半无限横观各向同性介质中三维裂纹问题数值分析  

A Rectangular Crack in Transversely Isotropic Half Space Subjected to Normal or Tangential Tractions

作　　者：王炳军[1] 肖洪天[1] 孙凌志[1] 岳中琦[2] 

机构地区：[1]山东科技大学土木建筑学院,山东青岛266590 [2]香港大学土木工程系

出　　处：《山东科技大学学报（自然科学版）》2012年第6期20-29,共10页Journal of Shandong University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(51079081)

摘　　要：采用对偶边界元方法分析了沿裂纹面分别作用法向和切向均布力时半无限横观各向同性介质中的三维矩形裂纹。裂纹面及半无限域自由面平行于材料各向同性面。该方法基于双层横观各向同性材料基本解,以裂纹面间断位移为未知量建立了面力超奇异边界积分方程。根据求得的间断位移计算了该类裂纹的应力强度因子。最后讨论了自由面、矩形裂纹边长比、材料弹性系数对应力强度因子的影响。结果表明,自由面对作用法向均布力的该类矩形裂纹应力强度因子有明显影响,对作用切向均布力的该类矩形裂纹应力强度因子影响较小,且自由面的这种影响主要与裂纹面到自由面的距离有关,与矩形裂纹边长比基本无关。A rectangular crack was analyzed in a transversely isotropic half space by using the boundary element method. The crack face and the free surface of a transversely isotropic half space are parallel to the isotropic plane of a transversely isotropic material. The crack face is subjected to normal and tangential uniformly distributed loads respectively. The stress intensity factor （SIF） values associated with the rectangular crack are calculated from the crack opening displacements. According to the numerical results, the effects of the free surface of the half space, side ratios （a/b） of the rectangular crack,the elastic coefficients of the transversely isotropic material on the SIF values are considered. The results show that the free surface has substantial effects on the SIF values of the rectangular crack subjected to normal loads and has relatively little impact on the SIF values when the tangential loads act on the rectangular crack surface. Furthermore, the influence of the free surface on the SIF values mainly depends on the distance from the crack surface to the free surface, but it is almost independent of the side ratios （a/b） of the rectangu-lar crack.

关 键 词：矩形裂纹 应力强度因子 对偶边界元法 横观各向同性材料 半无限域 

分 类 号：O346.1[理学—固体力学]