The terms and define a trivial null state of stress and are ignored.
The stress components can be obtained by substituting the Michell solution into the equations for stress in terms of the Airy stress function (in cylindrical coordinates). A table of stress components is shown below [from J. R. Barber (2002) ].
Displacements can be obtained from the Michell solution by using the stress-strain and strain-displacement relations. A table of displacement components corresponding the terms in the Airy stress function for the Michell solution is given below. In this table
Note that you can superpose a rigid body displacement on the Michell solution of the form
to obtain an admissible displacement field.
- Michell, J. H. (1899-04-01). "On the direct determination of stress in an elastic solid, with application to the theory of plates". Proc. London Math. Soc. 31 (1): 100–124. doi:10.1112/plms/s1-31.1.100. Retrieved 2008-06-25.
- J. R. Barber, 2002, Elasticity: 2nd Edition, Kluwer Academic Publishers.