S型功能梯度扁球壳非线性屈曲的渐近分析

本文利用渐近迭代法获得了边界弹性支撑的功能梯度扁球壳的非线性屈曲问题的理论解．假设材料组分体积分数沿壳体厚度方向呈sigmoid幂函数变化，边界上考虑一般的弹性支撑约束．基于经典的薄壳理论和几何非线性关系，导出了S型功能梯度扁球壳的非线性屈曲问题的控制方程．采用渐近迭代法通过两次迭代得到了无量纲挠度和均布荷载之间的非线性特征关系．通过与已有有限元方法和其他数值方法的结果对比，验证了本文解的有效性和高精度．同时，通过计算阐述了缺陷因子、材料参数、边界约束系数及特征几何参数对壳体临界屈曲荷载的影响．

Asymptotic Buckling Analysis of S-FGM Shallow Spherical Shells

This paper presents an analytical solution for non-linear buckling of shallow spherical shells made of Sigmoid functionally graded material (S-FGM) with imperfections under uniform pressure by using the asymptotic iteration method. Material property is assumed to change in the thickness direction of the shell following a Sigmoid power law in terms of the volume fractions of the material constituents. The governing equations are derived by using the classical thin shell theory and geometrical nonlinear relations. For an elastically constrained shell, a non-linear analytical characteristic relationship between the external load and the central deflection is obtained after two iteration steps. The accuracy of the present model is verified by comparison with the results from finite element method and other available numerical methods . Numerical examples are given to illustarte the influences of geometrical imperfection, edge-restraint coefficients, material constitutive parameters and characteristic geometrical parameter on the critical buckling loads.