1.5.4 Patch test for axisymmetric elements

Products: ABAQUS/Standard ABAQUS/Explicit

Elements tested

CAX3 CAX3H CAX3T CAX4 CAX4H CAX4I CAX4IH CAX4R CAX4RH CAX4RHT CAX4RT

CAX6 CAX6H CAX6M CAX6MH CAX8 CAX8H CAX8R CAX8RH

Problem description

Material:

Linear elastic, Young's modulus = 1.0 × 10⁶, Poisson's ratio = 0.25.

For coupled temperature-displacement elements dummy thermal properties are prescribed to complete the material definition.

Loading for Step 1:

Displacement boundary conditions applied to all exterior nodes: 10^–3r, 10^–3.

Nonuniform body force: To maintain a constant shear stress 400 and preserve equilibrium, an equilibrating body force, BZNU, is defined in user subroutine DLOAD as BZNU –400, where r is the radius of the integration point.

In the ABAQUS/Explicit simulations this step is followed by an intermediate step in which the model is returned to its unloaded state.

Loading for Step 2:

Displacement boundary conditions applied to all exterior nodes: 10^–2r, 10^–2z.

Loading for Step 3:

Displacement boundary conditions applied to the deformed geometry of Step 2 at all exterior nodes: 10^–3r, 10^–3.

Nonuniform body force (as described for Step 1): BZNU –400.

In the ABAQUS/Standard simulations this step is defined as a perturbation step; in the ABAQUS/Explicit simulations a velocity boundary condition that gives rise to the perturbation is specified instead.

Reference solution

The analytical results for each step are presented below.

Step 1: PERTURBATION

2000.
400.
10^–3.
10^–3.

Step 2: NLGEOM

19900.
0
9.95 × 10^–3.
0.

In the ABAQUS/Explicit simulations this is the third step. (The second step in the ABAQUS/Explicit simulations returns the model to its unloaded state.)

Step 3: PERTURBATION

2000.
400.
1 × 10^–3.
1 × 10^–3.

In the ABAQUS/Explicit simulations this is the fourth step. The results from the third step in the ABAQUS/Explicit simulations must be subtracted from the results of the fourth step to obtain the perturbation about the loaded state.