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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 831419, 4 pages
http://dx.doi.org/10.1155/2015/831419
Research Article

Antiplane Problem of Periodically Stacked Parallel Cracks in an Infinite Orthotropic Plate

School of Mechanical & Electronic Engineering, Zhongyuan University of Technology, Zhengzhou 450007, China

Received 14 May 2014; Accepted 16 July 2014

Academic Editor: Oluwole Daniel Makinde

Copyright © 2015 Long Wu and Pengcheng Du. 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 antiplane problem of the periodic parallel cracks in an infinite linear elastic orthotropic composite plate is studied in this paper. The antiplane problem is turned into the boundary value problem of partial differential equation. By constructing proper Westergaard stress function and using the periodicity of the hyperbolic function, the antiplane problem of the periodic parallel cracks degenerates into an algebra problem. Using the complex variable function method and the undetermined coefficients method, as well as with the help of boundary conditions, the boundary value problem of partial differential equation can be solved, and the analytic expressions for stress intensity factor, stress, and displacement near the periodical parallel cracks tip are obtained. When the cracks spacing tends to infinity, the antiplane problem of the periodic parallel cracks degenerates into the case of the antiplane problem of a single central crack.