基于新型流形法的三维应力强度因子求解  

Computing 3D stress intensity factors based on new manifold method

作　　者：祁勇峰[1] 苏海东[1] 龚亚琦[1] QI Yongfeng;SU Haidong;GONG Yaqi(Material and Engineering Structure Department,Research Center on Water Engineering Safety and Disaster Prevention of Ministry of Water Resources, Yangtze River Scientific Research Institute, Wuhan 430010, P. R. China)

机构地区：[1]长江科学院材料与结构研究所,水利部水工程安全和病害防治工程技术研究中心,武汉430010

出　　处：《土木与环境工程学报（中英文）》2021年第5期58-65,共8页Journal of Civil and Environmental Engineering

基　　金：国家自然科学基金(51779019、51809017);中央级公益性科研院基本科研业务费(CKSF2020065/CL)。

摘　　要：为保证在裂纹尖端具有最佳的逼近,裂纹尖端的解析解与其周边数值解联合应用的新型流形法可用来求解应力强度因子,但仅限于平面问题的Ⅰ型和Ⅱ型裂纹。沿用解析解与数值解联合应用的思路,以三维穿透直裂纹为研究对象,在裂纹尖端引入Williams解析解级数,应用解析覆盖与周边数值覆盖联合求解三维应力强度因子,相对于其他数值方法而言,计算精度高。推导相应的刚度矩阵和应变矩阵的表达式,通过典型算例验证了三维应力强度因子精确求解方法的有效性。This paper proposes a new manifold method combined with the analytical solutions of the crack tip and its surrounding numerical solutions is used to solve the stress intensity factor to ensure the best approximation at the crack tip.But this method is limited to type I and type II cracks in the plane problem.This method follows the idea of combined application of analytical and numerical solutions.Taking the three-dimensional penetrating straight crack as the research object,the Williams analytical solution series is introduced at the crack tip,and the analytical covers and the surrounding numerical covers are combined to solve the 3D stress intensity factor.Compared with other numerical methods,this method has higher computational precision.Meanwhile,the corresponding formulas of the stiffness matrix and the strain matrix have been deduced,and typical numerical examples shows the validity of the method in solving the exact solution of the 3D stress intensity factor.

关 键 词：三维应力强度因子 数值流形方法 裂纹尖端Williams解析级数 解析覆盖 数值覆盖 

分 类 号：O343.2[理学—固体力学]