This article is cited in 23 papers

Nonclassical models of the theory of plates and shells

B. D. Annin^ab, Yu. M. Volchkov<sup>ab

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

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.

UDC: 539.3

Received: 21.09.2016

DOI: 10.15372/PMTF20160501

 English version: Journal of Applied Mechanics and Technical Physics, 2016, 57:5, 769–776

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