 | | 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: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4810 |
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| G. Z. Sharafutdinov, "Stresses in an infinite plate with a free elliptic hole," Mech. Solids. 37 (5), 90-99 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
5 |
Pages |
90-99 |
| Title |
Stresses in an infinite plate with a free elliptic hole |
| Author(s) |
G. Z. Sharafutdinov (Moscow) |
| Abstract |
This paper deals with the problem of the uniaxial tension of
an infinite thin plate with a free elliptic hole. The problem
is considered in 3D formulation and treated in terms of functions
of a complex variable. To that end, a third complex potential
is introduced in addition to the Kolosov-Muskhelishvili
potentials. The representations of the displacement vector,
the stress tensor, and the strain tensor in terms of the three
complex potentials are given. To solve the problem, we utilize
a conformal mapping. The solution is sought in the form of
power series. It is established that the tangential components
of the stress tensor neglected in the plane problem exert
a significant influence. A number of numerical results
characterizing the solution of the problem are presented.
An asymptotic behavior of the stresses as the eccentricity of
the elliptic hole increases without limit is established.
As is known [1], the solutions of problems of elasticity for
the plane stress state are approximate. The refinement of these
solutions by considering 3D formulation of the problem is
of considerable interest. This is especially important for
nonlinear mechanics of solids when determining real stress
and strain fields. The characteristics of these fields are
frequently utilized to identify critical parameters, such as
the ultimate strength, the limit of elasticity
or the yield stress. For the problem under consideration,
such an analysis is particularly important when estimating
the stress-strain state near the tip of a crack modelled
by an elliptic hole in the plate. |
| References |
| 1. | S. P. Timoshenko and J. Goodier,
Theory of Elasticity [Russian translation], Nauka, Moscow, 1975. |
| 2. | N. I. Muskhelishvili, Some Basic Problems of the
Mathematical Theory of Elasticity [in Russian], Nauka, Moscow, 1966. |
| 3. | A. E. H Love, A Treatise on the Mathematical Theory of Elasticity
[Russian translation], ONTI, Moscow, Lenengrad, 1935. |
|
| Received |
04 September 2000 |
| << Previous article | Volume 37, Issue 5 / 2002 | Next article >> |
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