满足断裂过程区裂纹张开位移条件应力函数的半解析解法  

A Semi-Analytical Method for Stress Functions Meeting Crack Opening Displacements in Fracture Process Zones

作　　者：侯永康 段树金 安蕊梅[1] HOU Yongkang;DUAN Shujin;AN Ruimei(School of Civil Engineering,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China;Key Laboratory of Roads and Railway Engineering Safety Control of Ministry of Education,Shijiazhuang Tiedao University,Shijiazhuang 050043,P.R.China)

机构地区：[1]石家庄铁道大学土木工程学院,石家庄050043 [2]石家庄铁道大学道路与铁道工程安全保障省部共建教育部重点实验室,石家庄050043

出　　处：《应用数学和力学》2018年第8期979-988,共10页Applied Mathematics and Mechanics

基　　金：河北省自然科学基金(A2015210029);河北省教育厅青年基金项目(QN2014062);河北省研究生创新资助项目(CXZZBS2017132)

摘　　要：基于Duan-Nakagawa模型,采用加权积分法,提出了一种满足断裂过程区裂纹张开位移条件应力函数的半解析解法.该方法结合边界选点法,通过叠加含有相同裂纹长度但断裂过程区长度不同的解析函数,得到满足给定裂纹张开位移的权函数,再进行加权积分得到相应的应力函数和位移函数.以带板对称边裂纹I型问题为例,应用上述方法成功导出了特定的应力函数和位移函数,以及相应的拉应变软化曲线和断裂能.Based on the Duan-Nakagawa model,with the weighted integral method,a semi-analytical method for stress functions meeting crack opening displacements in fracture process zones was proposed.The weighted function was determined by means of the boundary selected point method and the superposition of analytical functions with the same crack length but different fracture process zone lengths,to meet the given crack opening displacement in the fracture process zone,and then the final stress function and displacement function can be obtained with the weighted integral method. As an example,a special analytical solution for a double edge notched plate under Mode-I loading was derived,and the tensile strain softening curve and the fracture energy were obtained.

关 键 词：断裂力学 断裂过程区 半解析解法 应力函数 裂纹张开位移 拉应变软化曲线 对称边裂纹 

分 类 号：TU528[建筑科学—建筑技术科学] O346[理学—固体力学]