Nonclassical Models of the Theory of Plates and Shells
B. D. Annin1, Yu. M. Volchkov1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
Keywords: уравнения теории оболочек, слоистые и композитные оболочки, контактные задачи, полиномы Лежандра, equations of the theory of shells, layered and composite shells, contact problems, Legendre polynomials
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.
DOI: 10.1134/S0021894416050011
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