 | | 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. I. Argatov, "Asymptotic modeling of equilibrium of a rigid body based on the plane surface of an elastic foundation at several points," Mech. Solids. 37 (1), 74-84 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
1 |
Pages |
74-84 |
| Title |
Asymptotic modeling of equilibrium of a rigid body based on the plane surface of an elastic foundation at several points |
| Author(s) |
I. I. Argatov (St. Petersburg) |
| Abstract |
The method of matching of asymptotic expansions is utilized to solve
the contact problem of linear elasticity for the pressure of a system
of rigidly connected punches on an elastic half-space. The diameters
of contact areas are assumed to be small in comparison with the distance
between the punches. A separation of the punches from the foundation
surface is allowed. A mathematical model taking into account
the interaction of contact spots is constructed. The complete set
of governing relations involves the equations of static equilibrium
and compatibility conditions for displacements.
It is well known that the problem of the equilibrium of a rigid body
on a smooth horizontal plane is statically indeterminate for the number of
supporting points exceeding three. Therefore, to determine
the constraint forces, one has to resort to additional assumptions
as regards the elasticity of the foundation. The simplest mathematical
model ([1], Section 112, Subsection 4; [2], Chapter 13, Exercise 26) involves
the concept of the keyboard foundation [3]. In the present paper,
the compatibility relations for the displacements of the rigid body
and the elastic foundation are derived by the method of asymptotic
analysis of the contact problem of elasticity [4-6]. The statement
of this problem allows a separation of the contacting surface of the body
from the foundation. An asymptotically exact model taking into account
the interaction of contact spots is constructed. |
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|
| Received |
10 December 1999 |
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