Torsion of a two-layer elastic rod with a box section

A two-layer rod with a box section twisted under the action of tangential stresses at angle $\theta$ is considered. It is assumed that the deformations in the rod are elastic and its lateral surface is stress-free. The layers have different elastic properties and different thicknesses. The layer contact line is assumed to be rigid, i.e., the stresses on it coincide. An exact solution describing the stress state of the given structure is constructed using conservation laws. The stress state is determined at each point of the cross section using integrals over external contours.