反平面塑性V形切口尖端应力和位移渐近解

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。

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

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 eigen-functions 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 anti-plane shear, has the advantages of great versatility and high accuracy. Typical examples were given to demonstrate the accuracy and effectiveness of this method.