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Mathematical Problems in Engineering
Volume 2014, Article ID 979216, 9 pages
Research Article

The Incremental Hybrid Natural Element Method for Elastoplasticity Problems

1Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
2Department of Mechanics, Shanghai University, Shanghai 200444, China

Received 6 November 2013; Revised 4 February 2014; Accepted 6 February 2014; Published 30 March 2014

Academic Editor: Wenqing Wang

Copyright © 2014 Yongqi Ma 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.


An incremental hybrid natural element method (HNEM) is proposed to solve the two-dimensional elasto-plastic problems in the paper. The corresponding formulae of this method are obtained by consolidating the hybrid stress element and the incremental Hellinger-Reissner variational principle into the NEM. Using this method, the stress and displacement variables at each node can be directly obtained after the stress and displacement interpolation functions are properly constructed. The numerical examples are given to show the advantages of the proposed algorithm of the HNEM, and the solutions for the elasto-plastic problems are better than those of the NEM. In addition, the performance of the proposed algorithm is better than the recover stress method using moving least square interpolation.