Element Tests: Solids

1. Axisymmetric analysis of long thin-walled cylinder

A long thin-walled cylinder under internal pressure q is modelled by 2 axisymmetric Q8 elements:

Thin walled cylinder

Figure 119. Thin walled cylinder

Ri is the inner radius, Ro the outer radius, and Rm the mean radius for which the theoretical solution is calculated. The analytical solution is given by the 'pressure vessel formula' for the increase in radius Δ r :

Δ r = q r 2 E t

and for the hoop stress σ zz :

σ zz = q r t

With values Ro = 1010, Ri = 1000, Rm = 1005, t = 10, q = 1.00 and E = 210000.0, one gets Δr = 0.481 and σ zz = 105.0 .