{"title":"使用改进的 Muskhelishvili 方法对孔缘裂缝的应力场和应力集中因子进行半解析求解","authors":"Haibiao Gao, Yixiao Qin, Linhao Wang","doi":"10.1142/s1758825124500443","DOIUrl":null,"url":null,"abstract":"<p>A semi-analytical solution is provided to obtain the stress intensity factors (SIFs) of hole-edge cracks with different configurations and the stress fields along the crack propagation direction in an infinite isotropic plane. The complicated solution procedure while using the Muskhelishvili method is improved by expanding an irrational mapping function into an approximate rational function so that singular integral equations could be converted to linear equations. The proposed method used to obtain the SIFs of symmetrical cracks emanating from circular or elliptical holes and a single crack emanating from a circular hole is compared with other methods in the literature. The results show that this method is universal and accurate for hole-edge cracks. In addition, the effects of the lengths of the asymmetrical cracks and the ratio of the semi-axes of the elliptical hole (<span><math altimg=\"eq-00001.gif\" display=\"inline\" overflow=\"scroll\"><mi>a</mi></math></span><span></span>/<span><math altimg=\"eq-00002.gif\" display=\"inline\" overflow=\"scroll\"><mi>b</mi><mo stretchy=\"false\">)</mo></math></span><span></span> on the SIFs are studied, which have not been previously reported.</p>","PeriodicalId":49186,"journal":{"name":"International Journal of Applied Mechanics","volume":"18 1","pages":""},"PeriodicalIF":2.9000,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Semi-Analytical Solution for the Stress Field and Stress Intensity Factor of Hole-Edge Cracks Using Improved Muskhelishvili Method\",\"authors\":\"Haibiao Gao, Yixiao Qin, Linhao Wang\",\"doi\":\"10.1142/s1758825124500443\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>A semi-analytical solution is provided to obtain the stress intensity factors (SIFs) of hole-edge cracks with different configurations and the stress fields along the crack propagation direction in an infinite isotropic plane. The complicated solution procedure while using the Muskhelishvili method is improved by expanding an irrational mapping function into an approximate rational function so that singular integral equations could be converted to linear equations. The proposed method used to obtain the SIFs of symmetrical cracks emanating from circular or elliptical holes and a single crack emanating from a circular hole is compared with other methods in the literature. The results show that this method is universal and accurate for hole-edge cracks. In addition, the effects of the lengths of the asymmetrical cracks and the ratio of the semi-axes of the elliptical hole (<span><math altimg=\\\"eq-00001.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>a</mi></math></span><span></span>/<span><math altimg=\\\"eq-00002.gif\\\" display=\\\"inline\\\" overflow=\\\"scroll\\\"><mi>b</mi><mo stretchy=\\\"false\\\">)</mo></math></span><span></span> on the SIFs are studied, which have not been previously reported.</p>\",\"PeriodicalId\":49186,\"journal\":{\"name\":\"International Journal of Applied Mechanics\",\"volume\":\"18 1\",\"pages\":\"\"},\"PeriodicalIF\":2.9000,\"publicationDate\":\"2024-03-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Applied Mechanics\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1142/s1758825124500443\",\"RegionNum\":3,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Applied Mechanics","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1142/s1758825124500443","RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MECHANICS","Score":null,"Total":0}
A Semi-Analytical Solution for the Stress Field and Stress Intensity Factor of Hole-Edge Cracks Using Improved Muskhelishvili Method
A semi-analytical solution is provided to obtain the stress intensity factors (SIFs) of hole-edge cracks with different configurations and the stress fields along the crack propagation direction in an infinite isotropic plane. The complicated solution procedure while using the Muskhelishvili method is improved by expanding an irrational mapping function into an approximate rational function so that singular integral equations could be converted to linear equations. The proposed method used to obtain the SIFs of symmetrical cracks emanating from circular or elliptical holes and a single crack emanating from a circular hole is compared with other methods in the literature. The results show that this method is universal and accurate for hole-edge cracks. In addition, the effects of the lengths of the asymmetrical cracks and the ratio of the semi-axes of the elliptical hole (/ on the SIFs are studied, which have not been previously reported.
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The journal has as its objective the publication and wide electronic dissemination of innovative and consequential research in applied mechanics. IJAM welcomes high-quality original research papers in all aspects of applied mechanics from contributors throughout the world. The journal aims to promote the international exchange of new knowledge and recent development information in all aspects of applied mechanics. In addition to covering the classical branches of applied mechanics, namely solid mechanics, fluid mechanics, thermodynamics, and material science, the journal also encourages contributions from newly emerging areas such as biomechanics, electromechanics, the mechanical behavior of advanced materials, nanomechanics, and many other inter-disciplinary research areas in which the concepts of applied mechanics are extensively applied and developed.
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