Governing Equations:
$$
\sigma_z = q \left[ 1 - \left\{ \frac{1}{1 + \left( \frac{R}{z} \right)^2} \right\}^{3/2} \right]
$$
$$
\sigma_r = \sigma_\theta = \frac{q}{2} \left[ (1 + 2\nu) - \frac{2(1 + \nu)}{\left\{ 1 + \left( \frac{R}{z} \right)^2 \right\}^{1/2}} + \frac{1}{\left\{ 1 + \left( \frac{R}{z} \right)^2 \right\}^{3/2}} \right]
$$
