Modified decomposition method applied to laminated thick plates in nonlinear bending

Abstract

The paper aims at the application of a modified version of the Adomian Decomposition Method (ADM) to nonlinear bending of laminated thick plates. The Mindlin plate theory along with the equivalent single layer concept is used in this study. The nonlinearity is taken into account through the von Kármán equations. The governing equations of the problem are decomposed into linear and nonlinear terms while the solution is expanded in series, as a requirement for constructing the ADM recursive system. The first approximation (first term of the series) corresponds to the linear response of the problem. The subsequent ones are incorporations of the problem’s nonlinearity, obtained with the aid of the Adomian’s polynomials: generalised Taylor series around the linear solution particularly tailored for the specific nonlinearity. pb-2 Rayleigh-Ritz method is employed to determine the problem’s stationary point. An incremental procedure is also introduced in order to increase the convergence radius. Numerical results are shown and compared with those found in the literature. Good agreement was found in all evaluated cases.