Probabilistic-based nonlinear stability analysis of randomly reinforced microshells under combined axial-lateral load using meshfree strain gradient formulations

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In the present exploration, an effective numerical strategy is developed to examine for the first time different microstructural-dependent features in the nonlinear stability behavior of nanocomposite microshells containing randomly dispersed nanofillers under combinations of axial and lateral compressive loads. Correspondingly, the modified strain gradient theory of elasticity incorporating dilatation, deviatoric stretch, and rotation gradient tensors is applied to the third-order shear flexible shell framework to accommodate the size dependency. The efficacious material properties are captured via Tsai homogenization approach together with a Monte-Carlo simulation based upon a probabilistic-based homogenization scheme. By employing the constructed moving Kriging meshfree-based numerical strategy, the essential boundary conditions are directly enforced at nodes and the Kronecker delta is satisfied comprehensively using correct type of moving Kriging shape function. For the combined loading condition having domination of axial compression, it is seen that by taking a lateral compressive load into account, the region of snap-through experience becomes wider and the associated minimum load switches to a more induced deflection, while a smaller shortening. Furthermore, for particular values of volume fraction and specific area of graphene nanofillers, combining of axial or lateral compressive load causes that the roles of microscale-dependent gradient tensors in the value of critical stability loads of combined compressed microsized shells becomes a bit less.