微分求积法计算双材料反平面V形切口应力奇性指数  

The calculation of stress singularity orders of anti-plane V-notch in bi-materials using differential quadrature method

作　　者：葛仁余[1] 张佳宸 吕良伟 朱浩杰 邹令令 牛忠荣[2] Ge Renyu;Zhang Jiachen;LV Liangwei;Zhu Haojie;Zou Lingling;Niu Zhongrong(Key Laboratory for Mechanics,Anhui Polytechnic University,241000,Wuhu,China;School of Civil Engineering,Hefei University of Technology,230009,Hefei,China)

机构地区：[1]安徽工程大学力学重点实验室,芜湖241000 [2]合肥工业大学土木与水利工程学院,合肥230009

出　　处：《应用力学学报》2021年第2期787-793,共7页Chinese Journal of Applied Mechanics

基　　金：安徽省自然科学基金(1808085ME147);国家级大学生创新创业训练计划项目(201910363089)。

摘　　要：首次将微分求积法应用到工程断裂力学的研究领域,运用该方法计算了双材料反平面V形切口端部区域的应力奇性指数。首先基于弹性力学理论,将反平面V形切口端部应力奇性指数的计算转化为常微分方程组的特征值问题,再由微分求积法理论将常微分方程组的特征值问题转化为标准型广义代数方程组的特征值问题,由QR法可一次性计算出双材料反平面V形切口端部应力奇性指数及其相应的特征角函数。数值计算结果表明:随着区间离散单元数n的加倍增加,不同材料组合的反平面V形切口应力奇性指数的微分求积法计算值加速收敛,当n≥16时,本文计算值与精确解有5位有效数字相同,证明了采用微分求积法计算双材料反平面V形切口应力奇性指数的有效性和精确性。In this paper,the differential quadrature method is applied to the research of engineering fracture mechanics for the first time,and the stress singularity index of the end region of bi-material anti-plane V-notch is calculated by using this method.Firstly,based on the theory of elasticity,the calculation of stress singularity index at the end of anti-plane V-shaped notch is transformed into the eigenvalue problem of ordinary differential equations.Then,the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of standard generalized algebraic equations by differential quadrature method.The stress singularity index and the corresponding characteristic angle function can be calculated by QR method at one time.The numerical results show that with the increase of the number of interval discrete elements n,the value of differential quadrature method for calculating the stress singularity index of anti-plane V-notch with different material combinations converges rapidly.When n≥16,the value of this paper is the same as that of the exact solution,which proves the effectiveness and precision of the differential quadrature method in calculating the stress singularity index of bi-material anti plane V-notch.

关 键 词：反平面V形切口 双材料 应力奇异性 微分求积法 

分 类 号：O343.4[理学—固体力学]