Nonlocal nonlinear analysis of functionally graded plates using natural neighbour Galerkin method

Abstract

In the present work, flexural response of functionally graded plates subjected to transverse loads have been investigated using the meshless natural neighbor Galerkin method (NNGM). The plate formulation has been developed based on the Reddy’s (Mechanics of laminated composite plates and shells: theory and analysis, 2nd edition, CRC Press, Boca Raton, 2014) third-order shear deformation theory (TSDT) using the von Karman nonlinear strains. The governing equations of the TSDT have been derived accounting for the length scale/size effects considering the Eringen’s nonlocal stress-gradient model (Eringen in Microcontinuum filed theories—I: foundations and solids, Springer-Verlag, 1998). The C1 continuous shape functions have been computed using the sibson’s interpolant and generalizing a Bezier patch over the domain. The nonlocal nonlinear model of the resulting governing equations has been developed, and Newton’s iterative procedure is used for the solution of nonlinear algebraic equations. The mechanical properties of functionally graded plate are assumed to vary continuously through the thickness and obey a power-law distribution of the volume fraction of the constituents. The variation of volume fractions through the thickness have been computed using two different homogenization techniques, namely, the rule of mixtures and the Mori–Tanaka scheme. A detailed parametric study to show the effect of side-to-thickness ratio, power-law index, and nonlocal parameter on the load-deflection characteristics of plates have been presented. The central deflections obtained using (NNGM) have been compared with the results from literature based on finite element method. The results have been compared with the two homogenization schemes and also with results computed with the first-order shear deformation theory (FSDT) to show the accuracy of nonlocal nonlinear formulation based on TSDT.