New higher-order shear deformation theory for bending analysis of the two-dimensionally functionally graded nanoplates

Abstract

In this study, we focus on the bending analysis of the 2 D FG nanoplate based on a new high-order shear deformation theory (HSDT). This kind of HSDT is one of the most accurate HSDT because the shape functions are selected as an accurate combination of exponential, trigonometric and polynomial functions. The mechanical properties of the nanoplate vary along the length and thickness, based on arbitrary functions. The small scale effect of the nanostructure is modeled according to the nonlocal theory of elasticity. The governing equations of the problem are obtained from Hamilton’s principle, whereas the Galerkin method is proposed for a closed-form solution of the structural problem for simply-supported nanostructures. The work provides a unified framework for the mechanical analysis of both thin and thick plates. The effect of several parameters, such as the nonlocal parameter, as well as the mechanical and geometrical properties and FG indexes, are investigated on the bending deflection of the 2 D FG nanoplates. The numerical results from our investigation could be considered as valid benchmarks in the literature for possible further analyses of nanoplates.