Transient analysis of functionally graded graphene oxide powders-reinforced porous composite beams resting on elastic foundations using the reproducing kernel meshless method

In this paper, we propose a numerical algorithm, combining the reproducing kernel particle collocation (RKPC) meshless method with the implicit Newmark time integration scheme to examine the transient response of porous composite beams (PCB) strengthened with functionally graded (FG) graphene oxide powders (GOP), and resting on elastic foundations (EF). The PCB are subjected to dynamic loads (DL) with different boundary conditions (BC), and rested on EF modeled using the Winkler-Pasternak foundation model. The first-order shear deformation theory (FSDT) is employed to model the studied PCB reinforced with FG-GOP. The Halpin-Tsai homogenization technique and the rule of mixture are used to determine the effective material properties of the PCB taking the porosity into consideration. The obtained equations of motion using the principle of virtual displacement, are rewritten in a matrix-vector strong form and solved using the adopted numerical strategy. The performance and efficiency of the present approach are validated by comparison with numerical results of the finite element method (FEM). Parametric studies are performed to investigate the effect of GOP weight fraction, GOP distribution patterns, boundary conditions, porosity volume fraction, size of GOP, and elastic foundation stiffness on the transient behavior of FG-GOP reinforced PCB.