On linear and nonlinear bending of functionally graded graphene nanoplatelet reinforced composite beams using Gram-Schmidt-Ritz method

Abstract

The current study examined the linear and nonlinear bending results of functionally graded graphene nanoplatelet reinforced composite beams. The equation system was constructed using Reddy's third order shear deformation theory and a von Kármán type nonlinear strain-displacement relationship. The nonlinear bending results of this system were solved using the Gram-Schmidt-Ritz method in conjunction with the direct iteration technique. By employing the Gram-Schmidt orthogonalization procedure for generating shape functions in the method, numerically stable functions for nonlinear bending analysis of beams were obtained. Our solutions were validated for accuracy by comparing them to some published results. The numerical results indicate that the geometrical nonlinearity of beams subjected to uniform distributed load is greater than that of beams subjected to sinusoidal, linear, or parabolic distributed loads. New results on several significant effects of reinforcement patterns, graphene nanoplatelet weight fraction, and different types of distributed loads are presented and discussed in this study, in which the findings can serve as a benchmark for future research.