中文摘要：

研究具有点间隙约束的两端固定的功能梯度梁在横向非均匀升温下的过屈曲行为．基于轴向可伸长Euler-Bernoulli梁的几何非线性理论，建立横向非均匀升温下功能梯度梁在点间隙约束下的过屈凸大变形控制方程，将问题归结为含有7个基本未知函数的非线性常微分方程边值问题．假设功能梯度梁的材料性质沿厚度方向按照幂函数变化；点间隙约束位于梁的中点上下两侧，且间隙值是在梁的热过屈曲变形范围之内．采用打靶法数值求解所得强非线性两点边值问题，获得横向非均匀升温下两端固定功能梯度梁的热过屈曲响应．着重分析梁的中心挠度达到给定间隙值而受到点约束后的热过屈曲变形和内力的变化特性，给出与中点约束力相关的平衡构形和平衡路径曲线．

英文摘要：

Thermal post-buckling behavior of functionally graded material beams with fixed-fixed ends and a point-space constraint and subjected to transversely non-uniform temperature rise was studied. Based on the geometrically nonlinear theory and linear thermal strain-temperature relation for the axially extensional Euler-Bernoulli beams, the governing equations, with seven basic unknown functions were established for large post-buckling deformation of FGM beams with a point-space constraint and subjected to transversely non-uniformly thermal loads. It was assumed that the material properties of the beam would vary continu- ously as a power function of the thickness coordinate and the point-space constraint would be around the middle point of the beam and the space value would be in the range of thermal post-buckling deformation. By using shooting method to solve numerically the above mentioned strong nonlinear two-point boundary value problem, the thermal post-buckling response of the transversely non-uniformly heated FGM beams was obtained. Especially, changes in the characteristics of the thermal post-buckling deformation and the internal forces of the beam were emphatically analyzed when its middle point deflection reaching the gap value and at the same time the constraint force arising. Curves of equilibrium paths and configurations of the beams correlative to the middle point-space constraint force were presented.