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三维横观各向同性介质界面裂纹的边界积分方程方法
引用本文:赵明皞,李冬霞,沈亚鹏.三维横观各向同性介质界面裂纹的边界积分方程方法[J].应用数学和力学,2005,26(12):1394-1400.
作者姓名:赵明皞  李冬霞  沈亚鹏
作者单位:1. 郑州大学,工程力学系,郑州,450002
2. 中原工学院,基础部,郑州,450007
3. 西安交通大学,工程力学系,西安,710049
基金项目:河南省高校新世纪优秀人才支持计划资助项目
摘    要:基于两相三维横观各向同性介质的基本解和Somigliana恒等式,对三维横观各向同性介质中的任意形状的平片界面裂纹,以裂纹面上的不连续位移为待求参量建立了超奇异积分_微分方程,界面平行于横观各向同性面.根据发散积分的有限部积分理论,应用积分方程方法研究得到裂纹前沿的位移和应力场的表达式、奇性指数以及应力强度因子的不连续位移表达式.在非震荡情形下,超奇异积分_微分方程退化为超奇异积分方程,与均匀介质的超奇异积分方程形式完全相同.

关 键 词:三维两相介质  横观各向同性  界面裂纹  应力强度因子  积分-微分方程
文章编号:1000-0887(2005)12-1394-07
收稿时间:05 17 2004 12:00AM
修稿时间:08 17 2005 12:00AM

Interfacial Crack Analysis in Three-Dimensional Transversely Isotropic Bi-Materials by Boundary Integral Equation Method
ZHAO Ming-hao,LI Dong-xia,SHEN Ya-peng.Interfacial Crack Analysis in Three-Dimensional Transversely Isotropic Bi-Materials by Boundary Integral Equation Method[J].Applied Mathematics and Mechanics,2005,26(12):1394-1400.
Authors:ZHAO Ming-hao  LI Dong-xia  SHEN Ya-peng
Abstract:The integral-differential equations for three-dimensional planar interfacial cracks of arbitrary shape in transversely isotropic bimaterials were derived by virtue of the Somigliana identity and the fundamental solutions,in which the displacement discontinuities across the crack faces are the unknowns to be determined.The interface is parallel to both the planes of isotropy.The singular behaviors of displacement and stress near the crack border were analyzed and the stress singularity indexes were obtained by integral equation method.The stress intensity factors were expressed in terms of the displacement discontinuities. In the non-oscillatory case,the hyper-singular boundary integral-differential equations were reduced to hyper-singular boundary integral equations similar to those of homogeneously isotropic materials.
Keywords:three-dimensional bi-material  transversely isotropic  interfacial crack  stress intensity factor  integral-differential equation
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