Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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in January 1966
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IssuesArchive of Issues2004-1pp.65-72

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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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