{"title":"利用奇异积分方程法分析一维正交准晶体中的复杂平面裂缝","authors":"Di Sun , Taiyan Qin , Xiao-Wei Gao","doi":"10.1016/j.enganabound.2024.105929","DOIUrl":null,"url":null,"abstract":"<div><p>A singular integral equation method is proposed to analyze the complex plane cracks in one-dimensional (1D) orthorhombic quasicrystals. Using the Somigliana formula, the singular integral equations of the curved crack are derived. Based on the general situation of the curved crack, the singular integral equations of the inclined crack and the arc crack are given. Then the analytical solutions for the singular phonon and phason stresses near the tips of the inclined and the arc crack are obtained. Gauss-Chebyshev quadrature method is introduced to calculate the singular integral equations, and a numerical algorithm for solving the stress intensity factor (SIF) is proposed. Numerical solutions for the phonon and phason SIFs of some examples are solved and discussed.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":"168 ","pages":"Article 105929"},"PeriodicalIF":4.2000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis for complex plane cracks in 1D orthorhombic quasicrystals using the singular integral equation method\",\"authors\":\"Di Sun , Taiyan Qin , Xiao-Wei Gao\",\"doi\":\"10.1016/j.enganabound.2024.105929\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>A singular integral equation method is proposed to analyze the complex plane cracks in one-dimensional (1D) orthorhombic quasicrystals. Using the Somigliana formula, the singular integral equations of the curved crack are derived. Based on the general situation of the curved crack, the singular integral equations of the inclined crack and the arc crack are given. Then the analytical solutions for the singular phonon and phason stresses near the tips of the inclined and the arc crack are obtained. Gauss-Chebyshev quadrature method is introduced to calculate the singular integral equations, and a numerical algorithm for solving the stress intensity factor (SIF) is proposed. Numerical solutions for the phonon and phason SIFs of some examples are solved and discussed.</p></div>\",\"PeriodicalId\":51039,\"journal\":{\"name\":\"Engineering Analysis with Boundary Elements\",\"volume\":\"168 \",\"pages\":\"Article 105929\"},\"PeriodicalIF\":4.2000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Engineering Analysis with Boundary Elements\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S095579972400403X\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ENGINEERING, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Engineering Analysis with Boundary Elements","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S095579972400403X","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ENGINEERING, MULTIDISCIPLINARY","Score":null,"Total":0}
Analysis for complex plane cracks in 1D orthorhombic quasicrystals using the singular integral equation method
A singular integral equation method is proposed to analyze the complex plane cracks in one-dimensional (1D) orthorhombic quasicrystals. Using the Somigliana formula, the singular integral equations of the curved crack are derived. Based on the general situation of the curved crack, the singular integral equations of the inclined crack and the arc crack are given. Then the analytical solutions for the singular phonon and phason stresses near the tips of the inclined and the arc crack are obtained. Gauss-Chebyshev quadrature method is introduced to calculate the singular integral equations, and a numerical algorithm for solving the stress intensity factor (SIF) is proposed. Numerical solutions for the phonon and phason SIFs of some examples are solved and discussed.
期刊介绍：
This journal is specifically dedicated to the dissemination of the latest developments of new engineering analysis techniques using boundary elements and other mesh reduction methods.
Boundary element (BEM) and mesh reduction methods (MRM) are very active areas of research with the techniques being applied to solve increasingly complex problems. The journal stresses the importance of these applications as well as their computational aspects, reliability and robustness.
The main criteria for publication will be the originality of the work being reported, its potential usefulness and applications of the methods to new fields.
In addition to regular issues, the journal publishes a series of special issues dealing with specific areas of current research.
The journal has, for many years, provided a channel of communication between academics and industrial researchers working in mesh reduction methods
Fields Covered:
• Boundary Element Methods (BEM)
• Mesh Reduction Methods (MRM)
• Meshless Methods
• Integral Equations
• Applications of BEM/MRM in Engineering
• Numerical Methods related to BEM/MRM
• Computational Techniques
• Combination of Different Methods
• Advanced Formulations.
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