 | | 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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| P. V. Galpchyan, "A boundary value problem for antiplane deformation of a composite cylinder with cross-section having the form of a circular sector," Mech. Solids. 37 (2), 56-62 (2002) |
| Year |
2002 |
Volume |
37 |
Number |
2 |
Pages |
56-62 |
| Title |
A boundary value problem for antiplane deformation of a composite cylinder with cross-section having the form of a circular sector |
| Author(s) |
P. V. Galpchyan (Erevan) |
| Abstract |
The boundary value problem for the Laplace equation in a two-dimensional
domain in the form of a circular sector is solved by using a
generalization of the Fourier method. The domain
under consideration consists of two circular sectors corresponding to
homogeneous isotropic materials with different shear moduli.
The problem of torsion of composite cylinders has been considered in [1, 2]
where the solution was investigated near the corner point of the
cross-section contour. The case was considered where the interface between
the materials with different shear moduli passes through the corner point.
However, the solution of the boundary value problem in [1] is incomplete,
since the formulas for the stress singularity coefficients determining the
stress state behavior in the vicinity of the singular point were not
obtained. In [2], only the case where the equation determining
the eigenvalues has simple roots was considered.
In [3], the problem of the plane steady-state temperature field in the
composite circular sector was considered. The temperature distribution was
represented as a series expansion in terms of the eigenfunctions of the
corresponding three-point boundary value problem.
In [4], the total spectrum of eigenvalues of the boundary value problem
under consideration was investigated. It was shown that there are three
different kinds of problems, each being of special interest as regards
the construction of the corresponding solutions.
In the present paper we consider the case where the ratio α/β is
a rational number. |
| References |
| 1. | K. S. Chobanyan, Stresses in Composite Elastic Solids [in Russian],
Izd-vo AN ArmSSR, Erevan, 1987. |
| 2. | R. K. Aleksanyan and S. A. Melik-Sarkisyan, "On the torsion of an
anisotropic prismatic rod with a cross-section formed by elliptic sectors,"
Izv. AN ArmSSR. Mekhanika, Vol. 31, No. 1, pp. 40-47, 1978. |
| 3. | R. K. Aleksanyan, "Steady-state temperature field in a composite
circular sector," Izv. AN ArmSSR. Mekhanika, Vol. 24, No. 6, pp. 14-23,
1971. |
| 4. | P. V. Galpchyan, "Boundary value problems for antiplane deformation
of a cylinder composed of different materials." Doklady NAN Armenii,
Vol. 99, No. 1, pp. 22-27, 1999. |
|
| Received |
07 March 2000 |
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