反平面塑性V形切口尖端应力和位移渐近解

Asymptotic Solutions of Plastic Stress and Displacement at V-Notch Tips Under Anti-Plane Shear

提出了一种确定幂硬化材料反平面V形切口尖端应力和位移渐近解的主导项和高阶项的有效方法.首先通过在弹塑性理论基本方程中引入V形切口尖端应力场和位移场的渐近级数展开,建立以应力和位移为特征函数的非线性和线性常微分方程组.然后采用插值矩阵法求解常微分方程组,可得到多阶应力特征指数和其相对应的特征函数.该方法具有通用性强、精度高等优点,可处理任意开口角度和应变硬化指数的V形切口.典型算例验证了该方法的准确性和有效性.

An efficient method was developed to determine the first-and high-order terms of asymptotic solutions of plastic stress and displacement near V-notch tips under anti-plane shear in power-law hardening materials.Through introduction of the asymptotic series expansions of stress and displacement fields around the V-notch tip into the fundamental equations of the elastoplastic theory,the governing ordinary differential equations(ODEs) with the stress and displacement eigenfunctions were established.Then the interpolating matrix method was employed to solve the resulting nonlinear and linear ODEs.Consequently,the high-order stress exponents and the associated eigen-solutions were obtained.The presented method,being capable of dealing with the V-notches with arbitrary opening angles and strain hardening indexes under antiplane shear,has the advantages of great versatility and high accuracy.Typical examples were given to demonstrate the accuracy and effectiveness of this method.