Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep
The analytical method for nonlinear problem of steady-state creep solving for pure shear of stochastically inhomogeneous plane on the basis of the second approximation method of small parameter was developed. It is supposed that elastic deformations are insignificant and they can be neglected. Stoch...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Samara State Technical University
2012-12-01
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| Series: | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| Subjects: | |
| Online Access: | https://journals.eco-vector.com/1991-8615/article/viewFile/20814/17073 |
| _version_ | 1828380688164847616 |
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| author | Nikolay N Popov Olga O Chernova |
| author_facet | Nikolay N Popov Olga O Chernova |
| author_sort | Nikolay N Popov |
| collection | DOAJ |
| description | The analytical method for nonlinear problem of steady-state creep solving for pure shear of stochastically inhomogeneous plane on the basis of the second approximation method of small parameter was developed. It is supposed that elastic deformations are insignificant and they can be neglected. Stochasticity was introduced into the determinative creep equation, which was taken in accordance with the nonlinear theory of viscous flow, through a homogeneous random function of coordinates. By using the decomposition technique of stress tensor components in a small parameter to the members of the second order of smallness, partial differential system of the first and the second approximation of stress was obtained. This system was solved by the introduction of the stress function. The mathematical expectation and variances of the random stress field were calculated. The analysis of the results in the first and second approximations was obtained. |
| first_indexed | 2024-12-10T04:02:39Z |
| format | Article |
| id | doaj.art-8ff58e4be28d4dbd90f926f5a90b4a8d |
| institution | Directory Open Access Journal |
| issn | 1991-8615 2310-7081 |
| language | English |
| last_indexed | 2024-12-10T04:02:39Z |
| publishDate | 2012-12-01 |
| publisher | Samara State Technical University |
| record_format | Article |
| series | Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki |
| spelling | doaj.art-8ff58e4be28d4dbd90f926f5a90b4a8d2022-12-22T02:02:57ZengSamara State Technical UniversityVestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki1991-86152310-70812012-12-011649710518231Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creepNikolay N Popov0Olga O Chernova1Samara State Technical UniversitySamara State Technical UniversityThe analytical method for nonlinear problem of steady-state creep solving for pure shear of stochastically inhomogeneous plane on the basis of the second approximation method of small parameter was developed. It is supposed that elastic deformations are insignificant and they can be neglected. Stochasticity was introduced into the determinative creep equation, which was taken in accordance with the nonlinear theory of viscous flow, through a homogeneous random function of coordinates. By using the decomposition technique of stress tensor components in a small parameter to the members of the second order of smallness, partial differential system of the first and the second approximation of stress was obtained. This system was solved by the introduction of the stress function. The mathematical expectation and variances of the random stress field were calculated. The analysis of the results in the first and second approximations was obtained.https://journals.eco-vector.com/1991-8615/article/viewFile/20814/17073pure shearsmall parameter methodsteady-state creepsecond approximationstochastic problem |
| spellingShingle | Nikolay N Popov Olga O Chernova Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki pure shear small parameter method steady-state creep second approximation stochastic problem |
| title | Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep |
| title_full | Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep |
| title_fullStr | Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep |
| title_full_unstemmed | Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep |
| title_short | Method of pure shear problem solving for stochastically inhomogeneous plane in a steady-state creep |
| title_sort | method of pure shear problem solving for stochastically inhomogeneous plane in a steady state creep |
| topic | pure shear small parameter method steady-state creep second approximation stochastic problem |
| url | https://journals.eco-vector.com/1991-8615/article/viewFile/20814/17073 |
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