Thermal Stresses in Chiral Elastic Beams

Abstract

The chiral effects cannot be described by means of the classical thermoelasticity. In the context of the linear theory of Cosserat thermoelasticity we study the deformation of a chiral beam subjected to a prescribed thermal field. This paper points out the importance of the generalized plane strain problem in the analysis of thermal stresses in chiral elastic beams. First, we investigate the effects of a thermal field which is linear in the axial coordinate. It is shown that this temperature variation produces extension, bending, torsion, flexure and a plane deformation. Then, we study the deformation of the beam when the thermal field is a polynomial of degree m (m > 1) in the axial coordinate. The solution is reduced to the solving of some two-dimensional problems. The method is used to solve the problem of a circular cylinder subjected to a temperature that is independent of the axial coordinate.