A nonlinear shaft model can be taken into account. The nonlinear model calculates equilibrium of loads in the deformed state.
A beam fixed on one side and radially loaded on the other side will show only radial deflections in the linear model. In the nonlinear model the end point will also move axially and the length of the beam will not increase. A beam fixed on both sides will show an increased stiffness against loading in the center, the stiffness will increase with the loading because of generated axial loads. The nonlinear model is only needed on large deflections; normal shafts in mechanical engineering do not require a nonlinear model.
Currently the nonlinear shaft model cannot be used together with the calculation of natural frequencies if thermal stresses are considered.