Antiplane strain of a body undergoing large-rotations

V. D. Bondar'

Novosibirsk State University, Novosibirsk, 630090

Abstract: Antiplane strain of a cylindrical elastic body undergoing large rotations under surface load in the absence of body loads is studied. The form of the elastic potential corresponding to this strain is found. The stresses, the strains, and the displacement are expressed in terms of pressure and two independent strains and the pressure is expressed in terms of the linear strain invariant. For the strains and displacement, nonlinear boundary-value problems are formulated and their ellipticity conditions are given. The linear problem for the displacement is obtained by transformation of variables. An example of determining the displacement is considered.

Keywords: displacement, Almansi strains, rotations, Cauchy stresses, elastic potential, nonlinearity, boundary-value problem.

UDC: 539.3

Received: 04.07.2006

 English version: Journal of Applied Mechanics and Technical Physics, 2007, 48:3, 460–466

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