角度非均匀连续介质材料反平面V形切口应力奇性分析  

Stress Singularity Analysis of Anti Plane V-notch in Angular Inhomogeneous Continuous Media

作　　者：姜伟 葛仁余 李浚淇 潘家雨 尚悦 JIANG Wei;GE Renyu;LI Junqi;PAN Jiayu;SHANG Yue(School of Architecture and Civil Engineering,Anhui Polytechnic University,Wuhu 241000,China)

机构地区：[1]安徽工程大学建筑工程学院,安徽芜湖241000

出　　处：《安徽工程大学学报》2023年第4期56-63,共8页Journal of Anhui Polytechnic University

基　　金：国家级大学生创新创业训练计划基金资助项目(202110363125)。

摘　　要：由于角度非均匀连续介质材料本构关系的复杂性,即材料参数随角度坐标连续变化,致使V形切口的奇性特征分析的控制方程是一组非线性、变系数的常微分方程组,数学上面临求解的困难。论文运用微分求积法(DQM)计算角度非均匀连续介质材料反平面V形切口端部应力奇性指数,首先基于弹性力学理论,将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DQM理论将常微分方程组的特征值问题转化为一组标准型广义代数方程的特征值问题,最后正交三角分解(QR)法可一次性计算出角度非均匀连续介质材料反平面V形切口端部应力奇性指数及其特征角函数。数值计算结果表明,DQM计算值与已有文献计算结果完全一致,证明了DQM分析角度非均匀连续介质材料反平面V形切口应力奇性的可行性和精确性。Due to the complexity of the constitutive relationship of angular inhomogeneous continuous media materials,the material parameters change continuously with the angular coordinates,so the control equations for singularity characteristics analysis of V-notch are a set of nonlinear,variable coefficient ordinary differential equations,it is difficult to solve mathematically.This paper employs the differential quadrature method to calculate the stress singularity index at the end of the anti-plane V-shaped notch of angular inhomogeneous continuous media materials.Firstly,based on the theory of elasticity,the calculation of the stress singularity index at the end of the notch is transformed into the eigenvalue problem of ordinary differential equations,and then the eigenvalue problem of ordinary differential equations is transformed into the eigenvalue problem of a group of standard generalized algebraic equations by the theory of differential quadrature method.Finally,the stress singularity index and its characteristic angle function at the end of the anti-plane V-notch can be calculated by the orthogonal triangular decomposition method.The numerical results show that the calculated values of differential quadrature method are completely consistent with those of the existing literature,which proves the feasibility and accuracy of differential quadrature method in analyzing the stress singularity of anti plane V-notch of angular inhomogeneous continuous media.

关 键 词：反平面V形切口 非均匀连续介质材料 应力奇异性 微分求积法 

分 类 号：O341[理学—固体力学]