 | | 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. V. Firsanov, "A method for calculating stress-strain state in elastic systems with unilateral constraints," Mech. Solids. 38 (1), 122-132 (2003) |
| Year |
2003 |
Volume |
38 |
Number |
1 |
Pages |
122-132 |
| Title |
A method for calculating stress-strain state in elastic systems with unilateral constraints |
| Author(s) |
V. V. Firsanov (Moscow) |
| Abstract |
We consider a unified method for calculating the stress-strain state
in an elastic framed structure with nonlinearities accounted for by
unilateral constraints and friction in sliding pairs.
A distinctive feature of the proposed method is that it allows one to
automate calculations.
The method is based on the principle of summation of strain
increments and internal stress increments arising in the process of
proportional loading of the system by an external load depending on a single
parameter, which allows one to replace the corresponding nonlinear
equations by a recurrent sequence of linear equations.
As a result, it becomes possible to evaluate the external load level
at which the structural model should be changed. A cyclic repetition
of the procedure aimed at finding that level is the essence of
the step-by-step method proposed in the present paper.
It is shown that taking into account the unilateral character of
constraints and friction forces in sliding pairs
entails drastic changes in the stress-strain picture of elastic systems. |
| References |
| 1. | V. V. Firsanov,
"A method for the numerical stress-strain analysis of spacecraft members
with structural nonlinearities," Tekhn. Vozd. Flota, Vol. 71, No. 2,
pp. 42-49, 1997. |
| 2. | V. V. Firsanov,
"Strength properties calculation method for aviation constructions
involving constructive nonlinearities," in Proc. 4th MAI/BUAA Intern.
Symp. on Automatic Control [in Russian], pp. 92-96, Moscow, Russia, 1997. |
| 3. | I. M. Rabinovich,
Theoretical Problems of Static Design of Structures with Unilateral
Constraints [in Russian], Stroiizdat, Moscow, 1975. |
| 4. | V. N. Gordeev and A. V. Perl'muter,
"Design of elastic systems with unilateral constraints as a problem of
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No. 15, pp. 208-212, Stroiizdat, Moscow, 1967. |
| 5. | A. V. Perl'muter,
"Application of methods of quadratic programming
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Stroiizdat, Moscow, 1972. |
| 6. | E. N. Kuznetsov,
"Static-kinematic analysis of systems with unilateral constraints,"
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Stroiizdat, Moscow, 1972. |
| 7. | V. A. Bazhenov and V. I. Gulyaev,
"An investigation of loading trajectories for mechanical systems with
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Doklady AN USSR. Ser. Fiz.-Mat. i Tekhn. Nauk., No. 2, pp. 25-28, 1980. |
| 8. | A. Kh. Astrakhan,
"Design of structures with unilateral constraints subject to variable
loads," in Mechanics of Framed Structures and Continuum [in Russian], pp. 64-72,
Leningrad. Inzh. Stroit. In-t, Leningrad, 1980. |
| 9. | L. P. Portaev,
"Design of systems with unilateral constraints subject to increasing
loads," Izv. AN SSSR. MTT [Mechanics of Solids], No. 1, pp. 183-186,
1978. |
| 10. | A. V. Vovkushevskii,
"A computer program for the design of structures with unilateral constraints
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Vol. 120, pp. 43-46, 1978. |
| 11. | A. V. Vovkushanskii and V. A. Durnev,
"Numerical implementation of some methods for solving the
Signorini problem with friction,"
in Finite Element Method and Design of Structures [in Russian],
Trydy Leningrad. Politekh. In-ta, No. 405, pp. 14-19, Leningrad.
Politekh. In-t, Leningrad, 1985. |
| 12. | A. S. Kravchuk,
"To the theory of frictional contact problems," PMM [Applied Mathematics and Mechanics], Vol. 44, No. 1,
pp. 122-129, 1984. |
| 13. | B. R. Torstenfelt,
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Fizmatgiz, Moscow, 1959. |
| 15. | I. F. Obraztsov, L. A. Bulychev, V. V. Vasil'ev, et al.,
Structural Mechanics of Aircraft [in Russian], Mashinostroenie, Moscow, 1986. |
|
| Received |
10 August 2001 |
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