An analytical solution of multi-layered thick-walled tubes in thermo-elasticity with application to gas-wells

Gas-wells are composed of several layers of different materials and undergo at least axial loads, internal and external pressure and temperature differences from inside to outside. In this article, an analytical solution for thick-walled tubes under internal and external pressure, constant axial deformation and a stationary heat distribution is provided. Here, we restrict ourselves to the case of small strain thermo-elasticity. As an example, a gas-well with several layers in the production region is investigated, where the temperature distribution can vary due to temperature cycles. The solution can also be used as verification example for finite element simulations or for comparing it to approximate solutions.