Plane strain problem for an incompressible nonlinearly elastic solid

V. D. Bondar'

Novosibirsk State University, Novosibirsk, 630090, Russia

Abstract: The plane strain of an incompressible body is studied with geometrical and physical nonlinearity and potential forces taken into account. A nonlinear system of equations for strains is obtained in actual variables, and conditions of its ellipticity are derived in terms of the elastic potential. Boundary conditions for strains are found from specified loads. Analytical solutions of the boundary problem in strains and their corresponding stress fields are found for the case of identical elongations.

Keywords: stresses, strains, elongations, potential forces, incompressibility, nonlinearity, ellipticity.

UDC: 539.3

Received: 07.07.2008

 English version: Journal of Applied Mechanics and Technical Physics, 2009, 50:2, 352–359

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