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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 parametrized-tetrahedralization-tool on the SimScale platform and the meshes used in (C) and (D) were meshed with Salome, resulting in four different modelizations.

Import validation project into workspace

Geometry

HollowCylinderInPlainStrainCondition-geometry

Geometry of the hollow cylinder

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

HollowCylinderInPlainStrainCondition-mesh-a

Mesh used for the SimScale case (A)

HollowCylinderInPlainStrainCondition-mesh-c

Mesh used for the SimScale case (C)

Simulation Setup

Material:

  • isotropic: E = 200 GPa, \(\nu\) = 0.3

Constraints:

  • Face EFE’F’ zero normal-displacement

  • Face ABA’B’ zero y-displacement

  • Face ABEF and face A’B’E’F’ zero z-displacements 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].

Comparison of the results at point A

Case

Quantity

[SSLV04_A]

[SSLV04]

SimScale

Error (%)

(A)

\(d_X\) [m]

5.90E-005

5.89E-005

5.72E-005

-3.10

(B)

\(d_X\) [m]

5.90E-005

5.90E-005

5.72E-005

-3.05

(C)

\(d_X\) [m]

5.90E-005

5.90E-005

5.71E-005

-3.14

(D)

\(d_X\) [m]

5.90E-005

5.89E-005

5.72E-005

-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)

\(\epsilon_{XX}\)

-4.50E-004

-4.33E-004

-4.53E-004

0.71

(B)

\(\epsilon_{XX}\)

-4.50E-004

-4.49E-004

-4.68E-004

3.98

(C)

\(\epsilon_{XX}\)

-4.50E-004

-4.47E-004

-4.35E-004

-3.36

(D)

\(\epsilon_{XX}\)

-4.50E-004

-4.47E-004

-4.67E-004

3.86

(A)

\(\epsilon_{YY}\)

5.90E-004

5.75E-004

5.71E-004

-3.14

(B)

\(\epsilon_{YY}\)

5.90E-004

5.88E-004

5.72E-004

-3.05

(C)

\(\epsilon_{YY}\)

5.90E-004

5.90E-004

5.71E-004

-3.26

(D)

\(\epsilon_{YY}\)

5.90E-004

5.87E-004

5.72E-004

-3.13

References

SSLV04_A(1,2,3)

Analytical Solution from [SSLV04]

SSLV04(1,2,3,4)

SSLV04 - Cylindre creux en contraintes planes