Size-dependent finite element buckling analysis of porous cylindrical micro-shells reinforced by graphene platelets

This study introduces a spatial shear deformable rectangular element formulation to investigate the size-dependent buckling behavior of porous graphene platelets (GPL) reinforced micro-shells within the framework of the modified couple stress theory (MCST) for the first time in the worldwide term. The rectangular element, characterized by 4 nodes with 19 degrees of freedom each and possessing weak continuity of order C1, incorporates a length scale parameter enabling size-dependent analyses of shells. The research considers three distinct functions for the distribution of porosity combined with three different patterns of the GPL distribution (called by patterns A to C) along the micro-shell thickness. The elastic modulus of the nanocomposite in the absence of porosity is obtained using the Halpin-Tsai micromechanics model. Subsequently, the study meticulously validates the modeling accuracy and then investigates variations in the critical buckling load with respect to porosity distribution functions, distribution patterns of GPL, porosity coefficient, weight percentage of GPL, geometric parameters of the cylinder, and the length-scale parameter. The results reveal that the combination of the GPL pattern A with the first symmetric type porosity distribution yields the highest critical buckling loads. On the contrary, if the pattern B is combined with the second symmetric type of porosity distribution, the lowest critical buckling load will be observed. Given the accuracy of the results obtained and the versatility of the finite element method (FEM) in handling complex geometries together with diverse boundary conditions, the developed element holds promise for analyzing shells of various shapes under different boundary conditions.