平面V型缺口尖端应力强度因子确定的广义参数有限元法  

Determination of stress intensity factor of planar V-notch by the finite element method with generalized degrees of freedom

作　　者：徐华[1,2,3] 谭克实 杨绿峰 李朝阳[1,2,3] XU Hua;TAN Keshi;YANG Lufeng;LI Zhaoyang(School of Civil Engineering and Architecture,Guangxi University,Nanning 530004,China;Key Laboratory of Disaster Prevention and Structural Safety of Ministry of Education,Nanning 530004,China;Guangxi Key Laboratory of Disaster Prevention and Engineering Safety,Nanning 530004,China)

机构地区：[1]广西大学土木建筑工程学院,广西南宁530004 [2]工程防灾与结构安全教育部重点实验室,广西南宁530004 [3]广西防灾减灾与工程安全重点实验室,广西南宁530004

出　　处：《广西大学学报（自然科学版）》2023年第5期1031-1041,共11页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金重点项目(51738004);广西自然科学基金项目(2019GXNSFAA245012);中国教育后勤协会重点课题(ZDKT2022005)。

摘　　要：针对工程结构中存在的V型缺口在外荷载作用下容易发生断裂的现象,基于广义参数有限元法和V型缺口尖端Williams级数位移场推导建立了V型缺口应力强度因子(stress intensity factors,SIFs)分析的Williams单元(简记W单元),通过求解整体控制方程,将相应的特征值和广义参数直接代入公式即可获得较高精度的SIFs。结合边界V型缺口算例研究表明:W单元对相对奇异区尺寸和网格加密均不敏感,对W单元的3个重要参数径向离散因子α、径向离散单元数n、级数截取项数m,建议取m=10,α=0.9,n=100,其结果收敛并具有较高的计算精度,且与裂纹研究中给定的建议值相同。通过对非中心缺口不同位置和角度进行算例分析验证了W单元具有高精性,同时参数取值具有通用性。For the phenomenon that V-notches in engineering structures are prone to fracture under external loads,based on the Williams series of the V-notch tip displacement field and the finite element method with generalized degrees of freedom,the Williams element(W element)for the analysis of stress intensity factors(SIFs)is established,which can obtain SIFs with high accuracy by solving the integral control equation and directly bringing corresponding eigenvalues and generalized parameters into the equation.It is shown that W element is insensitive to the relative size of singular region and mesh encryption.The three important parameters radial discrete scale factorα,radial discrete elements n and series terms m of W element are analyzed.It is suggested that m=10,α=0.9,n=100 which results are of convergence and high accuracy and are identical with the suggested value for the study of cracks.On this basis,The example analysis of different notch positions and angles verifies that the W element has high precision,and the parameter values are universal.

关 键 词：V型缺口 应力强度因子 广义参数 Williams单元 

分 类 号：TU473.1[建筑科学—结构工程]