This test lets you check the periodicity. The disc is pierced, the inner surface is fit and the outer surface is submitted to a plane torsion. Thus, the geometry and the limit conditions are periodic.


3D model with linear hexahedron elements (HE8), computed with CATIA.


Geometry Specifications

R1 = 0.05 m

R2 = 0.1 m

h = 0.02 m

For symmetry reasons, only 1/8 of the body is modeled. The given results are the same for 1/8 or for the whole body.

Analysis Specifications

Young Modulus (material):
E = 200 GPa

Poisson's Ratio (material):
ν = 0.3

Mesh Specifications:

  • Linear hexahedron elements (HE8)

  • Mesh size: 10 mm

Clamp on surface A (inner cylinder)

Loads (Surface force density):
Tangent to surface B (outer cylinder): 100 N/m2



The table below presents the analysis results:

Type of values

Full disc model (reference)

1/8 disc model

Normalized results (1/8 model / full model)

Maximum displacement amplitude (mm)

1.95247 x 10-7

1.9552 x 10-7


Maximum Von Mises (N/m2)




To Perform the Test:

The periodicity_full.CATAnalysis document presents a complete analysis, computed with a mesh formed of linear hexahedron elements (HE8).

The periodicity_partial.CATAnalysis document presents a partial analysis, computed with a mesh formed of linear hexahedron elements (HE8).

To compute the case, proceed as follow:

  1. Open one of the CATAnalysis documents.

  2. Compute the case in the Generative Structural Analysis workbench.

  3. Create local sensors (Displacement magnitude and Von Mises stress).