Axisymmetric deformation of cylinders made of homogeneous and fiber-reinforced elastic materials in butt-end torsion

The equations of axisymmetric deformation of a circular cylinder made of homogeneous and weakly fiber-reinforced materials in a macroscopically two-dimensional problem statement are presented. The fibers are placed in the axial, circumferential, and radial directions and along spirals in the cylinder wall. They also can lie along opposite spirals in adjacent cylindrical layers, forming an angle-ply reinforcement scheme. At a low content of fibers, it is assumed that they are in the uniaxial stress state, determined by the axial tension or constraint compression in the deformed cylinder. Based on this mathematical model, the deformation of homogeneous and fiber-reinforced elastic cylinders of various length, with free outer surfaces, in butt-end torsion is investigated. The effect of length of the cylinders on their deformation character in torsion is evaluated. The torsion of the cylinders under the conditions of sliding fit along the inner surface and under the action of pressure on the surface, when the initial and deformed configurations are practically congruent, is considered.