Mathematical Problems in Engineering
Volume 2012 (2012), Article ID 750605, 14 pages
http://dx.doi.org/10.1155/2012/750605
Research Article

A Pseudospectral Approach for Kirchhoff Plate Bending Problems with Uncertainties

Ling Guo1,2 and Jianguo Huang2,3

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
3Division of Computational Science, E-Institute of Shanghai Universities and Scientific Computing, Key Laboratory of Shanghai Universities, Shanghai Normal University, China

Received 4 January 2012; Accepted 19 March 2012

Academic Editor: Gradimir V. Milovanović

Copyright © 2012 Ling Guo and Jianguo Huang. 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

This paper proposes a pseudospectral approach for the Kirchhoff plate bending problem with uncertainties. The Karhunen-Loève expansion is used to transform the original problem to a stochastic fourth-order PDE depending only on a finite number of random variables. For the latter problem, its exact solution is approximated by a gPC expansion, with the coefficients obtained by the sparse grid method. The main novelty of the method is that it can be carried out in parallel directly while keeping the high accuracy and fast convergence of the gPC expansion. Several numerical results are performed to show the accuracy and performance of the method.