Nonlinear three-dimensional oscillations of probabilistic reinforced nanocomposite shells at microscale via modified strain gradient meshfree formulations

A numerical solution process based on the moving Kriging meshfree is developed in the current exploration to predict microstructural-dependent three-dimensional nonlinear large-deflection oscillation response of probabilistic nanocomposite microsized shells considering deviatoric stretch, rotation, and dilatation gradient tensors. To do so, the modified strain gradient theory of mechanics is applied within the three-dimensional elasticity framework. Probabilistic composite microshells are prepared from nanocomposites reinforced by graphene nanofillers dispersed in different checkerboard schemes. Material properties are determined using a combination of the Monte-Carlo simulation and probabilistic-based micromechanical scheme. Thereafter, correct meshfree polynomial-based functions associated with a considered nodding system are applied to satisfy the essential boundary conditions correctly. It is described that the strengthening character corresponding to deviatoric stretch, rotation and dilatation, gradient tensors is stronger for probabilistic composite microshells containing nanofillers with larger aspect ratios and higher volume fractions. Also, a peak is observed for a certain three-dimensional frequency ratio at a specific ratio of the length to radius of the microshell. Considering microstructural gradient tensors, frequency ratio peak appears at a lower ratio of the length to radius of the microshell.