Non-linear mathematical model of viscoelastic thin plates with its applications

In this paper, the nonlinear mathematical model of viscoelastic thin prates , by the Karman's hypotheses of a large deflection plate and the Boltzmann' s law of anisotropic viscoelastic materials, is established by means of the Laplace transformation and its inverse as well as so-called structural fun ctions introduced in this paper. In the case of isotropic viscoelastic mate rials with Poisson's ratio nu = const, the quasi-static problems of a simpl y-supported rectangular plate are investigated by using the Galerkin method for the spatial domain and two finite difference schemes for the temporal domain. It could be seen that the numerical method in this paper is Very si mple and has some advantages, such as, smaller storage and quicker computat ional speed. (C) 1998 Elsevier Science S.A. All rights reserved.