QUAZILINEARIZATION METHOD FOR THE SOLUTION TO THE PROBLEM OF PLATE WITH THE CENTRAL CIRCULAR HOLE UNDER CREEP REGIME
- Authors: Stepanova L.V.1, Zhabbarov R.M.1
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Affiliations:
- Samara National Research University
- Issue: Vol 23, No 2 (2017)
- Pages: 44-50
- Section: Articles
- URL: https://journals.ssau.ru/est/article/view/5151
- DOI: https://doi.org/10.18287/2541-7525-2017-23-2-44-50
- ID: 5151
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Abstract
The approximation solution of the problem for an infinite plate with the circular hole under creep regime is obtained by the quazilinearization method. Four approximations of the solution of the nonlinear problems are found. It is shown that with increasing of the number of approximations the solution converges to the limit numerical solution. It is worth to note that the tangential stress reaches its maximum value not at the circular hole but at the internal point of the plate. It is also shown that quazilinearization method is an effective method for nonlinear problems.
About the authors
L. V. Stepanova
Samara National Research University
Author for correspondence.
Email: morenov@ssau.ru
Russian Federation
R. M. Zhabbarov
Samara National Research University
Email: morenov@ssau.ru
Russian Federation
References
- Kudryashov N.A. Metody nelineinoi matematicheskoi fiziki . Dolgoprudny: Izdatel’skii dom ”Intellekt”, 2010, 368 p. .
- Andrianov I., Avreytsevich Ya. Metody asimptoticheskogo analiza i sinteza v nelineinoi dinamike i mekhanike deformiruemogo tverdogo tela, 2013, 276 p. .
- Bellman R.E., Kalaba R.E. Kvazilinearizatsiia i nelineinye kraevye zadachi . M.: Mir, 1968, 184 p. .
- Stepanova L.V. Matematicheskie metody mekhaniki razrusheniia . Samara: Samarskii universitet, 2006, 242 p. .
- Boyle J.T., Spence J. Analiz napriazhenii v konstruktsiiakh pri polzuchesti . M.: Mir, 1986, 360 p. .
- Stepanova L.V. Eigenspectra and orders of stress singularity at a mode I crack tip for a power – low medium. Comptes Rendus – Mechanique, 2008, №1–2, pp. 232–237 .
- Shifrin E.I. Symmetry properties of the recipricity gap functional in the linear elasticity. International Journal of Fracture, 2009, Vol. 159, no. 2, pp. 209–218 .
- Shifrin E.I., Shushpannikov P.S. Identification of a spheroidal defect in an elastic solid using a reciprocity gap functional. Inverse problems, 2010, Vol. 26, no. 5, p. 055001 .
- Shifrin E.I., Shushpannikov P.S. Identification of small well-separated defects in an isotropic elastic body using boundary measurements. International Journal of Solids and Structures, 2013, Vol. 50, no. 22-23, pp. 3707–3716 .
- Shifrin E.I., Shushpannikov P.S. Reconstruction of an ellipsoidal defect an anisotropic elastic solid, using results of one static test. Inverse Problems in Science and Egineering, 2013, Vol. 21, no. 5, pp. 781–800 .