On the deformation of orthotropic Cosserat elastic cylinders

Abstract

In this article we are concerned with the linear theory of inhomogeneous and orthotropic Cosserat elastic solids. We study the equilibrium problem for a right cylinder which is subjected to body loads, surface tractions on the lateral surface, and to resultant forces and resultant moments on the ends. The constitutive coefficients are independent of the axial coordinate. First, we study the plane strain problem and establish the solution of the extension and torsion problem. Then, we present a method to derive the solution to the problem of loaded cylinders. The method is new even in the case of homogeneous and isotropic Cosserat elastic bodies. By this method the solution of the three-dimensional problem is reduced to the study of some plane problems. The method is applied to investigate the deformation of a circular cylinder subjected to a uniform load.