A refined nonlocal isogeometric model for multilayer functionally graded graphene platelet-reinforced composite nanoplates

Abstract

This article presents an effective and simple approach based on the four-variable refined plate theory (RPT) and isogeometric analysis (IGA) for bending and free vibration analyses of multilayer functionally graded graphene platelet-reinforced composite (FG GPLRC) nanoplates. The Eringen’s nonlocal elasticity theory is employed to take account of the size-dependent effect of nanoplates. Different distribution patterns of graphene platelets (GPLs) including uniform and non-uniform in the polymer matrix are considered. Governing equations of FG GPLRC nanoplates are then deduced from the principle of virtual work and resolved utilizing NURBS basis functions in the IGA framework. Accordingly, the requirement of third-order derivatives of approximate variables in the nonlocal formulation is fulfilled. Obtained outcomes indicate that the GPLs reinforcement can dramatically improve the stiffness of nanoplates, and GPLs rich at the bottom and the top of the nanoplate can be considered as the best reinforcing effect. Several new results are also considered as benchmark solutions for further studies on the FG GPLRC nanoplates.