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Mathematical Problems in Engineering
Volume 2018, Article ID 4079035, 18 pages
https://doi.org/10.1155/2018/4079035
Research Article

Discontinuous Deformation Analysis Based on Wachspress Interpolation Function for Detailed Stress Distribution

1Hubei Key Laboratory of Disaster Prevention and Mitigation, China Three Gorges University, Yichang, Hubei 443002, China
2State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan 430071, China

Correspondence should be addressed to W. Jiang; moc.361@noiliewgnaij

Received 5 April 2018; Accepted 1 June 2018; Published 26 June 2018

Academic Editor: Petr Krysl

Copyright © 2018 W. Jiang 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 the original discontinuous deformation analysis (DDA) method, the complete first-order displacement function is used to describe block movement and deformation, which induce constant stress and strain throughout the block. To achieve a more detailed stress distribution, Wachspress interpolation displacement function is employed to express the displacement of blocks in DDA, and the interactions between blocks are still governed under the original DDA. Displacements of the vertexes of all blocks constitute new freedom vectors, and the stiffness and force matrix formulations are derived again. In the new formulation, Wachspress interpolation ensures that the edges of the blocks are straight; therefore, contact detection can be processed based on the original DDA. Several classical examples are analyzed. The results show that the new formulation obtains similar configurations as the original DDA but provides more detailed and continuous stress distributions within block element.