{"title":"用新型无网格伽勒金方法模拟静态热弹性断裂问题","authors":"","doi":"10.1016/j.enganabound.2024.105893","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, a linear gradient smoothed meshless Galerkin method (LGSM) is presented to solve the static thermoelastic fracture problems. To accurately represent the discontinuity of temperature and displacement fields across the crack surface as well as the singularity of heat flux and stress fields near the crack tip, the diffraction method is combined with intrinsic enrichment basis to construct meshless approximation. Meanwhile, to effectively save computational cost, the smoothed temperature gradient and the smoothed strain fields are expressed as the linear forms with respect to the center point in each smoothing domain by using the recently proposed linear-gradient smoothed integral (LGSI) scheme, respectively. This leads to substantial reduction of the number of Gaussian integration points without lowing the accuracy of meshless method. The thermal stress intensity factor is evaluated using interaction integrals that considering thermal effects. The novelty of the current work is the extension of LGSI scheme to solve thermoelastic fracture problems, which further verifies that the LGSI scheme is accurate, efficiency, and stable for the integration computation in meshless Galerkin method based on polynomial basis as well as intrinsic enrichment basis. Several numerical examples have been performed to validate the accuracy, efficiency, and robustness of the presented LGSM.</p></div>","PeriodicalId":51039,"journal":{"name":"Engineering Analysis with Boundary Elements","volume":null,"pages":null},"PeriodicalIF":4.2000,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Simulation of static thermoelastic fracture problems by a novel meshless Galerkin method\",\"authors\":\"\",\"doi\":\"10.1016/j.enganabound.2024.105893\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, a linear gradient smoothed meshless Galerkin method (LGSM) is presented to solve the static thermoelastic fracture problems. To accurately represent the discontinuity of temperature and displacement fields across the crack surface as well as the singularity of heat flux and stress fields near the crack tip, the diffraction method is combined with intrinsic enrichment basis to construct meshless approximation. Meanwhile, to effectively save computational cost, the smoothed temperature gradient and the smoothed strain fields are expressed as the linear forms with respect to the center point in each smoothing domain by using the recently proposed linear-gradient smoothed integral (LGSI) scheme, respectively. This leads to substantial reduction of the number of Gaussian integration points without lowing the accuracy of meshless method. The thermal stress intensity factor is evaluated using interaction integrals that considering thermal effects. The novelty of the current work is the extension of LGSI scheme to solve thermoelastic fracture problems, which further verifies that the LGSI scheme is accurate, efficiency, and stable for the integration computation in meshless Galerkin method based on polynomial basis as well as intrinsic enrichment basis. Several numerical examples have been performed to validate the accuracy, efficiency, and robustness of the presented LGSM.</p></div>\",\"PeriodicalId\":51039,\"journal\":{\"name\":\"Engineering Analysis with Boundary Elements\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.2000,\"publicationDate\":\"2024-08-05\",\"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/S0955799724003679\",\"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/S0955799724003679","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}
Simulation of static thermoelastic fracture problems by a novel meshless Galerkin method
In this paper, a linear gradient smoothed meshless Galerkin method (LGSM) is presented to solve the static thermoelastic fracture problems. To accurately represent the discontinuity of temperature and displacement fields across the crack surface as well as the singularity of heat flux and stress fields near the crack tip, the diffraction method is combined with intrinsic enrichment basis to construct meshless approximation. Meanwhile, to effectively save computational cost, the smoothed temperature gradient and the smoothed strain fields are expressed as the linear forms with respect to the center point in each smoothing domain by using the recently proposed linear-gradient smoothed integral (LGSI) scheme, respectively. This leads to substantial reduction of the number of Gaussian integration points without lowing the accuracy of meshless method. The thermal stress intensity factor is evaluated using interaction integrals that considering thermal effects. The novelty of the current work is the extension of LGSI scheme to solve thermoelastic fracture problems, which further verifies that the LGSI scheme is accurate, efficiency, and stable for the integration computation in meshless Galerkin method based on polynomial basis as well as intrinsic enrichment basis. Several numerical examples have been performed to validate the accuracy, efficiency, and robustness of the presented LGSM.
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.