 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| V. A. Postnov and G. A. Tumashik, "Stability optimization of a cantilever beam subjected to a non-conservative compressive force," Mech. Solids. 41 (2), 72-80 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
2 |
Pages |
72-80 |
| Title |
Stability optimization of a cantilever beam subjected to a non-conservative compressive force |
| Author(s) |
V. A. Postnov (St. Petersburg)
G. A. Tumashik (St. Petersburg) |
| Abstract |
For a cantilever beam subjected to a retarded follower force, the increase
of the critical load by means of the material redistribution along the beam
length is considered. The influence of the time delay parameter
is studied in detail. It is shown that the optimization of a
non-conservatively loaded beam can result in substantial (up to
several times) increase in the critical load. For the optimized beams,
only the flutter instability is observed. As the system
non-conservativeness increases, the critical load multiplicity (i.e., the
number of coinciding local optima) for the optimal beam also
increases. |
| References |
| 1. | V. V. Bolotin, Dynamic Stability of Elastic Systems [in
Russian], Gostekhizdat, Moscow, 1956. |
| 2. | V. V. Bolotin, Non-conservative Problems of the Theory of
Elastic Stability [in Russian], Fizmatgiz, Moscow, 1961. |
| 3. | Ya. G. Panovko and I. I. Gubanova, Stability and Vibrations of
Elastic Systems [in Russian], Nauka, Moscow, 1987. |
| 4. | H. Ziegler, Basic Principles of the Theory of Stability of
Structures [Russian translation], Mir, Moscow, 1971. |
| 5. | V. V. Bolotin, "Dynaimc instabilities in mechanics of structures,"
Applied Mechanics Review, Vol. 52, No. 1, pp. 1-9, 1999. |
| 6. | F. N. Shklyarchuk and T. V. Grishanina, Vibrations in
Non-conservative Systems [in Russian], Izd-vo MAI, Moscow, 1999. |
| 7. | I. Elishakoff, "Elastic stability: From Euler to Koiter;
there was none like Koiter," Meccanica, Vol. 35, pp. 375-380, 2000. |
| 8. | W. T. Koiter, "Unrealistic follower forces," J. Sound and
Vibration, Vol. 196, No. 4, pp. 636-638, 1996. |
| 9. | Y. Sugiyama, M. A. Langthjem, and B.-J. Ryu, "Realistic
follower forces," J. Sound and Vibration, Vol. 199, No. 4,
pp. 779-782, 1999. |
| 10. | A. Pflüger, Stabilitätsprobleme der Elastostatik, Berlin: Göttingen, 1950. |
| 11. | V. I. Feodos'ev, Selected Problems and Questions on the Strength
of Materials [in Russian], Nauka, Moscow, 1996. |
| 12. | M. Beck, "Die Knicklast des einseutig eingespannten,
tangentialen gedrückten Stabes," Zeitschrift für Angewandte
Mathematik und Physik, Vol. 3, pp. 225-228, 476-477, 1952. |
| 13. | K. S. Deineko and M. Ya. Leonov, "Dynamic method for the
buckling analysis of a compressed beam," PMM [Applied Mathematics and Mechanics], Vol. 19, No. 6,
pp. 738-744, 1955. |
| 14. | G. Yu. Dzhanelidze, "On the stability of a beam under a
follower force," Tr. LPI, No. 192, pp. 21-27, 1958. |
| 15. | Z. Celep, "On the vibration and stability of Beck's column
subjected to vertical and follower forces," Zeitschrift für
Angewandte Mathematik und Physik, Vol. 57, pp. 555-557, 1977. |
| 16. | Q. H. Zuo and H. L. Schreyer, "Flutter and divergence instability
of nonconservative
beams and plates," Intern. J. of Solids and Structures, Vol. 33, No. 9,
pp. 1355-1367, 1966. |
| 17. | K. Vepa, "Generalization of an energetic optimality
condition for non-conservative systems," J. Struct. Mech., No. 2,
pp. 229-257, 1973. |
| 18. | F. Odeh, and I. Tadjbakhsh, "The shape of the strongest
column with a follower load," J. Opt. Theory Appl., Vol. 15,
pp. 103-118, 1975. |
| 19. | J. L. Claudon, "Characteristic curves and optimal design of
two structures subjected to circulatory loads," J. de Méchanique,
Vol. 14, No. 3, pp. 531-543, 1975. |
| 20. | M. Hanaoka and K. Washizu, "Optimal design of Beck's column,"
Comput. Struct., Vol. 11, pp. 473-480, 1980. |
| 21. | W. Gutkowski, O. Mahrenholz, and M. Pyrz, "Minimum weight
design of structures under nonconservative forces," in Optimization
of Large Structural Systems, pp. 1087-1100, Kluwer, Dortrecht, 1993. |
| 22. | U. T. Ringertz, "On the design of Beck's column,"
Struct. Optimization, No. 8, pp. 120-124, 1994. |
| 23. | M. A. Langthjem and Y. Sugiyama, "Optimal design of
cantilevered columns under the combined action of conservative and
nonconservative loads," Comput. Struct., Vol. 74, pp. 385-408, 2000. |
| 24. | I. Tadjbakhsh and J. B. Keller, "Strongest columns and
isoperimetric inequalities for eigenvalues," Trans. ASME. Ser. E. J.
Appl. Mech., Vol. 29, No. 1, pp. 159-164, 1962. |
| 25. | V. A. Postnov and G. A. Tumashik, "Optimization of a
cantilever prismatic beam with respect to the critical flutter
load," Probl. Prochnosti i Plastichnosti [in Russian], NNGU, Nizhnii
Novgorod, No. 63, pp. 104-111, 2001. |
|
| Received |
07 October 2005 |
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