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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。
The buckling and post-buckling behavior of functionally graded material (FGM) strut under uniform load is analyzed. Based on the large deformation theory of the rod, taking into account the axial extension of the rod, the geometrical nonlinear equilibrium equation of the elongated FGM rod subjected to uniform load is established, in which the properties of the FGM rod are assumed to vary continuously along the thickness direction according to the power function. Using the shooting method and analytical continuation method to solve the nonlinear two-point boundary value problem, the numerical solution of post-buckling of free-end fixed FGM rod is obtained. The post-buckling characteristic curves of FGM rods under different gradient indexes are given. The corresponding characteristics of two kinds of single-phase metal and ceramic rods are compared. The influence of the material’s gradient parameters on the rod deformation is analyzed and discussed. The results show that the post-buckling behavior of the FGM rod is very different from that of the isotropic homogeneous rod, and the gradient index has a significant effect on the bending load of the rod and the post-buckling morphology.