A recursive methodology for the solution of semi-analytical rectangular anisotropic thin plates in linear bending

•Novel application of Adomian Decomposition Method for elasticity problems.•New semi-analytical solutions of anisotropic thin plate in bending.•A new recursive methodology driven by a constitutive decomposition.•A starting isotropic solution progressively enhanced by anisotropic influence.•Plate results for several aspect and anisotropic ratios and boundary conditions. A new recursive methodology is introduced to solve anisotropic thin plates bending problems, which is based on three concepts: (a) the plate differential operator additively decomposed obeying a material constitutive hierarchy; (b) the plate displacement field expanded into an infinite series and (c) an homotopy-like scheme applied to determine each term of the series. The pb-2 Rayleigh–Ritz Method is adopted to construct the solution space. Convergence conditions are presented and related to the differential operator decomposition and material’s anisotropy degree. Different cases of geometry, loading and boundary conditions were studied using the methodology and excellent agreement with available solutions was found.