任意多椭圆孔多裂纹无限大板的应力强度因子与M积分  

THE SIFS AND M-INTEGRAL OF THE INFINITE PLATE WITH MULTIPLE ELLIPTICAL HOLES AND CRACKS

作　　者：郭树祥[1] 许希武[1] 

机构地区：[1]南京航空航天大学航空宇航学院结构强度研究所,南京210016

出　　处：《固体力学学报》2006年第1期6-14,共9页Chinese Journal of Solid Mechanics

基　　金：江苏省自然科学基金(BK99117);教育部跨世纪优秀人才计划;教育部优秀年轻教师基金资助

摘　　要：基于弹性力学中平面问题的复势方法,应用保角映射技术,以Faber级数为工具,导出含任意多椭圆孔及裂纹群无限大板在任意载荷作用下其应力场和位移场的级数解,并在此基础上计算了任意多裂纹板的应力强度因子和M积分,数值结果表明,该方法具有计算精度高、收敛速度快、方便快捷等解析法特有的优点。通过算例分析了不同裂纹倾角时M积分值随载荷方向的变化关系,并讨论了裂纹长度、裂纹间距及裂纹倾角等参数对应力强度因子的影响规律,获得了一些重要结论.Based on the complex potential method in the plane theory of elastic mechanics, the stress and displacement distributions in the infinite plate containing multiple elliptical holes and cracks subjected to arbitrary loads are obtained with the help of the conformal mappings and the Faber series expansion. The stress intensity factors of crack tips and the value of M-Integral are also calculated in this paper using the stress and displacement fields acquired. Some examples about the relation between the values of M and the inclined angle of cracks are dis- cussed and the effects of various graphic parameters on the stress intensity factors are studied in detail. Several conclusions valuable to practices are drawn. Numerical results indicate that high accurate and convergent solutions can be achieved using this method.

关 键 词：裂纹群 应力强度因子 M积分 复势方法 Faber级数 

分 类 号：O346.1[理学—固体力学] U416.01[理学—力学]