Hollow cylinder in plain strain condition¶
Overview¶
The aim of this test case is to validate the following functions:
distributed pressure
symmmetry BC
nodal displacements
strains and nodal stresses
The simulation results of SimScale were compared to the analytical results in [SSLV04_A] and the numerical results in [SSLV04]. The meshes used in (A) and (B) were created with the parametrizedtetrahedralizationtool on the SimScale platform and the meshes used in (C) and (D) were meshed with Salome, resulting in four different modelizations.
Geometry¶
A 
B 
E 
F 
A’ 
B’ 
E’ 
F’ 


x [m] 
0.1 
0.2 
2/2 
2 
0.1 
0.2 
2/2 
2 
y [m] 
0 
0 
2/2 
2 
0 
0 
2/2 
2 
z [m] 
0 
0 
0 
0 
0.01 
0.01 
0.01 
0.01 
Analysis type and Domain¶
Tool Type : Code_Aster
Analysis Type : Static (linear elastic)
Mesh and Element types :
Case 
Mesh type 
Number of nodes 
Element type 

(A) 
linear tetrahedral 
1542 
3D isoparametric 
(B) 
quadratic tetrahedral 
9623 
3D isoparametric 
(C) 
linear hexahedral 
768 
3D isoparametric 
(D) 
quadratic hexahedral 
2720 
3D isoparametric 
Simulation Setup¶
Material:
isotropic: E = 200 GPa, \(\nu\) = 0.3
Constraints:
Face EFE’F’ zero normaldisplacement
Face ABA’B’ zero ydisplacement
Face ABEF and face A’B’E’F’ zero zdisplacements fixed
Loads:
Pressure of 60 MPa on Face AEA’E’
Results¶
Comparison of the displacements and stresse at point A obtained with SimScale with the results presented in [SSLV04]. The Error was calculated with respect to [SSLV04_A].
Case 
Quantity 
SimScale 
Error (%) 


(A) 
\(d_X\) [m] 
5.90E005 
5.89E005 
5.72E005 
3.10 
(B) 
\(d_X\) [m] 
5.90E005 
5.90E005 
5.72E005 
3.05 
(C) 
\(d_X\) [m] 
5.90E005 
5.90E005 
5.71E005 
3.14 
(D) 
\(d_X\) [m] 
5.90E005 
5.89E005 
5.72E005 
3.05 
(A) 
\(\sigma_{XX}\) [Mpa] 
6.00E+001 
5.72E+001 
5.61E+001 
6.45 
(B) 
\(\sigma_{XX}\) [Mpa] 
6.00E+001 
6.04E+001 
6.00E+001 
0.02 
(C) 
\(\sigma_{XX}\) [Mpa] 
6.00E+001 
5.92E+001 
5.12E+001 
14.63 
(D) 
\(\sigma_{XX}\) [Mpa] 
6.00E+001 
5.94E+001 
5.99E+001 
0.19 
(A) 
\(\sigma_{YY}\) [Mpa] 
1.00E+002 
9.79E+001 
1.02E+002 
1.51 
(B) 
\(\sigma_{YY}\) [Mpa] 
1.00E+002 
9.92E+001 
1.00E+002 
0.00 
(C) 
\(\sigma_{YY}\) [Mpa] 
1.00E+002 
1.00E+002 
1.03E+002 
3.49 
(D) 
\(\sigma_{YY}\) [Mpa] 
1.00E+002 
9.96E+001 
9.99E+001 
0.06 
(A) 
\(\epsilon_{XX}\) 
4.50E004 
4.33E004 
4.53E004 
0.71 
(B) 
\(\epsilon_{XX}\) 
4.50E004 
4.49E004 
4.68E004 
3.98 
(C) 
\(\epsilon_{XX}\) 
4.50E004 
4.47E004 
4.35E004 
3.36 
(D) 
\(\epsilon_{XX}\) 
4.50E004 
4.47E004 
4.67E004 
3.86 
(A) 
\(\epsilon_{YY}\) 
5.90E004 
5.75E004 
5.71E004 
3.14 
(B) 
\(\epsilon_{YY}\) 
5.90E004 
5.88E004 
5.72E004 
3.05 
(C) 
\(\epsilon_{YY}\) 
5.90E004 
5.90E004 
5.71E004 
3.26 
(D) 
\(\epsilon_{YY}\) 
5.90E004 
5.87E004 
5.72E004 
3.13 