Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

doi:10.1007/s10483-017-2161-9

Applied Mathematics and Mechanics (English Edition) ›› 2017, Vol. 38 ›› Issue (2): 173-190.doi: https://doi.org/10.1007/s10483-017-2161-9

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Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

Haitao LIU¹, Zhengong ZHOU²

1. School of Mechanical Engineering, Hebei University of Technology, Tianjin 300130, China;
2. Center for Composite Materials and Structures, Harbin Institute of Technology, Harbin 150080, China

Received:2016-01-25 Revised:2016-07-11 Online:2017-02-01 Published:2017-02-01
Contact: Haitao LIU E-mail:liuhaitao-dahai@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Nos.11272105 and 11572101)

Abstract

Abstract:

The dynamic behavior of a rectangular crack in a three-dimensional(3D) orthotropic elastic medium is investigated under a harmonic stress wave based on the non-local theory. The two-dimensional(2D) Fourier transform is applied, and the mixedboundary value problems are converted into three pairs of dual integral equations with the unknown variables being the displacement jumps across the crack surfaces. The effects of the geometric shape of the rectangular crack, the circular frequency of the incident waves, and the lattice parameter of the orthotropic elastic medium on the dynamic stress field near the crack edges are analyzed. The present solution exhibits no stress singularity at the rectangular crack edges, and the dynamic stress field near the rectangular crack edges is finite.

Key words: orthotropic elastic medium, non-local theory, time-harmonic P-wave, rectangular crack

2010 MSC Number:

O343.2

Haitao LIU, Zhengong ZHOU. Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory. Applied Mathematics and Mechanics (English Edition), 2017, 38(2): 173-190.

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Dynamic behavior of rectangular crack in three-dimensional orthotropic elastic medium by means of non-local theory

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