Elasticity Solution of a Thick Wall Cylinder

The thick wall cylinder shown in Fig. 9.1 is a good example of a problem which is solved using the stress function approach to the solution of two dimensional plane stress or plane strain problems of engineering importance. In this approach, stress fields are derived from a set of potentials, , 

All the elasticity equations given by Eqs. 9.29 - 9.32 as well as the biharmonic stress function equation can be developed for cylindrical coordinates (see, Timoshenko and Goodier, (1970)). The biharmonic equation is written as, 

For axisymmetric problems there can be no dependence on the angle 0 and Eq. 9.40 becomes. 

Using the definition of the relationship between the stress function and stresses in polar coordinates, the stresses in any axisymmetric boundary value problem can be found and are. 

2 Elasticity Solution for a Reinforced Thick Wall Cylinder (Solid Propellant Rocket Problem) 

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