Nonlocal nonlinear analysis of functionally graded plates using third-order shear deformation theory

Abstract

In this work, nonlocal nonlinear analysis of functionally graded plates subjected to static loads is studied. The nonlocal nonlinear formulation is developed based on the third-order shear deformation theory (TSDT) of Reddy (1984, 2004). The von Kármán nonlinear strains are used and the governing equations of the TSDT are derived accounting for Eringen’s nonlocal stress-gradient model (Eringen, 1998). The nonlinear displacement finite element model of the resulting governing equations is 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 the 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 stress results are compared with the first-order shear deformation theory (FSDT) to show the accuracy of nonlocal nonlinear TSDT formulation.