Case 1

Case 2

Case 3

Case 4

$\underset{Z\to \infty }{\lim }\left\{{{\sigma }_{\theta \theta }^{\ast }|}_{r=R}\right\}$

$\alpha$ - arbitrary

$\underset{\alpha \to 0}{\lim }\left\{{{\sigma }_{\theta \theta }^{\ast }|}_{r=R}\right\}$

z- of course

$\underset{Z\to 0}{\lim }\left\{{{\sigma }_{\theta \theta }|}_{r=R}\right\}$

$\alpha \to 0$

$\underset{\alpha \to 0}{\lim }\left\{{\underset{r\to \infty }{\lim }{\sigma }_{\theta \theta }|}_{r=R}\right\}$

$\alpha$ - of course

Dynamic solution for a plane wave.

Static solution, linear source of expansion waves.

Static solution, pure shear state.

The static problem of the flat deformed state.