This article is cited in 1 paper

Theory of large-strain torsion of prismatic bodies with moment stresses

A. A. Zelenina

Vorovich Institute of Mechanics and Applied Mathematics, Rostov-on-Don State University, Rostov-on-Don, 344090

Abstract: The problem of the torsion and tension-compression of a prismatic bar with a stress-free lateral surface is studied using three-dimensional elasticity theory for materials with moment stresses. A substitution is found that allows one to separate one variable in the nonlinear equilibrium equations for a Cosserat continuum and boundary conditions on the lateral surface. This substitution reduces the original spatial problem of the equilibrium of a micropolar body to a two-dimensional nonlinear boundary-value problem for a plane region shaped like the cross section of the prismatic bar. Variational formulations of the two-dimensional problem for the section are given that differ in the sets of varied functions and the constraints imposed on their boundary values.

Keywords: large strains, moment stresses, nonlinear Saint Venant’s problem.

UDC: 539.3

Received: 12.09.2005

 English version: Journal of Applied Mechanics and Technical Physics, 2006, 47:4, 600–607

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