Nonlinear analysis of laminated FG-GPLRC beams resting on an elastic foundation based on the two-phase stress-driven nonlocal model

Abstract

In this paper, a nonlinear formulation for beam-type structures is presented within the framework of two-phase stress-driven (SD) nonlocal theory. Various boundary conditions are considered for the beams, and it is assumed that they are on the Winkler- and Pasternak-type elastic foundations. It is considered that the beams are made of laminated functionally graded-graphene platelet-reinforced composite (FG-GPLRC) whose properties are estimated by means of the Halpin–Tsai model. The Euler–Bernoulli beam theory is also used for the modeling. The governing equations are derived based on the integral form of SD nonlocal theory using a variational approach considering geometrical nonlinearity. The equations of the SD model in differential form in conjunction with associated constitutive boundary conditions are also obtained. Moreover, a numerical approach based upon the generalized differential quadrature (GDQ) method is developed for the solution of the nonlinear bending problem. The influences of volume fraction/distribution pattern of GPLs, nonlocality, elastic foundation, and geometrical parameters on the bending response of beams under different end conditions are investigated. Furthermore, comparisons are given between the linear and nonlinear results.