On the torsion of inhomogeneous and anisotropic bars

Abstract

This paper is concerned with the torsion of anisotropic, linearly elastic cylindrical bars. The solution of the problem in the case where the medium has a plane of elastic symmetry which contains the axis of the cylinder is established. We consider the case of inhomogeneous cylinders where the elastic coefficients are independent of the axial coordinate. We prove that, in general, the torsion induces extension and bending. The solution is new even for homogeneous bodies. The results are used to study the torsion of an anisotropic circular cylinder.

The interlayer shear stress in a double-layered tube of finite length with cylindrical orthotropy and radial inhomogeneity subjected to end torsional loads

“…As to the fundamental expressions of stresses and displacements of a circular hollow tube subjected to torsion, based on the theory of Saint Venant, it is well known that the stress distribution inside the layer body is quite simple: only longitudinal shear stress will be induced if the material anisotropy is not beyond the cylindrically orthotropic [7,8]. And, on this basis, they can be determined using a semi-inverse method, such as [6,[9][10][11] among others, and therefore most of the results express the stress distributions no matter whether on the end surfaces or any cross section are of the same. The expressions obtained through relaxing the boundary effects cannot correctly reflect the real stress and displacement distributions near the boundary, except for the particular boundary conditions coinciding with the Saint Venant distributions.…”