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

In this paper, the nonlinear mathematical model of viscoelastic thin plates, by the Karmanʹs hypotheses of a large deflection plate and the Boltzmannʹs law of anisotropic viscoelastic materials, is established by means of the Laplace transformation and its inverse as well as so-called structural functions introduced in this paper. In the case of isotropic viscoelastic materials with Poissonʹs ratio v = const, the quasi-static problems of a simply-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 simple and has some advantages, such as, smaller storage and quicker computational speed.