Microstructural Size Dependency in Nonlinear Lateral Stability of Random Reinforced Microshells via Meshfree-Based Applied Mathematical Modeling

The prime objective of this research work is to develop an efficient small scale-dependent computational framework incorporating microstructural tensors of dilatation gradient, rotation gradient, and deviatoric stretch gradient to analyze nonlinear lateral stability of cylindrical microshells. The numerical strategy is established based upon a mixed formation of the third-order shear deformable shell model and modified strain gradient continuum mechanics. The graphene nanoplatelet reinforcements are assumed to be randomly dispersed in a checkerboard scheme within the resin matrix. Accordingly, to extract the effective material properties, the Monte Carlo simulation together with a probabilistic technique are employed. The numerical solution for the microstructural-dependent nonlinear problem is carried out via the moving Kriging meshfree method having the capability to accommodate accurately the essential boundary conditions using proper moving Kriging shape function. It is represented that the role of the stiffening characters related to the effect of microstructural dilatation gradient, rotation gradient, and deviatoric stretch reduces continuously by going to deeper territory of the load-deflection stability path. Moreover, it is indicated that among various microstructural gradient tensors, the stiffening character of the rotation gradient is higher than deviatoric stretch gradient, and the stiffening character of the latter is more considerable than the dilatation gradient tensor.

Automated summary

The research aims to develop an efficient computational framework for analyzing the nonlinear stability of cylindrical microshells by incorporating microstructural tensors and using a mixed formation of deformable shell model and strain gradient continuum mechanics, with graphene nanoplatelet reinforcements randomly dispersed in a checkerboard scheme. Numerical solutions show a decrease in stiffening characters related to microstructural gradients as load-deflection stability path progresses, with the rotation gradient having higher stiffening character than deviatoric stretch gradient, and the latter having a more considerable stiffening character than the dilatation gradient tensor.