This article is cited 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

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.

UDC: 539.3

Received: 30.10.2006

 English version: Journal of Applied Mechanics and Technical Physics, 2007, 48:3, 450–459

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