Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection

In this paper, post-buckling behavior of geometrically imperfect porous beams reinforced with graphene platelets (GPLs) and resting on nonlinear hardening foundation is investigated. GPLs are uniformly and non-uniformly distributed thorough the thickness direction. Different porosity distributions called uniform, symmetric and asymmetric are considered. The elastic properties of the nanocomposite are obtained by employing Halpin-Tsai micromechanics model. The present refined beam model satisfies the shear deformation effect needless of any shear correction factor. The post-buckling load-deflection relation is obtained by solving the governing equations having cubic nonlinearity applying Galerkin's method needless of any iteration process. New results show the importance of porosity coefficient, porosity distribution, GPL distribution, GPL weight fraction, geometrical imperfection and foundation parameters on nonlinear buckling behavior of porous beams. Specially, porosities and GPL reinforcement have a great impact on post-buckling configuration of both ideal and imperfect nanocomposite beams.