 | | 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. I. Gorbachev and V. A. Simakov, "An operator method for solving the equilibrium problem for an elastic inhomogeneous anisotropic slab," Mech. Solids. 39 (2), 43-49 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
2 |
Pages |
43-49 |
| Title |
An operator method for solving the equilibrium problem for an elastic inhomogeneous anisotropic slab |
| Author(s) |
V. I. Gorbachev (Moscow)
V. A. Simakov (Moscow) |
| Abstract |
A unit thickness slab bounded by two parallel face planes
and the lateral surface Σ is considered. The surface Σ
can be formed by the motion of a line segment normal to the midplane
Σ0 along the contour Γ that lies in this plane.
The material of the slab is elastic, anisotropic, and inhomogeneous.
The slab is in a state of equilibrium under the action of loads
distributed over the face planes and the lateral surface. The
load on the lateral surface can be reduced to the forces and
torques applied to the midsurface contour. In the present paper,
a method for solving the problem of elasticity for a slab
(or an infinite layer) is developed. This method applies both
for isotropic (homogeneous or inhomogeneous) and anisotropic
(homogeneous or inhomogeneous) slabs. The method is based
on the introduction of three stress functions so as to satisfy
the equilibrium equations and the boundary conditions on the face
planes. These stress functions are determined by solving
an integro-differential operator equation. Using this method,
we obtained exact (in the sense of Saint-Venant) analytical
solutions for a class of elementary equilibrium problems for
a slab. These solutions are given in the present paper.
For some problems of this class, the solutions have been obtained
previously. In addition, the exact solution of the problem of
the compression of a thickness-inhomogeneous slab by a polynomial
load is solved in this paper. |
| References |
| 1. | B. E. Pobedrya, Lectures on the Tensor Analysis
[in Russian], Izd-vo MGU, Moscow, 1979. |
| 2. | S. P. Timoshenko and S. Woinowsky-Krieger,
Theory of Plates and Shells
[Russian translation], Nauka, Moscow, 1966. |
| 3. | S. G. Lekhnitskii, Anisotropic Plates
[in Russian], Gostekhizdat, 1957. |
| 4. | V. A. Lomakin, Theory of Elasticity of
Inhomogeneous Bodies
[in Russian], Izd-vo MGU, Moscow, 1976. |
| 5. | A. Yu. Ishlinskii,
"On an integro-differential relation in the theory of
an elastic thread (rope) of variable length,"
Ukr. Matem. Zh., Vol. 5, No. 4, pp. 370-374, 1953. |
|
| Received |
14 December 2002 |
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