 | | 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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| V. L. Leont'ev, "A variational-grid method involving orthogonal finite functions for solving problems of natural vibrations of 3D elastic solids," Mech. Solids. 37 (3), 101-109 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
3 |
Pages |
101-109 |
| Title |
A variational-grid method involving orthogonal finite functions for solving problems of natural vibrations of 3D elastic solids |
| Author(s) |
V. L. Leont'ev (Ulyanovsk) |
| Abstract |
In the present paper we consider an application of orthogonal finite
functions in a combined variational-grid method of the mechanics of elastic
deformable solids. The method possesses all advantages of combined methods,
but is characterized by a reduced number of nodal unknowns due to the
orthogonality of the basis functions. As compared with the Ritz
method utilizing the Courant functions the proposed method has better
computational characteristics, specifically, it provides the splitting of
the global system of the grid equations into a number of subsystems and
improves its conditionality. The method allows one to find approximations to
the natural frequencies from below. In combination with the Ritz method, the
proposed method gives two-sided estimates of the natural frequencies. |
| References |
| 1. | I. Daubechies, "Orthonormal bases of compactly supported
wavelets," Communs Pure and Appl. Math., Vol. 41, No. 7, pp. 909-996,
1988. |
| 2. | V. L. Leont'ev, "On the generalization of the Courant functions,"
in Theory of Functions and Approximations. Proc. 7th Saratov Winter
School, 1994. Volume 3 [in Russian],
pp. 36-40, Izd-vo Saratov. Un-ta, Saratov, 1995. |
| 3. | V. L. Leontjew and M. P. Ziplow, "Uber eine projektionen netzlichen
Methode, die mit der Anwendung der miteinander orthogonalen ununterbrochen
en Basisfunktionen mit dem endlichen Trager verknupfen ist," in Des. 1
Russisch-Deutschen Symp. Intelligente Informationstechnologien in der
Entscheidigungfindung, S. 169-173, Moskau, 1995. |
| 4. | V. L. Leont'ev and N. Ch. Lukashanets, "On the grid bases of
orthogonal finite functions," Zh. Vychisl. Matematiki i
Matem. Fiziki [Computational Mathematics and Mathematical Physics],
Vol. 39, No. 7, pp. 1161-1171, 1999. |
| 5. | G. Strang and G. Fix, Theory of the Finite Element Method [Russian
translation], Mir, Moscow, 1977. |
| 6. | V. L. Leont'ev, Finite Element Method in the Theory of Elasticity
(Combined Variational Formulations) [in Russian], Izd-vo Srednevolzh. Nauch.
Tsentra, Ulyanovsk, 1998. |
| 7. | V. Ya. Arsenin, Methods of Mathematical Physics and Special
Functions [in Russian], Nauka, Moscow, 1974. |
|
| Received |
14 April 2000 |
| << Previous article | Volume 37, Issue 3 / 2002 | Next article >> |
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