 | | 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 and K. B. Ustinov, "Multipoles in an elastic multilayer structure in bending and their applications (continual approximation)," Mech. Solids. 44 (1), 31-44 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
1 |
Pages |
31-44 |
| DOI |
10.3103/S0025654409010038 |
| Title |
Multipoles in an elastic multilayer structure in bending and their applications (continual approximation) |
| Author(s) |
R. L. Salganik (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia)
K. B. Ustinov (Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr-t Vernadskogo 101, str. 1, Moscow, 119526, Russia, ustinov@ipmnet.ru) |
| Abstract |
We consider the equilibrium of a multilayer structure in bending. This structure is assumed to be formed by plane homogeneous and isotropic layers. The strain of each of the layers is described by the classical small bending theory of thin plates with regard to the fact that the layer is acted upon by the neighboring layers, which contact it either directly or through sufficiently compliant interlayers whose flexural rigidity can be neglected. The characteristic scales of variation in all the fields under study treated as functions of coordinates are assumed to exceed the layer thicknesses so much as to justify the description of the structure deformation in the continual approximation. We assume that the layer deflections are completely determined by the transverse loads and are not affected by tangential stresses. We consider multipoles in this structure. Attention is mainly paid to the multipole asymptotics and their applications to the study of solutions far from the regions where the action exerted on structure are mainly concentrated. We present the results of field computations with the use of these asymptotics and of the exact solutions of the corresponding problems for the plane and spatial cases. These results are used to discuss the possibilities of applying the multipole asymptotics for solving the problems approximately. |
| References |
| 1. | G. Sonntag, "Die in Schlichten Gliecher Dicke Reibungsfrei Geschichtete Halbebene mit Periodisch Verteilter Randbelasting," Forsch. Geb. Ing. 23(1/2), 3-8 (1957). |
| 2. | R. L. Salganik, "Continuum Approximation for Describing a Strained LayeredMass," Izv. Akad. Nauk SSSR. Mekh. Tverd. Tela, No. 3, 48-56 (1987) [Mech. Solids (Engl. Transl.)]. |
| 3. | R. L. Salganik, "Mixed Static Boundary-Value Problems for Laminated Elastic Structures Formed by Bending Resistant Layers (a Continuum Approximation)," Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 88-97 (2004) [Mech. Solids (Engl. Transl.) 39 (1), 65-72 (2004)]. |
| 4. | R. L. Salganik and A. N. Mokhel, Continual Approach to Description of Bending Strain and Folding in Bands of Geological Layers. Preprint No. 771, IPMekh RAN (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 2004) [in Russian]. |
| 5. | R. L. Salganik and L. V. Glushkova, Bending of Rectilinear Layers, which Form a Half-Infinite Solid Mass, under the Action of a Given Deflection on the Boundary Available from Urk. NIINTI 27.09.1988, No. 2476-Uk88 (Simferopol, 1988). |
| 6. | K. B. Ustinov and R. L. Salganik, Singularities in an Elastic Continuum Equivalent to a Multilayer Structure with Layers in Bending, Preprint No. 734, IPMekh RAN (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 2003) [in Russian]. |
| 7. | R. L. Salganik, V. G. Markov, A. N. Mokhel, and K. B. Ustinov, Strain of a Multilayer Structure under the Action of a Thermo-Elastic Effect Caused by Formation of a Thin Interlayer Inclusion of Different Temperature (Continual Approximation), Preprint No. 790, IPMekh RAN (Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 2005) [in Russian]. |
| 8. | J. C. Slater and N. H. Frank, Electromagnetism (Dover Publ., New York, 1969). |
| 9. | I. I. Meshkov and B. V. Chirikov, Electromagnetic Field, Vol. 1: Electricity and Magnetism (Nauka, Novosibirsk, 1987) [in Russian]. |
|
| Received |
15 June 2006 |
| Link to Fulltext |
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