Michell solution
The Michell solution is a general solution to the elasticity equations in polar coordinates (formula_1) developed by J. H. Michell. The solution is such that the stress components are in the form of a Fourier series in formula_2. Michell showed that the general solution can be expressed in terms of an Airy stress function of the form The terms formula_4 and formula_5 define a trivial null state of stress and are ignored. Stress components. 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. Displacement components. Displacements formula_6 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 where formula_8 is the Poisson's ratio, and formula_9 is the shear modulus. Note that a rigid body displacement can be superposed on the Michell solution of the form to obtain an admissible displacement field.