Adomian Decomposition Method applied to anisotropic thick plates in bending

Abstract

The aim of this report is to apply the Adomian Decomposition Method (ADM) to anisotropic rectangular moderately thick plates under linear bending using a first-order shear deformation theory. Given the plate's homogeneity, the transverse displacement and rotations degrees-of-freedom are globally interpolated by kinematically admissible polynomials functions. The Rayleigh-Ritz Method is employed to solve the equilibrium equations. As proposed by the original Adomian Decomposition Method, the degrees-of-freedom are expanded into an infinite series, but the differential operator is additively decomposed following constitutive hierarchy. The initial solution refers to a lower lower constitutive symmetry in the operator decomposition and is enhanced by non-isotropic ones. The recursive system requirements in order to have convergence are presented and they depend only on the anisotropic index. The results obtained by the methodology are discussed and compared to those found in the literature. Solutions for different boundary conditions types as well as different thickness under uniform loading are presented so as to provide benchmark solutions. Furthermore, analysis of the anticlastic curvature and the effects of the transverse shear at corners with soft simply-supported edges, largely ignored by the literature, are shown and discussed.