Nonlinear behaviour and stability of functionally graded porous arches with graphene platelets reinforcements

This research presents an analytical approach for nonlinear static responses and stability analysis of functionally graded porous (FGP) arches with graphene platelets (GPLs) reinforcements (i.e., FGP-GPLRC arches). The constitutive material composition of the FGP-GPLRC arch varies along the radial direction of the cross section specifically, so that the mechanical performance of the arch such as buckling strength and weight can be well controlled for various engineering design purposes. The effective Young's modulus of the FGP-GPLRC arch is determined by the volume fraction distribution of materials. Based on the Euler-Bernoulli hypothesis, the structural responses of the arch considering the geometric nonlinearity are derived by using the virtual work method. Two boundary conditions are considered which are including the pinned-pinned and the fixed-fixed supports. The loading condition is defined as uniformly distributed load in the radial direction of the arch. Different buckling modes are discussed by the illustration of the equilibrium paths. By adopting the developed analytical solution, the relationship between the structural response, buckling load, self-weight, porosity level and the percentage of content of the GPLs can be investigated efficiently. The applicability and effectiveness of the proposed analytical approach for the geometric nonlinear analysis of FGP-GPLRC arch structures are demonstrated through numerical examples. (C) 2018 Elsevier Ltd. All rights reserved.