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Mathematical Problems in Engineering
Volume 2016, Article ID 2549213, 11 pages
http://dx.doi.org/10.1155/2016/2549213
Research Article

A Numerical Method Based on Daubechies Wavelet Basis and B-Spline Patches for Elasticity Problems

China Special Equipment Inspection and Research Institute, Beijing 100029, China

Received 11 May 2016; Revised 6 July 2016; Accepted 25 July 2016

Academic Editor: Lihua Wang

Copyright © 2016 Yanan Liu and Keqin Din. 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

The Daubechies (DB) wavelets are used for solving 2D plane elasticity problems. In order to improve the accuracy and stability in computation, the DB wavelet scaling functions in comprising boundary scaling functions are chosen as basis functions for approximation. The B-spline patches used in isogeometry analysis method are constructed to describe the problem domain. Through the isoparametric analysis approach, the function approximation and relevant computation based on DB wavelet functions are implemented on B-spline patches. This work makes an attempt to break the limitation that problems only can be discretized on uniform grids in the traditional wavelet numerical method. Numerical examples of 2D elasticity problems illustrate that this kind of analysis method is effective and stable.