Nonlinear static and dynamic isogeometric analysis of functionally graded microplates with graphene-based nanofillers reinforcement

Abstract

The main contribution of this study is to propose an efficient and straightforward numerical model for exploring size-dependent geometrically nonlinear static and dynamic characteristics of functionally graded microplates reinforced by graphene nanofillers. To accomplish this purpose, modified couple stress theory including only one material length scale parameter is utilized to capture the size-dependent effect while the displacement field of small-scale structures is calculated by using four-variable refined plate theory and von-Kármán assumptions within the framework of isogeometric analysis. In this study, four dispersion patterns of graphene-based nanofillers along the thickness direction of microplate models are investigated under various static or dynamic loads. Solutions of nonlinear governing equation of motion can be obtained based on the Newton–Raphson iterative procedure and Newmark's time integration scheme. The Rayleigh damping is included, for the first time, to explore the influence of damping on the oscillations of functionally graded microplates reinforced by graphene nanofillers under three dynamic loads including step, triangular and half-sine pulses. Herein, several numerical examples are conducted to investigate the influences of a wide range of significant parameters on the geometrically nonlinear behaviors of functionally graded microplates with graphene nanofillers reinforcement. The significant outcomes of the present study can be referred to as benchmark results as well as provide valuable guides for designing small-scale structures with excellent features in the future.