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IssuesArchive of Issues2001-1pp.30-37

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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
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