摘要
建立了边界元法计算各向同性结合材料中与界面垂直相交V形切口奇异应力场的分析方法。首先将V形切口尖端附近区域的位移场和应力场用Williams渐近展开式表达,将其代入弹性力学基本方程中,由插值矩阵法获得应力奇异性指数及其对应的位移函数;然后在V形切口尖端区域挖取一个小扇形域,将该扇形区域的位移场表示为有限项奇性指数和特征角函数的线性组合,并对挖去小扇形域后的剩余结构建立边界积分方程;最后将扇形区域位移场表达式和边界积分方程联合求出其切口尖端位移场的组合系数,从而获得各向同性结合材料中与界面垂直相交V形切口尖端的应力强度因子。本文的计算结果与现有结果对比吻合良好,表明了本文方法的有效性。
In this paper, a new way to determine the singularity stress field near a V-notch perpendicular to an interface with two bounded dissimilar isotropic materials is proposed based on the boundary element method. Firstly, the displacement and stress fields of the characteristic radius region near a notch tip are expressed by the Williams asymptotic expansions. After the series expansion is substituted into the governing equation in elasticity, the stress singularity order and the corresponding angle function can be obtained by the interpolating matrix method. Secondly, a small sector region around the V-notch tip is dug out from the V-notch structures. The displacements and stresses in the sector region are expressed as the linear combinations of finite terms of the series expansion with several singularity orders. Then the expressions of displacements and stresses are combined with the boundary integral equations which are established in the V-notch structures without the sector region. The combination coefficients in the asymptotic displacement field can be obtained by solving the discretized boundary integral equations. The validity of the present method is confirmed by comparing with the existed results in the numerical examinations.
出处
《应用力学学报》
CAS
CSCD
北大核心
2016年第1期19-24,177,共6页
Chinese Journal of Applied Mechanics
基金
国家自然科学基金(11272111
11372094)
安徽省教育厅重点项目和提升计划一般项目(TSKJ2014B16)
关键词
V形切口
应力强度因子
边界元法
渐近展开
各向同性材料
V-notch
stress intensity factors
boundary element method
asymptotic expansion
isotropic materials
