剪切荷载作用下圆孔孔边裂纹的解  

Solutions for a Circular Hole With Edge Cracks Under Shear Load

作　　者：段士杰[1] 刘淑红[2,3] 

机构地区：[1]石家庄铁道大学继续教育学院,石家庄050043 [2]石家庄铁道大学工程力学系,石家庄050043 [3]河北省大型结构健康诊断与控制实验室,石家庄050043

出　　处：《应用数学和力学》2016年第7期740-747,共8页Applied Mathematics and Mechanics

基　　金：河北省自然科学基金(A2015210089);河北省高等学校科学技术研究重点项目(ZD2015101)

摘　　要：基于复变函数的方法,研究了在无限远处剪切荷载作用下,含两个径向不等边裂纹圆孔无限大板的平面问题,得到了应力函数和应力强度因子的解析解.通过算例,给出了通过应力函数得到的应力分量沿坐标轴方向和孔边的分布,同时给出了裂纹尖端的应力强度因子.可以看出,应力分量在裂纹尖端、孔附近变化剧烈,离缺陷稍远处趋于所加荷载,符合Saint Venant(圣维南)原理.另外,通过有限元计算了以上数值结果,与解析解的结果进行对比,吻合较好,说明了理论公式推导的正确性.A 2D mechanical analysis was performed on an infinite plate containing a circular hole with two collinear edge cracks of unequal lengths,under uniformly distributed shear load at infinity. Based on the complex variable function method,the analytic solutions of stress functions and stress intensity factors were obtained. Through an numerical example,the stress distributions along the coordinate axes and the hole edge were given in the graphical form,and the stress intensity factors were also calculated. The results show that,there is obvious stress concentration near the hole and the cracks,and the stress values far from the defects tend towards the applied load,which conforms to the Saint-Venant＇s principle. In addition,the results from the finite element simulation agree well with the analytic solutions,to prove the correctness of the theoretical derivation.

关 键 词：裂纹 应力函数 应力强度因子 复变函数 有限元 

分 类 号：O346.1[理学—固体力学]