The solution for the one-dimensional steady-state heat transfer problem is given in Heat transfer model change: steady state. The solution for the mechanical response of the model is
The expression for is integrated to give
The y-component of strain is given as
Integrating for v gives
where the boundary condition that v=0 at y=0 is used to eliminate the terms that are only functions of x. The condition that
is used to find , and the x-displacement is given as
These expressions are used to calculate the displacements in the model. The temperature distribution can be calculated with the expression from Heat transfer model change: steady state. The results for the axisymmetric case are obtained by replacing x with z and y with () in the relations for temperature and displacements. In addition, the displacements are multiplied by a factor of (), where is the Poisson's ratio. This takes into account the contribution from the approximately constant strain in the circumferential direction.