Analytical solution for spatially axisymmetric problem of thick-walled cylinder subjected to different linearly varying pressures along the axis and uniform pressures at two ends

To our best knowledge, in the open literature, there is no analytical solution of thick-walled cylinder subjected to uniform pressures at two ends and different inner-and outer-surface pressures that are constant circumferentially but vary linearly at different rates along the axis. We now present such a solution. After repeated trials, we have finally succeeded in finding a necessary new displacement function. Based on A. E. H. Love method, the stress, displacement and volume strain formulas are derived by using the new displacement function. The present results include the Lamé’s formulas as special cases. Furthermore, the results obtained here can be applied to not only the thick-walled cylinders subjected to uniform pressures on the inner and outer surface of the thick-walled cylinder, respectively, but also the cylinders subjected to uniform pressures at two ends and different inner-and outer-surface pressures that are constant circumferentially but vary linearly at different rates along the axis, respectively. Finally we give a numerical example to compare our exact method with the approximate method.