In the present study, the shell-type moving Kriging meshfree model is formulated to analyze the nonlinear stability characteristics of cylindrical microshells reinforced by graphene nanoplatelets in a random checkerboard pattern and subjected to an external lateral pressure. A probabilistic technique together with the Monte-Carlo approach is employed to extract the effective material properties of the nanocomposite. The size-dependent shell model is established via implementation of the modified couple stress continuum elasticity into the higher-order shear deformation shell theory incorporating geometrical nonlinearity. The established microstructural-dependent shell model is then numerically analyzed via the moving Kriging meshfree technique with the ability to take the essential boundary conditions into account accurately by employing proper moving Kriging shape function. It is deduced that the role of this stiffening character related to the microstructural effect of rotation gradient reduces continuously by going to deeper territory of the load–deflection stability path. Furthermore, for a specific graphene nanoplatelet volume fraction, a reduction in the length to width aspect ratio of nanofillers leads to make the role of couple stress size dependency more important in the critical lateral pressure and the associated critical shortening of composite microshells.

在本研究中，建立壳型移动克里金无网格模型来分析由石墨烯纳米片以随机棋盘图案增强并受到外部侧压力的圆柱形微壳的非线性稳定性特性。采用概率技术和蒙特卡罗方法来提取纳米复合材料的有效材料特性。尺寸相关壳模型是通过将修正的耦合应力连续体弹性实施到包含几何非线性的高阶剪切变形壳理论中来建立的。然后通过移动克里金无网格技术对建立的微观结构相关壳模型进行数值分析，该技术能够通过采用适当的移动克里金形状函数准确地考虑基本边界条件。据推断，与旋转梯度的微观结构效应相关的这种加强特性的作用随着载荷-挠度稳定性路径的更深区域而不断降低。此外，对于特定的石墨烯纳米片体积分数，纳米填料长宽比的降低导致耦合应力大小依赖性在临界侧压力和复合微壳的相关临界缩短中的作用更加重要。据推断，与旋转梯度的微观结构效应相关的这种加强特性的作用随着载荷-挠度稳定性路径的更深区域而不断降低。此外，对于特定的石墨烯纳米片体积分数，纳米填料长宽比的降低导致耦合应力大小依赖性在临界侧压力和复合微壳的相关临界缩短中的作用更加重要。据推断，与旋转梯度的微观结构效应相关的这种加强特性的作用随着载荷-挠度稳定性路径的更深区域而不断降低。此外，对于特定的石墨烯纳米片体积分数，纳米填料长宽比的降低导致耦合应力大小依赖性在临界侧压力和复合微壳的相关临界缩短中的作用更加重要。