Analysis of eigenvalues for problem on the transverse shear crack in material with power defining law
We research the non-linear eigenvalues problem which appears from the problem of determining the stress-strain state near the transverse shear crack tip in material with power relationship between strains and stresses. For the eigenvalues finding we use the perturbation method based on expanding the...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2007-06-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Online Access: | http://mi.mathnet.ru/eng/vsgtu531 |
| _version_ | 1811283245223903232 |
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| author | L. V. Stepanova M. E. Fedina |
| author_facet | L. V. Stepanova M. E. Fedina |
| author_sort | L. V. Stepanova |
| collection | DOAJ |
| description | We research the non-linear eigenvalues problem which appears from the problem of determining the stress-strain state near the transverse shear crack tip in material with power relationship between strains and stresses. For the eigenvalues finding we use the perturbation method based on expanding the eigenvalue, corresponding eigenfunction and the index of non-linearity of material in series in terms of powers of small parameter, which is the difference between the eigenvalues related to the linear and non-linear problems. The comparison between the found eigenvalues and the exact numerical solution of considered non-linear eigenvalues problem is given. |
| first_indexed | 2024-04-13T02:08:03Z |
| format | Article |
| id | doaj.art-4058c66c09df44b7beb6630632ad5840 |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-04-13T02:08:03Z |
| publishDate | 2007-06-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-4058c66c09df44b7beb6630632ad58402022-12-22T03:07:23ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812007-06-012(15)606810.14498/vsgtu531Analysis of eigenvalues for problem on the transverse shear crack in material with power defining lawL. V. StepanovaM. E. FedinaWe research the non-linear eigenvalues problem which appears from the problem of determining the stress-strain state near the transverse shear crack tip in material with power relationship between strains and stresses. For the eigenvalues finding we use the perturbation method based on expanding the eigenvalue, corresponding eigenfunction and the index of non-linearity of material in series in terms of powers of small parameter, which is the difference between the eigenvalues related to the linear and non-linear problems. The comparison between the found eigenvalues and the exact numerical solution of considered non-linear eigenvalues problem is given.http://mi.mathnet.ru/eng/vsgtu531 |
| spellingShingle | L. V. Stepanova M. E. Fedina Analysis of eigenvalues for problem on the transverse shear crack in material with power defining law Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| title | Analysis of eigenvalues for problem on the transverse shear crack in material with power defining law |
| title_full | Analysis of eigenvalues for problem on the transverse shear crack in material with power defining law |
| title_fullStr | Analysis of eigenvalues for problem on the transverse shear crack in material with power defining law |
| title_full_unstemmed | Analysis of eigenvalues for problem on the transverse shear crack in material with power defining law |
| title_short | Analysis of eigenvalues for problem on the transverse shear crack in material with power defining law |
| title_sort | analysis of eigenvalues for problem on the transverse shear crack in material with power defining law |
| url | http://mi.mathnet.ru/eng/vsgtu531 |
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