Loading [MathJax]/jax/output/SVG/config.js
Prikladnaya Mekhanika i Tekhnicheskaya Fizika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Prikl. Mekh. Tekh. Fiz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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}
Linking options:
  • https://www.mathnet.ru/eng/pmtf2043
  • https://www.mathnet.ru/eng/pmtf/v48/i3/p179
    • This publication is cited in the following 9 articles:
    1. Olga V. Egorova, Alexey S. Kurbatov, Lev N. Rabinskiy, Sergey I. Zhavoronok, “Modeling of the dynamics of plane functionally graded waveguides based on the different formulations of the plate theory of I. N. Vekua type”, Mechanics of Advanced Materials and Structures, 28:5 (2021), 506  crossref
    2. M. Nikabadze, A. Ulukhanyan, “On the Theory of Multilayer Thin Bodies”, Lobachevskii J Math, 42:8 (2021), 1900  crossref
    3. Mikhail Nikabadze, Armine Ulukhanyan, “Modeling of multilayer thin bodies”, Continuum Mech. Thermodyn., 32:3 (2020), 817  crossref
    4. M. Nikabadze, A. Ulukhanyan, “On the Decomposition of Equations of Micropolar Elasticity and Thin Body Theory”, Lobachevskii J Math, 41:10 (2020), 2060  crossref
    5. M U Nikabadze, M A Bogatyrev, A R Ulukhanyan, “On the Modeling of Thin Bodies of Revolution”, IOP Conf. Ser.: Mater. Sci. Eng., 683:1 (2019), 012017  crossref
    6. Mikhail Nikabadze, Armine Ulukhanyan, Andrey Khizhenkov, “On modeling of three-layered thin bodies”, IOP Conf. Ser.: Mater. Sci. Eng., 683:1 (2019), 012018  crossref
    7. Mikhail U. Nikabadze, Armine R. Ulukhanyan, Tamar Moseshvili, Ketevan Tskhakaia, Nodar Mardaleishvili, Zurab Arkania, “On the Modeling of Five-Layer Thin Prismatic Bodies”, MCA, 24:3 (2019), 69  crossref
    8. Ekaterina L. Kuznetsova, Elena L. Kuznetsova, Lev N. Rabinskiy, Sergey I. Zhavoronok, “On the equations of the analytical dynamics of the quasi-3D plate theory of I. N. Vekua type and some their solutions”, J. vibroeng., 20:2 (2018), 1108  crossref
    9. Boris D. Annin, Yuri M. Volchkov, AIP Conference Proceedings, 1903, 2017, 030030  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Prikladnaya Mekhanika i Tekhnicheskaya Fizika Prikladnaya Mekhanika i Tekhnicheskaya Fizika
    Statistics & downloads:
    Abstract page:50
    Full-text PDF :23
     
      Contact us:
    math-net2025_05@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025