带双裂纹的椭圆孔口的反平面剪切问题的解析解  

Analytic solutions of the anti-plane problems about an elliptic hole with two straight cracks

作　　者：赵志云[1] 郭怀民[1] 

机构地区：[1]包头师范学院数学科学学院,包头010043

出　　处：《黑龙江大学自然科学学报》2010年第6期836-840,共5页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金资助项目(10761005);包头师范学院科学基金资助项目(BSY200912017)

摘　　要：断裂现象始终是同材料与结构中的孔洞、缺口或裂纹相关联的,在材料的这种宏观不连续部分最明显的特点是应力分部极不均匀,从而导致应力集中。缺陷(孔洞、裂纹、位错等)和应力集中往往是造成结构破损的重要原因。利用复变函数方法,通过构造保角映射,研究了带双裂纹的椭圆孔口的反平面剪切问题,给出了Ⅲ型裂纹问题的应力强度因子,在极限情形下,不仅可以还原为已有的结果,而且求得带双裂纹的圆形孔口问题、十字纹问题在裂纹尖端处的Ⅲ型应力强度因子。The fracture phenomenon is always in relation to the holes,indentations or cracks in the material.The most obvious feature is that the stress distribution is not even in the material.This phenomenon is called stress concentration.The defects（holes,cracks,dislocation,etc.） and stress concentration are always the principal reasons which contribute to configuration damage.By means of the complex variable function method and using the technique of conformal mapping,the anti-plane shear problem about an elliptic hole with two straight cracks was investigated and the solution of the stress intensity factor（SIFs）of mode Ⅲ was found out.Under the condition of limitation,not only the known result can be obtained but also the solutions of the mode Ⅲ SIFs at the crack tip to a circular hole with two straight cracks and cross cracks are found out.

关 键 词：保角变换 带双裂纹的椭圆孔口 反平面剪切 十字裂纹 应力强度因子 

分 类 号：O346.1[理学—固体力学]