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Shock and Vibration
Volume 2014 (2014), Article ID 104347, 15 pages
http://dx.doi.org/10.1155/2014/104347
Research Article

A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis

The State Key Laboratory for Manufacturing Systems Engineering, School of Mechanical Engineering, Xi’an Jiaotong University, Xi’an 710049, China

Received 12 November 2013; Revised 8 April 2014; Accepted 22 April 2014; Published 8 May 2014

Academic Editor: Reza Jazar

Copyright © 2014 Xingwu Zhang 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

A stochastic finite element method based on B-spline wavelet on the interval (BSWI-SFEM) is presented for static analysis of 1D and 2D structures in this paper. Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. By means of virtual work principle and BSWI, the wavelet finite elements of beam, plate, and plane rigid frame are obtained. Combining the Monte Carlo method and the constructed BSWI elements together, the BSWI-SFEM is formulated. The constructed BSWI-SFEM can deal with the problems of structural response uncertainty caused by the variability of the material properties, static load amplitudes, and so on. Taking the widely used Timoshenko beam, the Mindlin plate, and the plane rigid frame as examples, numerical results have demonstrated that the proposed method can give a higher accuracy and a better constringency than the conventional stochastic finite element methods.