In the present paper, the geometrical nonlinear behaviour of the sandwich shallow spherical shells made of the functionally graded carbon nanotube-reinforced composites is assessed. In order to solve the proposed problem, the equilibrium, compatibility and constitutive equations are extended based on the first-order shear deformation theory. The obtained system of nonlinear differential equations is solved by employing an analytical approach based on the modified interactions method, which results a closed-form relationship between external load and deformation of the shell. Firstly, the obtained closed-form formula is validated by comparing the corresponding results with those obtained by other methods such as finite element method. After the validation procedure, the mentioned closed-form solution is employed to perform a comprehensive parametric study incorporating the mechanical and geometrical properties, such as the effects of CNTs agglomerating, depth and boundary conditions of the shell. The obtained results in the parametric studies show that all of the parameters can affect the buckling load, stability region and intensity of the instability (difference of upper and lower limit loads).

在本文中，评估了由功能梯度碳纳米管增强复合材料制成的夹心浅球壳的几何非线性行为。为了解决所提出的问题，基于一阶剪切变形理论扩展了平衡方程、相容性方程和本构方程。采用基于修正相互作用法的解析方法求解得到的非线性微分方程组，得到外载荷与壳变形之间的闭式关系。首先，通过将相应的结果与其他方法如有限元法得到的结果进行比较，对得到的封闭式公式进行验证。验证程序后，提到的封闭形式的解决方案用于执行综合参数研究，包括力学和几何特性，例如 CNT 聚集的影响、壳的深度和边界条件。参数化研究的结果表明，所有参数都会影响屈曲载荷、稳定区域和失稳强度（上限和下限载荷的差异）。