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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2007, Volume 48, Issue 3, Pages 179–190 (Mi pmtf2043)  

This article is cited in 9 scientific papers (total in 9 papers)

Reducing three-dimensional elasticity problems to two-dimensional problems by approximating stresses and displacements by Legendre polynomials

Yu. M. Volchkov, L. A. Dergileva

Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk, 630090
Full-text PDF (218 kB) Citations (9)
Abstract: Shell equations are constructed in orthogonal curvilinear coordinates using approximations of stresses and displacements by Legendre polynomials. The order of the constructed system of differential equations is independent of whether stresses and displacements or their combination are specified on the shell surfaces, which provides the correct formulation of the surface conditions in terms of both displacements and stresses. This allows the system of differential equations of laminated shells to be constructed using matching conditions for displacements and stresses on the contact surfaces.
Keywords: shell equations, Legendre polynomials, elastic curvilinear layer.
Received: 30.10.2006
English version:
Journal of Applied Mechanics and Technical Physics, 2007, Volume 48, Issue 3, Pages 450–459
DOI: https://doi.org/10.1007/s10808-007-0056-1
Bibliographic databases:
Document Type: Article
UDC: 539.3
Language: Russian
Citation: Yu. M. Volchkov, L. A. Dergileva, “Reducing three-dimensional elasticity problems to two-dimensional problems by approximating stresses and displacements by Legendre polynomials”, Prikl. Mekh. Tekh. Fiz., 48:3 (2007), 179–190; J. Appl. Mech. Tech. Phys., 48:3 (2007), 450–459
Citation in format AMSBIB
\Bibitem{VolDer07}
\by Yu.~M.~Volchkov, L.~A.~Dergileva
\paper Reducing three-dimensional elasticity problems to two-dimensional problems by approximating stresses and displacements by Legendre polynomials
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2007
\vol 48
\issue 3
\pages 179--190
\mathnet{http://mi.mathnet.ru/pmtf2043}
\elib{https://elibrary.ru/item.asp?id=17425632}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2007
\vol 48
\issue 3
\pages 450--459
\crossref{https://doi.org/10.1007/s10808-007-0056-1}
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  • https://www.mathnet.ru/eng/pmtf/v48/i3/p179
  • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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