 | | 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. G. Bazhenov, A. I. Kibets, Yu. I. Kibets, and A. N. Samygin, "Numerical solution of 3D nonlinear problems of unsteady deformation of thin-walled structures involving rod members," Mech. Solids. 37 (4), 121-126 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
4 |
Pages |
121-126 |
| Title |
Numerical solution of 3D nonlinear problems of unsteady deformation of thin-walled structures involving rod members |
| Author(s) |
V. G. Bazhenov (Nizhni Novgorod)
A. I. Kibets (Nizhni Novgorod)
Yu. I. Kibets (Nizhni Novgorod)
A. N. Samygin (Nizhni Novgorod) |
| Abstract |
Methods for solving problems of nonlinear deformation of rods
in static and dynamic formulations are presented in [1-6].
Rods can be utilized as components of more complex structures.
Therefore, it is reasonable to develop numerical models and algorithms
allowing one to efficiently solve 3D unsteady problems of
dynamics of composite structures in geometrically and physically
nonlinear formulation. As state equations we use the relations
of the theory of flow with kinematic isotropic hardening.
We use Jourdain's variational principle to derive
the equations of motion of the structure. The hypotheses
of the theory of thin-walled structural elements (rods, plates,
and shells) are introduced at the stage of discretization
of the governing system of equations. This allows one
to take into account specific features of the stress-strain
state of the members of the structure and to simplify the matching
of structural members of different types thereby increasing the
efficiency of this approach. The solution of the problem is based
on the finite element method and an implicit "cross-type"
finite-difference scheme utilized for integration with respect to
time. An 8-node isoparametric element with polylinear shape functions
is implemented to calculate the stress-strain state of massive bodies
and shells [7, 8]. The discretization of curved rods is based on 2-node
finite elements with linear shape functions [5]. In each of these elements,
a local basis is defined. The current position of this basis is determined
by the rod axis and the principal axes of inertia of the cross-section.
We assume the plane cross-section hypothesis and approximate the
rates of the rod displacements by linear functions determined by
the rate of displacement of the rod axis and the angles of rotation
of the cross-section. The rod finite elements are matched
in a common basis. To attach a rod to a massive body or a shell,
the displacement rates of the body or shell are transformed to
the generalized variables characterizing the motion of the rod
cross-section. To illustrate the efficiency of the technique proposed
we present the solution of the nonlinear impact problem for two
pipe-lines in accordance with the shell and shell-rod models. |
| References |
| 1. | V. A. Svetlitskii and O. S. Naraikin, Elastic Members of Machines
[in Russian], Mashinostroenie, Moscow, 1989. |
| 2. | A. A. Ilyukhin, "On constructing the relations of the theory
of elastic rods," in Mechanics of Solids [in Russian], No. 22, pp. 81-92,
Naukova Dumka, Kiev, 1990. |
| 3. | V. A. Polishchuk and V. D. Chuban',
"Equations of elastic deformation of a beam taking into
account an unconstrained warping in the form of the finite
element method,"
Uchenye Zapiski TsAGI, Vol. 15, No. 1, pp. 82-94, 1984. |
| 4. | S. N. Zaitsev, "A curved beam finite element taking
into account geometrically nonlinear deformations,"
Uchenye Zapiski TsAGI, Vol. 22, No. 5, pp. 102-117, 1991. |
| 5. | V. G. Bazhenov, A. I. Kibets, and Yu. I. Kibetz,
"Analysis of unsteady elastoplastic deformation of 3D rods,"
in Applied Problems of Strength and Plasticity [in Russian],
No. 58, pp. 122-128, Tov. Nauchn. Izd KMK, Moscow, 1998. |
| 6. | L. I. Shkutin, "An incremental model of deformation
of a shell," Zh. Prikl. Mechaniki i Tekhn. Fiziki, Vol. 40, No. 4,
pp. 229-235, 1999. |
| . | 7. V. G. Bazhenov and A. I. Kibets,
"Numerical finite element analysis of 3D problems of unsteady deformation
of elastoplastic structures,"
Izv. AN. MTT [Mechanics of Solids], No. 1, pp. 52-59, 1994. |
| 8. | V. G. Bazhenov, A. I. Kibets, and I. N. Tsvetkova,
Numerical simulation of unsteady processes of impact interaction
of deformable structural members,"
Problemy Mashinostroeniya i Nadezhnosti Mashin,
No. 2, pp. 20-26, 1995. |
| 9. | A. S. Vol'mir, Nonlinear Mechanics of Plates and Shells
[in Russian], Nauka, Moscow, 1972. |
|
| Received |
31 March 2000 |
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