 | | 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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| S. A. Kabrits, V. M. Mal'kov, and S. E. Mansurova, "Nonlinear equations of plane layer for three models of elastomer materials," Mech. Solids. 36 (1), 30-37 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
1 |
Pages |
30-37 |
| Title |
Nonlinear equations of plane layer for three models of elastomer materials |
| Author(s) |
S. A. Kabrits (St. Petersburg)
V. M. Mal'kov (St. Petersburg)
S. E. Mansurova (St. Petersburg) |
| Abstract |
For various models of materials (neo-Hookean, Mooney-Rivlin,
St. Venant-Kirchhoff, and others)
the construction of a nonlinear theory of thin elastomer layer is considered.
Numerical methods are developed for solving
the corresponding nonlinear boundary value problems on
the basis of either the
elasticity equations (in variational form) or
the two-dimensional equations of the layer. The results
of these two approaches are compared.
The perspective aim of the investigation is the creation of
computer programs for the numerical simulation of
large deformations of elastomer bearings
widely used
(in particular, for seismic isolation of buildings and other structures)
when combined loading (compression and shear) is involved.
The proposed methods are based on solving 2D nonlinear boundary value problems
instead of the 3D elasticity equations. The advantages of this approach
are obvious. Indeed, the layer equations do not contain
singularities arising from the small compressibility of the material and
the small thickness of the layer, which makes their
numerical solution much simpler. Our experience shows
that the solution of the nonlinear problem of plane elasticity
for a single thin elastomer layer by the finite element method
requires hours of a Pentium PC operation, whereas
the same problem can be solved
on the basis of the layer equations
within minutes, and the solutions obtained by these two methods
are in good agreement. |
| References |
| 1. | V. M. Mal'kov, Mechanics of Multi-Layer Elastomer Structures [in Russian],
Izd-vo SPbU, St. Petersburg, 1998. |
| 2. | V. M. Mal'kov, "Deformation of a thin layer of a material with
small compressibility," Izv. AN. MTT [Mechanics of Solids]old, No. 3, pp. 87-93, 1987. |
| 3. | P. G. Ciarlet, Mathematical Elasticity [Russian Translation],
Mir, Moscow, 1992. |
| 4. | W. W. Klingbeil and R. T. Shield,
"Large-deformation analysis of bonded elastic mounts,"
ZAMP, Bd. 17, H. 2, S. 281-305, 1966. |
| 5. | L. S. Porter and E. A. Meinecke, "Influence of compression upon
the shear properties of bonded rubber blocks,"
Rubber Chem. Technol, Vol. 53, No. 5, pp. 1133-1144, 1080. |
| 6. | J. M. Kelly, "Progress and prospects in seismic isolation,"
in Proc. Seminar on Base Isolation and Passive Energy Dissipation,
San Francisco, 1986. |
| 7. | P. W. Clark, I. D. Aiken, and J. M. Kelly,
"Experimental testing of reduced-scale seismic isolation bearings
for advanced liquid metal reactor," in
Report of Earthquake Engineering Research Center of the
University of California at Berkeley, 1995. |
|
| Received |
17 September 1999 |
| << Previous article | Volume 36, Issue 1 / 2001 | Next article >> |
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