角度非均匀材料平面V形切口应力奇性分析

提出了一种确定角度非均匀材料平面V形切口尖端应力奇性指数的有效方法。首先,在弹性力学基本方程中引入V形切口尖端位移场的级数渐近展开,建立以位移为特征函数的变系数和非线性微分方程组。然后,采用微分求积法(DQM)求解微分方程组,可得到多阶应力奇性指数及其相对应的特征函数,该法具有公式简单、编程方便、计算量少和精度高等优点,可处理任意开口角度和任意材料组合的V形切口。典型算例验证了微分求积法的有效性和精确性。

Stress singularity analysis of plane V-notch in angular non-uniform materials

This paper presents an effective method to determine the stress singularity index at the tip of plane V-notch in angular non-uniform materials.Firstly,the series asymptotic expansion of the displacement field at the tip of the V-notch is introduced into the basic equations of elasticity,and the nonlinear variable coefficient differential equations with displacement as the characteristic functions are established.Then the differential quadrature method (DQM) is used to solve the differential equations,and the multi-order stress singularity index and its corresponding characteristic function can be obtained.This method has the advantages of a simple formula,convenient programming,less calculation and high precision. It can deal with the V-shaped notch with any opening angle and any material combination. Typical examples verify the effectiveness and accuracy of the differential quadrature method.