Elastic contact of two cylinders

We study the axially-symmetric problem of contact of two long elastic cylinders one of which is placed into the other under the action of a load varying along the axis. It is shown that if the loaded area is small as compared to the length of the cylinders, then there exist regions of separation, which should be taken into account. The comparison of solutions obtained by taking into account and by neglecting these regions demonstrates that they indeed can be neglected in computing contact stresses (with accuracy sufficient for practical purposes). In addition, we pose and solve a problem of contact interaction of a long elastic cylindrical band with a cylinder placed inside it. For this system, we study the cases of fixed and unknown contact area.