Analytical calculation of stress intensity factors for orthotropic plates containing cracks emanating from a circular hole using Schwarz integration

IF 2.3 4区工程技术 Q1 MATHEMATICS, APPLIED

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik Pub Date : 2023-09-14 DOI:10.1002/zamm.202300429

Seyyed Hassan Moussavian, Mohammad Jafari, Mojtaba Hajimohammadi

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Abstract

Abstract In this paper, a new analytical method is presented to determine the stress intensity factors (SIFs) of a generally orthotropic plate with cracks emanating from a circular hole. Therefore, using the Schwartz integration method, for the first time, the analytical solution is provided based on the complex variable method. In order to use the Schwartz's theorem in solving complex integrals, a new presentation of the mapping function has been presented, which leads to providing a simpler solution. After calculating the potential functions, the SIFs are determined for the circular hole with one and two cracks. Then, the effect of parameters such as fiber angle, different and unequal crack lengths, and different loadings are studied. To validate the results of the present analytical solution, some results have been compared with the results from other references. Comparing the results showed that the current solution has good accuracy and is reliable and the fiber angle has a significant effect on the mode II SIF. In the case that the fibers are along the crack length and the loading is perpendicular to the crack direction, the mode II SIF is zero, but if the fibers are not along the crack length, the value of the mode II SIF will not be zero. It is also shown that increasing the length of one crack increases the SIF of another crack as well.

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用Schwarz积分解析计算含圆孔裂纹的正交各向异性板的应力强度因子

摘要本文提出了一种确定含圆孔裂纹的一般正交各向异性板的应力强度因子(SIFs)的解析方法。因此，利用Schwartz积分法，首次给出了基于复变量法的解析解。为了利用Schwartz定理求解复积分，本文给出了映射函数的一种新的表示形式，从而提供了一种更简单的解。通过对势函数的计算，确定了含裂纹圆孔和含裂纹圆孔的SIFs。然后，研究了纤维角度、不同及不等裂纹长度、不同载荷等参数对结构的影响。为了验证本文解析解的结果，将一些结果与其他文献的结果进行了比较。结果表明，当前解具有较好的精度和可靠性，光纤角度对II型SIF有显著影响。当纤维沿裂纹长度方向加载且载荷垂直于裂纹方向时，II型SIF为零，但当纤维不沿裂纹长度方向加载时，II型SIF不为零。增加一个裂纹的长度也会增加另一个裂纹的SIF。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Zamm-zeitschrift Fur Angewandte Mathematik Und Mechanik 数学-力学

CiteScore

3.30

自引率

8.70%

发文量

199

审稿时长

3.0 months

期刊介绍： ZAMM is one of the oldest journals in the field of applied mathematics and mechanics and is read by scientists all over the world. The aim and scope of ZAMM is the publication of new results and review articles and information on applied mathematics (mainly numerical mathematics and various applications of analysis, in particular numerical aspects of differential and integral equations), on the entire field of theoretical and applied mechanics (solid mechanics, fluid mechanics, thermodynamics). ZAMM is also open to essential contributions on mathematics in industrial applications.