中文摘要：

对受均布载荷作用功能梯度材料（FGM）压杆的屈曲及后屈曲行为进行了分析。基于杆的大变形理论,考虑杆的轴线伸长,建立了受均布载荷作用下细长FGM压杆的几何非线性平衡方程,其中假设FGM杆的性质沿厚度方向按照幂函数连续变化。采用打靶法和解析延拓法数值求解非线性两点边值问题,获得了一端自由一端固定FGM杆的后屈曲数值解。给出了不同梯度指标下FGM杆的后屈曲特征曲线,并与金属和陶瓷两种单相材料杆的相应特性进行了比较,分析和讨论了材料的梯度性质参数对杆变形的影响。结果表明：FGM杆后屈曲行为与各向同性均质杆有很大区别,梯度指数对杆的屈曲载荷以及后屈曲形态有明显的影响。

英文摘要：

The buckling and post-buckling behaviors of a functionally graded material（FGM） column under distributed load were analysed.Based on the large deformation theory and consideration of the axial extension of the column,the quilibrium equations with geometric nonlinearity of an elastic FGM column subjected to distributed load were established.In the analysis,it was assumed that the material properties of the column vary continuously as a power function of the thickness coordinate.By using shooting method and analytical continuation,the nonlinear boundary-value problem was solved numerically and buckling and post-buckling response of FGM column with free-fixed edges were obtained.The post-buckling characteristics curves of FGM column under the different graded index were plotted,which were compared with the those of pure metal and ceramic material columns.The effects of material gradient property on the buckling deformation and critical load of beam were discussed in details.The results show that the post-buckling behavior of the FGM column are different from that of homogenous column,and the gradient index of the material have significant effect on the bucking load and post-buckling behavior of the FGM columns.