B. D. Annin, Yu. M. Volchkov, “Nonclassical models of the theory of plates and shells”, Prikl. Mekh. Tekh. Fiz., 57:5 (2016), 5–14; J. Appl. Mech. Tech. Phys., 57:5 (2016), 769

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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2016, Volume 57, Issue 5, Pages 5–14
DOI: https://doi.org/10.15372/PMTF20160501 (Mi pmtf785)

This article is cited in 20 scientific papers (total in 20 papers)

Nonclassical models of the theory of plates and shells

B. D. Annin^ab, Yu. M. Volchkov^ab

^a Lavrentyev Institute of Hydrodynamics of Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 630090, Russia
^b Novosibirsk State University, Novosibirsk, 630090, Russia

Full-text PDF (194 kB) Citations (20)

DOI: https://doi.org/10.15372/PMTF20160501

Abstract: Publications dealing with the study of methods of reducing a three-dimensional problem of the elasticity theory to a two-dimensional problem of the theory of plates and shells are reviewed. Two approaches are considered: the use of kinematic and force hypotheses and expansion of solutions of the three-dimensional elasticity theory in terms of the full system of functions. Papers where a three-dimensional problem is reduced to a two-dimensional problem with the use of several approximations of each sought function (stresses and displacements) by segments of the Legendre polynomials are also reviewed.

Keywords: equations of the theory of shells, layered and composite shells, contact problems, Legendre polynomials.

Received: 21.09.2016

English version:
Journal of Applied Mechanics and Technical Physics, 2016, Volume 57, Issue 5, Pages 769–776
DOI: https://doi.org/10.1134/S0021894416050011

Bibliographic databases:

Document Type: Article

UDC: 539.3

Language: Russian

Citation: B. D. Annin, Yu. M. Volchkov, “Nonclassical models of the theory of plates and shells”, Prikl. Mekh. Tekh. Fiz., 57:5 (2016), 5–14; J. Appl. Mech. Tech. Phys., 57:5 (2016), 769–776

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/pmtf785

https://www.mathnet.ru/eng/pmtf/v57/i5/p5

This publication is cited in the following 20 articles:

E. Carrera, D. Scano, M. Petrolo, “Evaluation of Variable Kinematics Beam, Plate, and Shell Theories using the Asymptotic-Axiomatic Method”, Mech. Solids, 2025
Nikolay V. Boyev, Springer Proceedings in Materials, 41, Physics and Mechanics of New Materials and Their Applications, 2024, 399
S. K. Golushko, L. S. Bryndin, V. A. Belyaev, A. G. Gorynin, “A Cubic Version of the Least-Squares Collocation Method and Its Application to the Calculation of Plate Bending”, J. Appl. Ind. Math., 18:3 (2024), 448
S. M. Nguyen, D. R. Shelevaya, D. A. Krasnorutsky, “Using RBF-FD for calculation of hydroelastic vibrations of axisymmetric orthotropic shells of rotation”, Doklady Rossijskoj akademii nauk. Fizika, tehničeskie nauki, 516:1 (2024), 81
V. V. Vasiliev, “Non-Classical Theories of Beams, Plates and Shells (A Review)”, Mech. Solids, 59:6 (2024), 3267
I.S. Telyatnikov, A.V. Pavlova, “K modelirovaniyu medlennykh kolebanii i staticheskogo vzaimodeistviya litosfernykh otdelnostei, “Nauka yuga Rossii””, Science in the South of Russia, 2023, no. 3, 9
Anna G. Knyazeva, Advanced Structured Materials, 198, Advances in Linear and Nonlinear Continuum and Structural Mechanics, 2023, 215
Alla Pavlova, Ilya Telyatnikov, M. Sadriddinov, R. Abdullozoda, G. Devi, G. Khalmatjanova, “On the study of some geological structure models”, E3S Web of Conf., 463 (2023), 03011
S. I. Zhavoronok, A. S. Kurbatov, O. V. Egorova, “On Various Equations of the Analytical Mechanics of Thick-Walled Heterogeneous Shells and Some of Their Applications in Wave Dispersion Problems”, Lobachevskii J Math, 44:6 (2023), 2501
V. N. Bakulin, “MODEL FOR ANALYSIS OF THE STRESS-STRAIN STATE OF THREE-LAYER CYLINDRICAL SHELLS WITH RECTANGULAR CUTOUTS”, Mech. Solids, 57:1 (2022), 102
A. V. Lopatin, V. V. Moskvichev, A. E. Burov, “Solving the problems of mechanics of cylindrical anisogrid lattice bodies of spacecrafts”, J. Appl. Mech. Tech. Phys., 62:5 (2021), 816–827
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
V. N. Bakulin, “Block-Layer Approach for the Analysis of the Stress–Strain State of Three-Layer Irregular Cylindrical Shells of Rotation”, Mech. Solids, 56:7 (2021), 1451
E. Carrera, I. Elishakoff, M. Petrolo, “Who needs refined structural theories?”, Composite Structures, 264 (2021), 113671
V. N. Bakulin, “Layer-by-Layer Stress–Strain Analysis of Irregular Sandwich Shells of Revolution with Non-Zero Gaussian Curvature”, Mech. Solids, 56:7 (2021), 1439
Evgeny M. Zveryaev, Evgeniya M. Tupikova, “Iterative methods for constructing an equations of non-closed shells solution”, Struct. Mech. of Eng. Const. and Build, 17:6 (2021), 588
Mikhail Karavaichenko, Linar Gazaleev, “Numerical modeling of a double-walled spherical reservoir”, PMI, 245 (2020), 561
L N Rabinskiy, S I Zhavoronok, “Modeling of thin-walled structures interacting with acoustic media as constrained two-dimensional continua”, J. Phys.: Conf. Ser., 991 (2018), 012067
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
V. A. Belyaev, V. P. Shapeev, AIP Conference Proceedings, 1893, 2017, 030102

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Related articles in Google Scholar: Russian articles, English articles

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