Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 604368, 15 pages
http://dx.doi.org/10.1155/2014/604368
Research Article

Application of Galerkin Method to Kirchhoff Plates Stochastic Bending Problem

1NuMAT/PPGEM, Federal University of Technology of Parana, Avenue Seven of September, 3165 Curitiba, PR, Brazil
2PPGMNE/CESEC, Federal University of Parana, Polytechnic Center, Garden of the Americas, P.O. Box 19011, 81531-980 Curitiba, PR, Brazil

Received 9 December 2013; Accepted 16 April 2014; Published 15 May 2014

Academic Editors: A. Bairi, T. Y. Kam, and W. L. Li

Copyright © 2014 Cláudio Roberto Ávila da Silva Júnior et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper, the Galerkin method is used to obtain approximate solutions for Kirchhoff plates stochastic bending problem with uncertainty over plates flexural rigidity coefficient. The uncertainty in the rigidity coefficient is represented by means of parameterized stochastic processes. A theorem of Lax-Milgram type, about existence and uniqueness of the theoretical solutions, is presented and used in selection of the approximate solution space. The Wiener-Askey scheme of generalized polynomials chaos (gPC) is used to model the stochastic behavior of the displacement solutions. The performance of the approximate Galerkin solution scheme developed herein is evaluated by comparing first and second order moments of the approximate solution with the same moments evaluated from Monte Carlo simulation. Rapid convergence of approximate Galerkin's solution to the first and second order moments is observed, for the problems studied herein. Results also show that using the developed Galerkin's scheme one gets adequate estimates for accrued probability function to a random variable generated by the stochastic process of displacement.