
This test lets you check analysis results for a thick
cylinder under internal pressure, in the context of a static case. You will
use 3D meshes. 

Reference: AFNOR technique, SFM Paris, Guide de validation des progiciels de
calcul de structures, SSLL 04/89, pp.116117, 1990. 

Specifications
Geometry Specifications
Inner radius:
a = 0.1 m 

Outer radius:
b = 0.2 m 
Height:
h = 20 mm 

For symmetry reasons,
only one quarter of the cylinder is modeled. 


Analysis Specifications
Young Modulus (material):
E = 2 x 10^{5} MPa 

Poisson's Ratio (material):
ν
= 0.3 
Mesh Specifications:
Size = 10mm 
Restraints (Userdefined):
The normal direction is restraint for upper, downer and side faces 
Loads (Pressure):
P = 60 MPa on the inner face 


Results
 The analytical solution of this problem is:
For both components of the stress tensor within the part cylindrical
axis:
For the component of a displacement using the same axis:
 The computed results are presented in the table below:
Position in space 
Image type 
Reference value 
Computed value 
Linear tetrahedron (TE4) 
Parabolic tetrahedron (TE10) 
Linear hexahedron (HE8) 
Parabolic hexahedron (HE20) 




Inner quarter 
Stress principal tensor component (with C3 component
filter) [MPa] 
60 
56.8 
60.1 
52.7 
59.8 
Stress principal tensor component (with C1 component
filter) [MPa] 
100 
104 
100 
104 
101 
Translational displacement vector
[m] 
59 x 10^{6} 
57.2 x 10^{6} 
57.2 x 10^{6} 
57.1 x 10^{6} 
57.2 x 10^{6} 
Outer quarter 
Stress principal tensor component (with C3 component
filter) [MPa] 
0 
0.413 
0.068 
1.02 
0.0432 
Stress principal tensor component (with C1 component
filter) [MPa] 
40 
39 
40 
39.3 
39.7 
Translational displacement vector
[m] 
40 x 10^{6} 
36.2 x 10^{6} 
36.4 x 10^{6} 
36.3 x 10^{6} 
36.4 x 10^{6} 


To Perform the Test:
The
Thick_cylinder_TE10.CATAnalysis document presents a complete analysis,
computed with a mesh formed of parabolic tetrahedron elements (TE10).
The
Thick_cylinder_HE20.CATAnalysis document presents a complete analysis,
computed with a mesh formed of parabolic hexahedron elements (HE20).
To compute the case with linear tetrahedron elements (TE4)
and linear hexahedron elements (HE8), proceed as follow:

Open one of the CATAnalysis documents.

Enter the Advanced Meshing Tools workbench.

In the specification tree, doubleclick on the mesh:
The Global Parameters dialog
box appears.

Select the Linear element type.

Compute the case in the Generative Structural
Analysis workbench.
