Nonlinear bending of porous curved beams reinforced by functionally graded nanocomposite graphene platelets applying an efficient shear flexible finite element approach

In the present study, the nonlinear flexural bending of thick and thin porous curved composite beams reinforced and functionally graded by graphene platelets is carried out using a three-noded C1 continuous curved beam finite element developed introducing an efficient shear deformation theory based on trigonometric function. The nonlinearity through the strain–displacement relationship by introducing von Karman’s assumptions is considered. The nonlinear equilibrium equations resulting from minimum potential energy principle are numerically solved based on the direct iteration technique. The bending nonlinear features through the load–deflection relationship are presented by selecting various design parameters like long and short beams, shallow and deep curved cases, support conditions, the variation of graphene platelets in the metal foam and the existence of porosity. This investigation reveals that the level of nonlinearity gets noticeably affected by the depth coupled with the curved beam slenderness ratio. •Presented the load–deflection relationship for the curved beam having GPL reinforcement.•Shown the influence of dispersion patterns of GPLs/pores on the nonlinear bending behaviour.•Predicted the degree of nonlinear hardening characteristics of different types of curved beam.•Evaluated the boundary conditions and geometry of GPL effects on the beam nonlinearity.•Provided a parametric study for benchmarking the results evaluated by other approaches.