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Mathematical Problems in Engineering
Volume 2017, Article ID 1863714, 9 pages
https://doi.org/10.1155/2017/1863714
Research Article

A New and Efficient Boundary Element-Free Method for 2-D Crack Problems

1School of Water Conservancy and Environment, Zhengzhou University, Zhengzhou 450001, China
2School of Civil Engineering and Architecture, Zhongyuan University of Technology, Zhengzhou 450007, China

Correspondence should be addressed to Jinchao Yue; nc.ude.uzz@cjeuy and Yuzhou Sun; moc.621@nusuohzuy

Received 4 September 2016; Revised 14 December 2016; Accepted 24 January 2017; Published 21 February 2017

Academic Editor: Elisa Francomano

Copyright © 2017 Jinchao Yue 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

An efficient boundary element-free method is established for 2-D crack problems by combining a pair of boundary integral equations and the moving-least square approximation. The displacement boundary integral equation is collated on the on-crack boundary, and a new traction boundary integral equation is applied on the crack surface without the separate consideration of the upper and lower sides. In virtue of integration by parts, only singularity in order is involved in the integral kernels of new traction boundary integral equation, which brings convenience to the numerical implementation. Meanwhile, the integration by parts produces the new variables, the displacement density, and displacement dislocation density, and they are the coexisting unknowns along with the displacement and displacement dislocation. With the high-order continuity of the moving-least square approximation, these new variables are directly approximated with the nodal displacement or displacement dislocation, and the final system of equations contains the unknowns of nodal displacements and displacement dislocations only. The boundary element-free computational scheme is established, and several examples show the efficiency and flexibility of the proposed method.