A decomposition method for nonlinear bending of anisotropic thin plates

Abstract

A modified version of the Adomian decomposition method is applied to solve the differential equations of nonlinear bending of rectangular anisotropic thin plates. The von Kármám hypotheses are considered in the plate's kinematics. The nonlinear differential equations are decomposed into linear and nonlinear parts and the solution is expanded into series. Essentially, the approach is to embed the nonlinear effects into the anisotropic linear solution. Such incorporations are performed in a recursive fashion along with the Adomian's polynomials, which are responsible for the approximation of the nonlinear effects. In spite of the problem being three-dimensional, no partial solutions are required due to a modification of the standard method, which considers the inversion of the entire linear operator. As a result, the obtained solution respects the boundary conditions set and is independent of its symmetries. The pb-2 Rayleigh-Ritz method is used to obtain the plate's equilibrium path. A multistep procedure is proposed in order to increase the decomposition method convergence radius aiming at global convergence. Numeric results are obtained and compared to those found in the literature.