Exercise $2$: Thin cylinder under pressure $-$ dimension

A thin cylinder of radius $R,$ wall thickness $t$ and length $L$ is submitted to an internal pressure $P.$

Radius r

thickness $t$

The $3$ normal stresses are: ${}_r=0($since it is a thin cylinder$),{}_{}$ and ${}_z$

${}_z=\frac{PR}{2t},{}_{}=\frac{PR}{t}$

Considering linear elastic behavior $(E,v),$ Determine:

The $3$ normal strains ${}_r,{}_{}$ and ${}_z$

The change in thickness $(t),$ the change in length $(L)$ and change of radius $(R)$ when

${}_z=\frac{L}{L},{}_{}=\frac{R}{R},{}_r=\frac{t}{t}$

In addition to the stresses produced by internal pressure only, we consider an axial $($longitudinal$)$ compressive Force $F$

Define longitudinal strain ${}_z$ function of $P,F,rt,E$ and $v$

Define the change in length $(L)$ in this case.