Meshfree-based applied mathematical modeling for nonlinear stability analysis of couple stress-based lateral pressurized randomly reinforced microshells

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.