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Evaluation of notch stress intensity factors by the asymptotic expansion technique coupled with the finite element method

机译：渐近展开技术结合有限元法评估缺口应力强度因子

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摘要

A characteristic analysis method coupled with the finite element method is proposed to calculate stress intensity factors for V-notches, in which the notched structure is divided into a singular stress sector and the remained part. The asymptotic expansions are introduced into the singular stress region to transform elastic governing equations into characteristic ordinary differential equations. The established equations are solved by the interpolating matrix method to provide stress singular orders and characteristic angular functions. The asymptotic solution in the singular stress region is then coupled with finite element equations built on the remained structure by interfacial continuous conditions to establish the system equations. Thus, the amplitude coefficients in the stress asymptotic expansions can be determined. The notch stress intensity factors can be evaluated after the stress angular functions and amplitude coefficients being obtained. A symmetric V-notch and an inclined V-notch are respectively investigated to verify the accuracy of calculated notch stress intensity factors by the proposed method through comparing with the reference ones. Due to only conventional finite element method is needed, the proposed method can be freely implanted into commercial finite element software to analyze the singular stress for the V-notched engineering structures. This method can be also easily generalized to analyze the singular physical field for V-notches in composite materials.
机译：提出了一种结合有限元方法的特征分析方法来计算V型缺口的应力强度因子，将缺口结构分为奇异应力段和其余部分。将渐近展开引入奇异应力区域，以将弹性控制方程式转换为特征性常微分方程式。所建立的方程通过插值矩阵法求解，以提供应力奇异阶和特征角函数。然后，通过界面连续条件，将奇异应力区域中的渐近解与在剩余结构上建立的有限元方程式耦合，以建立系统方程式。因此，可以确定应力渐近扩展中的振幅系数。缺口应力强度因子可以在获得应力角函数和振幅系数后进行评估。分别研究了对称的V型缺口和倾斜的V型缺口，通过与参考值进行比较，验证了所提出的缺口应力强度因子的准确性。由于仅需要常规的有限元方法，因此该方法可以自由地植入到商业有限元软件中，以分析V形缺口工程结构的奇异应力。该方法也可以很容易地推广到分析复合材料中V形缺口的奇异物理场。

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