屈曲构形的闭合形式精确解,这个解是外加热载荷的函数.精确解显式地描述梁过屈曲后的非线性平衡路径,通过它可以更深刻地理解功能梯度梁的非线性变形现象.为了考察材料梯度和面内载荷的影响,给出一些数值算例,讨论梁在面内热载荷作用下的过屈曲行为.数值结果显示,面内热载荷作用下,材料性质介于陶瓷和金属之间的功能梯度梁,其挠度也在陶瓷和金属梁挠度之间.

英文摘要：

The basic equations of functionally graded material（FGM）beams subjected to uniform in-plane thermal loads are derived based on the theory of nonlinear classical beam and the concept of physical neutral surface.The two equations are simplified to a single nonlinear fourth-order integral-differential equation to beam＇s transverse deformations.The equation with its corresponding boundary conditions leads to a differential eigenvalue problem.Solving this nonlinear equation directly,a closed-form solution for thermal post-buckling deformation is obtained as a function of the applied thermal load.This exact solution will explicitly describe the nonlinear equilibrium paths of the buckled beam and thus is able to provide an insight into the deformation problem.To show the influence of in-plane loading and material gradients several,numerical examples are given based on the exact solutions,and the post-buckling responses of the beams are discussed.It will be shown by the numerical results obtained herein that under an in-plane thermal load,the deflection of any FGM beams with material property between that of ceramic and metal is an intermediate value between the deflection of the ceramic and metallic beams.