摘要
对构成裂纹尖端附近有限应力集中解析函数的方法进行了综述.含裂纹平面问题的应力函数可以用无理函数和指数函数两种型式表示.对单材料裂纹,将裂纹长度作为参数,对无理函数型解析函数采用直接加权积分可以消除裂纹尖端应力的奇异性,构造有限连续的应力函数和尖劈型的张开位移函数.对指数函数型解析函数的间接积分适用于界面裂纹问题,但会使积分区间的应力分布出现正负反转和不合理的张开位移形状;结合选择不同权函数的叠加可以得到满足精度要求的有限应力集中解析函数.给出了中心裂纹和对称边裂纹在面内拉伸、剪切和弯曲等6种受力状态下的基本解.阐述了作为解析函数何以回避裂纹尖端应力奇异性的理由.
The constructing methods for finite stress concentration analysis near the crack tip were summarized. The stress functions for plane problems with cracks were expressed with irrational or exponential functions. For the mono-material crack,with the crack length as the parameter,the direct weighted integration of the irrational-function-type analytic function was conducted to avoid stress singularity at the crack tip,and construct the finite stress concentration functions and the wedge-type opening displacement functions. The indirect integration of the exponential-function-type analytic function was suitable for the interface crack problem,but put the stress distribution within the integral interval into positive-negative inversion and irrational opening displacement shape,which can be improved through combining selection and superposition of different weight functions. The basic solutions for the central cracks and the symmetrical edge cracks were given in 6 stress states of plane stretching,shearing and bending,etc. The reason why the analytic function can avoid the stress singularity at the crack tip was given.
作者
段树金
藤井康寿
中川建治
DUAN Shujin;FUJII Koju;NAKAGAWA Kenji(College of Civil Engineering,Shijiazhuang Tiedao University, Shijiazhuang 050043,P.R.China;Faculty of Human Relations,Tokai Gakuin University, Kagamihara 504-8511,Japan;Faculty of Engineering,Gifu University,Gifu 501-1193,Japan)
出处
《应用数学和力学》
CSCD
北大核心
2018年第12期1364-1376,共13页
Applied Mathematics and Mechanics
基金
河北省自然科学基金(A2015210029)
关键词
裂纹
界面裂纹
内聚裂纹区
有限应力集中
解析函数
加权积分
crack
interface crack
cohesive crack zone
finite stress concentration
analytical function
weighted integration
