 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| M. V. Sorokin, "Application of the Monte-Carlo method to solving linear elasticity problems for an anisotropic medium," Mech. Solids. 39 (3), 27-32 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
3 |
Pages |
27-32 |
| Title |
Application of the Monte-Carlo method to solving linear elasticity problems for an anisotropic medium |
| Author(s) |
M. V. Sorokin (Moscow) |
| Abstract |
The random-walk-along-the-boundary method is considered as applied for solving linear elasticity problems. On the basis of the construction of the fundamental solution for static equations, this method is extended to the case of general anisotropy. This method has been previously applied for solving problems for isotropic media and has demonstrated a number of advantages over difference and variational methods. |
| References |
| 1. | B. E. Pobedrya, Numerical Methods in Elasticity and Plasticity [in Russian], Izd-vo MGU, Moscow, 1995. |
| 2. | B. E. Pobedrya and P. V. Chistyakov, "Solution of 3D elasticity problems by the Monte-Carlo method," PMM [Applied Mathematics and Mechanics],
Vol. 52, No. 3, pp. 341-345, 1988. |
| 3. | K. K. Sabelfeld, Monte-Carlo Methods for Solving Boundary-value Problems [in Russian], Nauka, Novosibirsk, 1989. |
| 4. | K. K. Sabelfeld and N. A. Simonov, Random Walks on Boundary for Solving PDEs, VSP, Utrecht, 1994. |
| 5. | D. Shia and C. Y. Hui, "A Monte-Carlo solution method
for linear elasticity," Int. J. Solids and Struct., Vol. 37,
pp. 6085-6105, 2000. |
| 6. | T. V. Burchuladze and T. G. Gezelia,
The Development of the Potential Method in Elasticity
[in Russian], Mitsniereba, Tbilisi, 1985. |
| 7. | V. D. Kupridze, T. G. Gegelia, M. O. Basheleishvili,
and T. V. Burchuladze, 3D Problems of Mathematical Elasticity and Thermoelasticity [in Russian], Nauka, Moscow, 1976. |
| 8. | B. E. Pobedrya, "The problem in terms of stresses for an anisotropic medium," PMM [Applied Mathematics and Mechanics], Vol. 58, No. 1, pp. 77-85,
1994. |
| 9. | B. E. Pobedrya, "The relationship between the geometric and physical nonlinearities in the theory of elasticity and the meaning of the displacement vector," Izv. AN ArmSSR. Mekhanika, Vol. 11, No. 4, pp. 15-26, 1987. |
|
| Received |
13 January 2003 |
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