 | | 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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| R. L. Salganik, "Mixed static boundary-value problems for laminated elastic structures formed by bending resistant layers (a continuum approximation)," Mech. Solids. 39 (1), 65-72 (2004) |
| Year |
2004 |
Volume |
39 |
Number |
1 |
Pages |
65-72 |
| Title |
Mixed static boundary-value problems for laminated elastic structures formed by bending resistant layers (a continuum approximation) |
| Author(s) |
R. L. Salganik (Moscow) |
| Abstract |
Static boundary-value problems of the elastic deformation of
laminated structures formed by bending resistant plane layers
(plates) are considered in continuum approximation. These are 2D
problems for a half-plane and 3D problems for a half-space, with
the boundaries being parallel to the layers. It is assumed that
the distribution of normal displacements (deflections) is
prescribed on part of the boundary, while the distribution of
normal stresses is prescribed on the remaining portion of the
boundary. The action of tangential stresses is neglected both on
the boundary of the structure and on the interfaces between the
layers. The normal pressure preventing from delamination is
assumed to act normally to the layers. It is assumed, in addition,
that this pressure is uniformly distributed and, hence, does not
affect the deflection. Loading along the layers is assumed absent
or as low as one can neglect the influence of this loading on the
deflection of the layers. Basic types of boundary relations
represented in the general form are considered. These relations
are utilized to solve special problems, first for the 2D case and
then for the 3D axially symmetric case. |
| References |
| 1. | G. Sonntag, "Die in Schichten gleicher Dicke reibungsfrei
geschischtee Halbebene mit periodisch verteilter Randbelastung,"
Forsch. Geb. Ingenieurwesens, Bd. 23, H, 1/2, S. 3-8, 1957. |
| 2. | R. L. Salganik, "Continuous medium approximation for the
description of the deformation of a laminated array," Izv. AN
SSSR. MTT [Mechanics of Solids], No. 3, pp. 48-56, 1987. |
| 3. | R. L. Salganik, "A long elastic surface wave propagating
between the material and an array of bending resistant layers,"
Izv. AN. MTT [Mechanics of Solids], No. 4, pp. 157-166, 2003. |
| 4. | S. P. Timoshenko and S. Woinowsky-Krieger, Theory of
Plates and Shells [Russian translation], Nauka, Moscow, 1966. |
| 5. | R. L. Salganik and L. V. Glushkova, "Bending of
rectilinear layers forming a semi-infinite array subjected to a
prescribed deflection on the boundary," Registered in Ukr. NIINTI
27.09.1988, No. 2476-Uk88. |
| 6. | C. J. Tranter, Integral Transforms in Mathematical Physics
[Russian translation], Gostekhizdat, Moscow, 1956. |
| 7. | I. M. Ryzhik and I. S. Gradshtein, Tables of Integrals,
Sums, Series, and Products [in Russian], Gostekhizdat, 1951. |
| 8. | I. N. Bronshtein and K. A. Semendyaev, Handbook of
Mathematics for Engineers and Higher School Students [in Russian],
Gostekhizdat, Moscow, 1954. |
| 9. | G. A. Korn and Th. M. Korn, Mathematical Handbook for
Scientists and Engineers [Russian translation], Nauka, Moscow,
1984. |
| 10. | H. Bateman and A. Erdélyi, Higher Transcendental
Functions: Bessel Functions, Parabolic Cylindrical Functions, and
Orthogonal Polynomials [Russian translation], Nauka, Moscow, 1966. |
|
| Received |
05 February 2003 |
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