Axisymmetric solid elements

A distributed pressure loading of 1000/area is applied on each face.

Response:

Stresses

At every integration point, ${\sigma }_{rr}={\sigma }_{\theta \theta }={\sigma }_{zz}=$ −1000, ${\sigma }_{rz}=$ 0.

Strains

${\epsilon }_{rr}={\epsilon }_{\theta \theta }={\epsilon }_{zz}=$ −1.3333 × 10⁻⁵, ${\epsilon }_{rz}=$ 0.

Displacements

$u_r=$ −1.33 × 10⁻² along $r=$ 1000, $u_z=$ −1.33 × 10⁻⁵z.

For lower-order elements the test description is complete. For higher-order elements, another step definition is included.

Hydrostatic pressure loading is applied along the two vertical faces, varying from 0 at the top to 1000/area at the bottom, in addition to the loads of Step 1.

The following reference solution is obtained for Step 2 using CAXA84 axisymmetric solid elements with nonlinear, asymmetric deformation (input file eref84s3.inp) and is given at $z=$ 0.5.

Stresses

${\sigma }_{rr}=$ −1500, ${\sigma }_{zz}=$ −1000, ${\sigma }_{\theta \theta }=$ −1500, ${\sigma }_{rz}=$ 0.

Strains

${\epsilon }_{rr}=$ −2.5 × 10⁻⁵, ${\epsilon }_{zz}=$ −3.33 × 10⁻⁶, ${\epsilon }_{\theta \theta }=$ −2.5 × 10⁻⁵, ${\epsilon }_{rz}=$ 0.