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研究幂硬化塑性材料V形切口和裂纹尖端区域的应力奇异性.首先在切口和裂纹区域采用自尖端径向度量的渐近位移场假设,将其代入塑性全量理论的基本微分方程后,推导出包含应力奇异指数和特征函数的非线性常微分方程特征值问题.然后采用插值矩阵法迭代求解导出的控制方程,得到一般的塑性材料V形切口和裂纹的前若干阶应力奇异阶和相应的特征函数.通过两个算例给出了前若干个阶的应力奇异指数和特征函数,表明文中方法计算一般塑性材料V形切口和裂纹应力奇异性的精度和有效性,并对一般塑性材料V形切口和裂纹的奇异应力特征进行了讨论.
The stress singularity of V-notch and crack tip region of power-hardening plastic material is studied.At first, the asymptotic displacement field hypothesis of radial tip metric is adopted in the notch and crack region, and then substituted into the basic differential equation of plastic total mass theory The problem of eigenvalue problems of nonlinear ordinary differential equations with stress singularity and eigenfunction is solved iteratively by using the interpolation matrix method to obtain the general order of V-notch and crack first order stress singularity and corresponding features The stress singular exponents and eigenfunctions of the first several orders are given by two examples, which shows the accuracy and effectiveness of the method for calculating the singularity of V-notch and crack stress of general plastic materials. The V- The singular stress characteristics of kerf and crack are discussed.