Almansi-Michell problem for heterogeneous chiral beams
Keywords:
chiral materials, heterogeneous cylinders, uniformly loaded beams, flexure, reinforced circular cylindersAbstract
This paper is concerned with the deformation of a cylinder composed by two different chiral elastic materials welded together along the surface of separation. We study the equilibrium of a cylinder which is subjected to body loads, to tractions on the lateral surface and to resultant forces and moments on the ends. The Almansi-Michell problem, where the body loads and the surface loading are independent of the axial coordinate, is studied. The intended applications of the solution are to bone implants and to various compound cylinders. The chiral effects cannot be described within classical elasticity. In this aper we use the theory of isotropic chiral Cosserat elastic bodies. The three-dimensional problem is reduced to the study of plane problems. The solution is used to study the deformation of a uniformly loaded circular cylinder reinforced by a longitudinal rod. It is shown that a uniform pressure acting on the lateral surface of the cylinder produces a twist around its axis.
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