Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip
The exact analytical solution has been obtained for a problem of orthotropic strip with central semi-infinite crack loaded normally with self-balanced system of forces applied far enough from the crack tip to be considered as applied at infinity. The general solution is expressed as a superposition...
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2019-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
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| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/34666/23015 |
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| author | Konstantin B. Ustinov Dmitry S. Lisovenko Alexander Victorovich Chentsov |
| author_facet | Konstantin B. Ustinov Dmitry S. Lisovenko Alexander Victorovich Chentsov |
| author_sort | Konstantin B. Ustinov |
| collection | DOAJ |
| description | The exact analytical solution has been obtained for a problem of orthotropic strip with central semi-infinite crack loaded normally with self-balanced system of forces applied far enough from the crack tip to be considered as applied at infinity. The general solution is expressed as a superposition of solutions for two modes of loading: (i) symmetrically applied moments; (ii) symmetrically applied transverse forces with compensating moments. The exact expressions for stress intensity factor (SIF) have been obtained. Due to symmetry only the opening mode of SIF is present for each case of loading. For both cases of loading the stress states are determined by two dimensionless parameters composed by four elastic constants. Expression for SIF for the case of loading with symmetrically applied moments is obtained in terms of elementary functions and coincides with the elementary solution due to beam theory. Expression for SIF for the case of loading with symmetrically applied transverse forces with compensating moments has been obtained in terms of one function of one of the parameters expressed as a single integral, multiplied by a power function of the second parameter. The solution for this case demonstrated good agreement with the existing numerical solution for the range of parameters, for which the latter had been obtained. The obtained solution covers all possible range of parameters. |
| first_indexed | 2024-04-13T15:55:56Z |
| format | Article |
| id | doaj.art-16382f63dc8b4a8c9476fa214671974f |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T15:55:56Z |
| publishDate | 2019-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-16382f63dc8b4a8c9476fa214671974f2022-12-22T02:40:41ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812019-12-0123465767031179Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tipKonstantin B. Ustinov0Dmitry S. Lisovenko1Alexander Victorovich Chentsov2Ishlinsky Institute for Problems in Mechanics of the Russian Academy of SciencesIshlinsky Institute for Problems in Mechanics of the Russian Academy of SciencesIshlinsky Institute for Problems in Mechanics of the Russian Academy of SciencesThe exact analytical solution has been obtained for a problem of orthotropic strip with central semi-infinite crack loaded normally with self-balanced system of forces applied far enough from the crack tip to be considered as applied at infinity. The general solution is expressed as a superposition of solutions for two modes of loading: (i) symmetrically applied moments; (ii) symmetrically applied transverse forces with compensating moments. The exact expressions for stress intensity factor (SIF) have been obtained. Due to symmetry only the opening mode of SIF is present for each case of loading. For both cases of loading the stress states are determined by two dimensionless parameters composed by four elastic constants. Expression for SIF for the case of loading with symmetrically applied moments is obtained in terms of elementary functions and coincides with the elementary solution due to beam theory. Expression for SIF for the case of loading with symmetrically applied transverse forces with compensating moments has been obtained in terms of one function of one of the parameters expressed as a single integral, multiplied by a power function of the second parameter. The solution for this case demonstrated good agreement with the existing numerical solution for the range of parameters, for which the latter had been obtained. The obtained solution covers all possible range of parameters.https://journals.eco-vector.com/1991-8615/article/viewFile/34666/23015stress intensity factordelaminationintegral transformwiener–hopf technique |
| spellingShingle | Konstantin B. Ustinov Dmitry S. Lisovenko Alexander Victorovich Chentsov Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki stress intensity factor delamination integral transform wiener–hopf technique |
| title | Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip |
| title_full | Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip |
| title_fullStr | Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip |
| title_full_unstemmed | Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip |
| title_short | Orthotropic strip with central semi-infinite crack under arbitrary loads applied far apart from the crack tip |
| title_sort | orthotropic strip with central semi infinite crack under arbitrary loads applied far apart from the crack tip |
| topic | stress intensity factor delamination integral transform wiener–hopf technique |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/34666/23015 |
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