 | | 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
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| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| I. S. Astapov, N. S. Astapov, and E. L. Vasil'eva, "Quadratic approximation of large displacements of a flexible compressed beam," Mech. Solids. 38 (1), 133-138 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
1 |
Pages |
133-138 |
| Title |
Quadratic approximation of large displacements of a flexible compressed beam |
| Author(s) |
I. S. Astapov (Moscow)
N. S. Astapov (Moscow)
E. L. Vasil'eva (Novosibirsk) |
| Abstract |
We consider examples of approximation of elliptic integrals which
demonstrate a method of quadratic approximation of functions
defined in terms of power series. This method is a modification of the
Padé rational approximation method. It is shown that the known formulas for
the approximation of the maximal deflection of a pinned flexible
beam subjected to longitudinal compression can be obtained by means
of the generalized Padé approximation of a complete elliptic integral of the
first kind. New simple formulas are obtained for the maximal deflection
and the shape of a flexible beam subject to plane bending. |
| References |
| 1. | G. A. Baker and P. R. Graves-Morris, Padé Approximants [Russian translation],
Mir, Moscow, 1986. |
| 2. | I. F. Obraztsov, B. V. Nerubailo, and I. V. Andrianov,
Asymptotic Methods in Structural Mechanics of Thin-walled Structures,
Mashinostroenie, Moscow, 1991. |
| 3. | A. H. Nayfeh, Introduction to Perturbation Techniques [Russian translation],
Mir, Moscow, 1984. |
| 4. | A. N. Krylov, "On buckling equilibrium shapes of compressed
columns subjected to longitudinal bending," in Selected Works [in Russian],
pp. 486-538, Izd-vo AN SSSR, Moscow, 1958. |
| 5. | Yu. S. Sikorskii,
Elements of the Theory of Elliptic Functions with Applications to Mechanics
[in Russian], OGIZ, Moscow, Leningrad, 1936. |
| 6. | N. S. Astapov,
"Approximate formulas for the deflection of compressed flexible beams,"
Zh. Prikl. Mekhaniki i Tekhn. Fiziki, Vol. 37, No. 4, pp. 135-138, 1996. |
| 7. | A. R. Rzhanitsyn, Equilibrium Stability of Elastic Systems [in Russian],
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| 10. | M. M. Mostkov,
Refined Solutions of Stability and Bending Problems[in Russian],
Gosizdat Beloruss., Minsk, 1936. |
| 11. | V. A. Kiselev,
Structural Mechanics: A Special Course. Dynamics and Stability of
Structures [in Russian], Stroiizdat, Moscow, 1980. |
| 12. | A. N. Dinnik,
Stability of Elastic Systems [in Russian], ONTI, Moscow, 1935. |
| 13. | E. L. Nikolai,
"On Euler's works on buckling theory," in E. L. Nikolai,
Works in Mechanics [in Russian], pp. 436-454, Gostekhteorizdat, Moscow, 1955. |
| 14. | A. S. Vol'mir,
Stability of Deformable Systems [in Russian], Nauka, Moscow, 1967. |
| 15. | J. M. T. Thompson,
Instability and Catastrophes in Science and Technology [Russian translation], Mir,
Moscow, 1985. |
| 16. | N. A. Alfutov,
Fundamentals of Stability Analysis of Elastic Systems [in Russian],
Mashinostroenie, Moscow, 1991. |
| 17. | R. von Mises, "Zur Steuermathematik,"
ZAMM, Bd. 4, H. 5, S. 436-438, 1924. |
| 18. | S. P. Timoshenko,
Stability of Elastic Systems [in Russian],
Gostekhizdat, Moscow, Leningrad, 1946. |
|
| Received |
28 December 2000 |
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