Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance
A study on the accuracy of an approximation of the stress field in a cracked body is presented. Crack-tip stress tensor is expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determ...
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| Format: | Article |
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Gruppo Italiano Frattura
2017-01-01
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| Series: | Fracture and Structural Integrity |
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| Online Access: | http://www.gruppofrattura.it/pdf/rivista/numero39/numero_39_art_14.pdf |
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| _version_ | 1841562298025508864 |
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| author | J. Sobek P. Frantík V. Veselý |
| author_facet | J. Sobek P. Frantík V. Veselý |
| author_sort | J. Sobek |
| collection | DOAJ |
| description | A study on the accuracy of an approximation of the stress field in a cracked body is presented. Crack-tip stress tensor is expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (ODM) for which results from finite element (FE) method computation are usually taken as inputs. Main attention is paid to a detailed analysis of a suitable selection of FE nodes whose results serve as the inputs to the employed method. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen body. Comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical WPS approximation of the stress field based on the FE results and the backward reconstruction of the field (again using WPS) from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study. |
| format | Article |
| id | doaj-art-2a720f475d8644eaaa0a92ddaa257862 |
| institution | Kabale University |
| issn | 1971-8993 1971-8993 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Gruppo Italiano Frattura |
| record_format | Article |
| series | Fracture and Structural Integrity |
| spelling | doaj-art-2a720f475d8644eaaa0a92ddaa2578622025-01-03T01:02:49ZengGruppo Italiano FratturaFracture and Structural Integrity1971-89931971-89932017-01-01113912914210.3221/IGF-ESIS.39.14Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performanceJ. Sobek0P. Frantík1V. Veselý2Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Brno, Czech RepublicBrno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Brno, Czech RepublicBrno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Brno, Czech RepublicA study on the accuracy of an approximation of the stress field in a cracked body is presented. Crack-tip stress tensor is expressed using the linear elastic fracture mechanics (LEFM) theory in this work, more precisely via its multi-parameter formulation, i.e. by Williams power series (WPS). Determination of coefficients of terms of this series is performed using a least squares-based regression technique known as over-deterministic method (ODM) for which results from finite element (FE) method computation are usually taken as inputs. Main attention is paid to a detailed analysis of a suitable selection of FE nodes whose results serve as the inputs to the employed method. Two different ways of FE nodal selection are compared – nodes selected from the crack tip vicinity lying at a ring of a certain radius versus nodes selected more or less uniformly from a specified part of the test specimen body. Comparison of these approaches is made with the help of procedures developed by the authors which enable both the determination of the coefficients of terms of the analytical WPS approximation of the stress field based on the FE results and the backward reconstruction of the field (again using WPS) from those determined terms’ coefficients/functions. The wedge-splitting test (WST) specimen with a crack is taken as example for the study.http://www.gruppofrattura.it/pdf/rivista/numero39/numero_39_art_14.pdfMulti-parameter fracture mechanicsWilliams power seriesCrack-tip fieldsOver-deterministic method |
| spellingShingle | J. Sobek P. Frantík V. Veselý Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance Fracture and Structural Integrity Multi-parameter fracture mechanics Williams power series Crack-tip fields Over-deterministic method |
| title | Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance |
| title_full | Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance |
| title_fullStr | Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance |
| title_full_unstemmed | Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance |
| title_short | Analysis of accuracy of Williams series approximation of stress field in cracked body – influence of area of interest around crack-tip on multi-parameter regression performance |
| title_sort | analysis of accuracy of williams series approximation of stress field in cracked body influence of area of interest around crack tip on multi parameter regression performance |
| topic | Multi-parameter fracture mechanics Williams power series Crack-tip fields Over-deterministic method |
| url | http://www.gruppofrattura.it/pdf/rivista/numero39/numero_39_art_14.pdf |
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