根据应力张量分量的有限元解法计算裂缝尖端场扩展系数的超定积分法程序

M. A. Fomchenkova, L. V. Stepanova
{"title":"根据应力张量分量的有限元解法计算裂缝尖端场扩展系数的超定积分法程序","authors":"M. A. Fomchenkova, L. V. Stepanova","doi":"10.18287/2541-7525-2024-30-2-54-66","DOIUrl":null,"url":null,"abstract":"The article proposes and implements a procedure for reconstructing the asymptotic series expansion of stress, strain and displacement fields in anisotropic materials, generalizing the Williams solution for linearly elastic isotropic materials, based on a finite element solution to the problem of deforming a sample with a defect in an anisotropic orthotropic material in the approximation of a plane problem of elasticity theory. The stress field expansion coefficients near the crack tip in an anisotropic material are determined using an overdeterministic method originally proposed to reconstruct the asymptotic expansion from experimental data of a photoelastic study. In this paper, this method is extended to anisotropic materials with various types of symmetry and the novelty of the proposed approach lies in the reconstruction of the asymptotic expansion from the finite element solution for the stress tensor components in the nodes of the finite element grid, which allows us not to exclude their displacement fields components corresponding to the displacement of a body as an absolutely solid body. In the proposed approach, it is possible to use data from finite element calculations directly in the scheme of the overdeterministic method. It is shown that the coefficients of higher approximations are reliably determined by an overdeterministic method based on the stress field found from finite element analysis.","PeriodicalId":427884,"journal":{"name":"Vestnik of Samara University. Natural Science Series","volume":"43 8","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Procedure of the overdeterminisctic method for finding the field expansion coefficients at the crack tip based on a finite element solution for the stress tensor components\",\"authors\":\"M. A. Fomchenkova, L. V. Stepanova\",\"doi\":\"10.18287/2541-7525-2024-30-2-54-66\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The article proposes and implements a procedure for reconstructing the asymptotic series expansion of stress, strain and displacement fields in anisotropic materials, generalizing the Williams solution for linearly elastic isotropic materials, based on a finite element solution to the problem of deforming a sample with a defect in an anisotropic orthotropic material in the approximation of a plane problem of elasticity theory. The stress field expansion coefficients near the crack tip in an anisotropic material are determined using an overdeterministic method originally proposed to reconstruct the asymptotic expansion from experimental data of a photoelastic study. In this paper, this method is extended to anisotropic materials with various types of symmetry and the novelty of the proposed approach lies in the reconstruction of the asymptotic expansion from the finite element solution for the stress tensor components in the nodes of the finite element grid, which allows us not to exclude their displacement fields components corresponding to the displacement of a body as an absolutely solid body. In the proposed approach, it is possible to use data from finite element calculations directly in the scheme of the overdeterministic method. It is shown that the coefficients of higher approximations are reliably determined by an overdeterministic method based on the stress field found from finite element analysis.\",\"PeriodicalId\":427884,\"journal\":{\"name\":\"Vestnik of Samara University. Natural Science Series\",\"volume\":\"43 8\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-07-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Vestnik of Samara University. Natural Science Series\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.18287/2541-7525-2024-30-2-54-66\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Vestnik of Samara University. Natural Science Series","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.18287/2541-7525-2024-30-2-54-66","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

文章提出并实施了一种重建各向异性材料中应力、应变和位移场渐近级数展开的程序,该程序概括了线性弹性各向同性材料的威廉斯解法,其基础是弹性理论平面问题近似中各向异性正交材料中带有缺陷的样品变形问题的有限元解法。各向异性材料裂纹尖端附近的应力场扩展系数是利用一种超确定性方法确定的,这种方法最初是为了从光弹性研究的实验数据中重建渐近扩展而提出的。本文将这种方法扩展到具有各种对称性的各向异性材料,所提方法的新颖之处在于从有限元解中重建了有限元网格节点中应力张量分量的渐近展开,这使得我们可以不排除与绝对实体位移相对应的位移场分量。在所提出的方法中,可以在超确定性方法方案中直接使用有限元计算的数据。结果表明,基于有限元分析得出的应力场的超确定性方法可以可靠地确定更高的近似系数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Procedure of the overdeterminisctic method for finding the field expansion coefficients at the crack tip based on a finite element solution for the stress tensor components
The article proposes and implements a procedure for reconstructing the asymptotic series expansion of stress, strain and displacement fields in anisotropic materials, generalizing the Williams solution for linearly elastic isotropic materials, based on a finite element solution to the problem of deforming a sample with a defect in an anisotropic orthotropic material in the approximation of a plane problem of elasticity theory. The stress field expansion coefficients near the crack tip in an anisotropic material are determined using an overdeterministic method originally proposed to reconstruct the asymptotic expansion from experimental data of a photoelastic study. In this paper, this method is extended to anisotropic materials with various types of symmetry and the novelty of the proposed approach lies in the reconstruction of the asymptotic expansion from the finite element solution for the stress tensor components in the nodes of the finite element grid, which allows us not to exclude their displacement fields components corresponding to the displacement of a body as an absolutely solid body. In the proposed approach, it is possible to use data from finite element calculations directly in the scheme of the overdeterministic method. It is shown that the coefficients of higher approximations are reliably determined by an overdeterministic method based on the stress field found from finite element analysis.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Solution of the inverse problem of tracer tests interpretation results for oil reservoirs in the presence of low resistance channels Procedure of the overdeterminisctic method for finding the field expansion coefficients at the crack tip based on a finite element solution for the stress tensor components On a de Branges space related to the Riemann zeta function A problem with nonlocal integral 1st kind conditions for 4th order partial differential equation Asymptotics of critical conditions in one combustion model
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1