Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms
A study on the accuracy of the values of Williams’ expansion terms influenced by rounding numbers is presented. The results are presented taking into account a three-point bend single edge notched beam. Crack tip stress tensor components are expressed using the linear elastic fracture mechanics (LEF...
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| Format: | Article |
| Language: | English |
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Gruppo Italiano Frattura
2017-09-01
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| Series: | Fracture and Structural Integrity |
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| Online Access: | https://www.fracturae.com/index.php/fis/article/view/1936 |
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| author | Vladimir Ruzicka Lucie Malikova Stanislav Seitl |
| author_facet | Vladimir Ruzicka Lucie Malikova Stanislav Seitl |
| author_sort | Vladimir Ruzicka |
| collection | DOAJ |
| description | A study on the accuracy of the values of Williams’ expansion terms influenced by rounding numbers is presented. The results are presented taking into account a three-point bend single edge notched beam. Crack tip stress tensor components are 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 the coefficients of the terms of this series is performed using the least squaresbased regression technique known as the over-deterministic method (ODM), for which displacements data obtained numerically in software ANSYS are taken as inputs. The values of Williams’ expansion terms based on the displacement data obtained are calculated by using various levels of rounding numbers and the results are compared and discussed. |
| format | Article |
| id | doaj-art-89384d248f744d69a3c9fad23ad9eabf |
| institution | Kabale University |
| issn | 1971-8993 |
| language | English |
| publishDate | 2017-09-01 |
| publisher | Gruppo Italiano Frattura |
| record_format | Article |
| series | Fracture and Structural Integrity |
| spelling | doaj-art-89384d248f744d69a3c9fad23ad9eabf2025-01-03T00:39:47ZengGruppo Italiano FratturaFracture and Structural Integrity1971-89932017-09-011142Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion termsVladimir Ruzicka0Lucie Malikova1Stanislav Seitl2Brno University of Technology, Faculty of Civil Engineering, Institute of Structural Mechanics, Veveří 331/95, 602 00 Brno, Czech RepublicAcademy of Sciences of the Czech Republic, Institute of Physics of Materials, v. v. i., Žižkova 22, 616 62 Brno, Czech RepublicAcademy of Sciences of the Czech Republic, Institute of Physics of Materials, v. v. i., Žižkova 22, 616 62 Brno, Czech RepublicA study on the accuracy of the values of Williams’ expansion terms influenced by rounding numbers is presented. The results are presented taking into account a three-point bend single edge notched beam. Crack tip stress tensor components are 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 the coefficients of the terms of this series is performed using the least squaresbased regression technique known as the over-deterministic method (ODM), for which displacements data obtained numerically in software ANSYS are taken as inputs. The values of Williams’ expansion terms based on the displacement data obtained are calculated by using various levels of rounding numbers and the results are compared and discussed.https://www.fracturae.com/index.php/fis/article/view/1936Over-deterministic methodRounding numbersWilliams’ expansionFracture mechanicsStress field |
| spellingShingle | Vladimir Ruzicka Lucie Malikova Stanislav Seitl Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms Fracture and Structural Integrity Over-deterministic method Rounding numbers Williams’ expansion Fracture mechanics Stress field |
| title | Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms |
| title_full | Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms |
| title_fullStr | Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms |
| title_full_unstemmed | Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms |
| title_short | Over-deterministic method: The influence of rounding numbers on the accuracy of the values of Williams’ expansion terms |
| title_sort | over deterministic method the influence of rounding numbers on the accuracy of the values of williams expansion terms |
| topic | Over-deterministic method Rounding numbers Williams’ expansion Fracture mechanics Stress field |
| url | https://www.fracturae.com/index.php/fis/article/view/1936 |
| work_keys_str_mv | AT vladimirruzicka overdeterministicmethodtheinfluenceofroundingnumbersontheaccuracyofthevaluesofwilliamsexpansionterms AT luciemalikova overdeterministicmethodtheinfluenceofroundingnumbersontheaccuracyofthevaluesofwilliamsexpansionterms AT stanislavseitl overdeterministicmethodtheinfluenceofroundingnumbersontheaccuracyofthevaluesofwilliamsexpansionterms |