 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| I. A. Brigadnov, "The dual approach to the evaluation of the load-carrying capacity of nonlinearly elastic bodies," Mech. Solids. 39 (2), 30-35 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
2 |
Pages |
30-35 |
| Title |
The dual approach to the evaluation of the load-carrying capacity of nonlinearly elastic bodies |
| Author(s) |
I. A. Brigadnov (St. Petersburg) |
| Abstract |
A variational problem associated with the limiting analysis of nonlinearly
elastic bodies the potentials of which linearly increase with the increase of
the modulus of the distortion tensor is considered. The limiting analysis dual
problem is formulated. The dual problem enables one to find a lower bound for
the limiting load - the magnitude of the external force beyond which
statically determinate deformed configurations stable with respect to finite
variations of the displacements do not exist.
By means of the finite-element approximation the limiting analysis
dual problem is reduced to the convex programming problem with linear
equality constraints. This problem is solved by the standard
conditional gradient method. The effectiveness of the approach proposed
is illustrated by examples. |
| References |
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[in Russian], Izd-vo LGU, 1988. |
| 3. | P. G. Ciarlet, Mathematical Elasticity
[Russian translation], Mir, Moscow, 1992. |
| 4. | J. M. Ball, "Convexity conditions and existence theorems
in nonlinear elasticity,"
Arch. Ration. Mech. Anal., Vol. 63, No. 4, pp. 337-403, 1977. |
| 5. | I. A. Brigadnov, "On the existence of the limiting load in some
problems of hyperelasticity," Izv. AN. MTT [Mechanics of Solids], No. 5,
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| 6. | I. A. Brigadnov, "Mathematical well-posedness of boundary value
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| 7. | I. A. Brigadnov, "Numerical methods in non-linear elasticity," in
Numerical Methods in Engineering, pp. 158-163, Wiley, Chichester, 1996. |
| 8. | I. A. Brigadnov, "Discontinuous solutions and their finite element
approximation in non-linear elasticity," in Advanced Computational Methods in
Engineering, pp. 141-148, Shaker Publishing B.V., Maastricht, 1998. |
| 9. | I. A. Brigadnov, "The limited analysis in finite elasticity," in
Finite Volumes for Complex Applications II, pp. 197-294, Hermes Science Publ.,
Paris, 1999. |
| 10. | I. A. Brigadnov, "The limited static load in finite elasticity," in
Constitutive Models for Rubber, pp. 37-43, Balkema, Rotterdam, 1999. |
| 11. | I. A. Brigadnov, "Evaluation of the bearing capacity of nonlinearly
elastic bodies," Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 6-15, 2001. |
| 12. | I. A. Brigadnov, "Discontinuous mappings and their approximation in
the nonlinear theory of elasticity," Izv. AN. MTT [Mechanics of Solids],
No. 2, pp. 42-53, 2001. |
| 13. | G. M. Bartenev and T. N. Khazanovich,
"The law of hyperelastic deformation of network polymers,"
Vysokomolekulyarnye Soedineniya, Vol. 2, No. 1, pp. 20-28,1960. |
| 14. | E. Giusti, Minimal Surfaces and Functions of Bounded Variation
[Russian translation], Mir, Moscow, 1989. |
| 15. | I. Ekeland and R. Témam,
Convex Analysis and Variational Problems
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| 16. | R. Témam, Mathematical Problems in Plasticity
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| 17. | N. V. Banichuk, Introduction to Structural Optimization
[in Russian], Nauka, Moscow, 1986. |
| 18. | A. Kufner and S. Fucik,
Nonlinear Differential Equations
[Russian translation], Nauka, Moscow, 1988. |
| 19. | Ya. A. Kamenyarzh, Limiting Analysis of Plastic Bodies
and Structures
[in Russian], Nauka, Moscow, 1997. |
| 20. | J. F. Bell, The Experimental Foundations of Solid Mechanics. Part 2.
Finite Strains [Russian translation], Nauka, Moscow, 1984. |
| 21. | M. A. Koltunov, A. S. Kravchuk, and V. P. Maiboroda,
Applied Mechanics of Solids
[in Russian], Vysshaya Shkola, Moscow, 1983. |
| 22. | P. G. Ciarlet, The Finite Element Method for Elliptic Problems
[Russian translation], Mir, Moscow, 1980. |
| 23. | V. G. Karmanov, Mathematical Programming
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| 24. | N. N. Moiseev, Yu. P. Ivanilov, and E. M. Stolyarova, Methods of
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|
| Received |
20 July 2001 |
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