Hollow Cylinder in Plain Strain Condition

Overview

The aim of this test case is to validate the following functions:

distributed pressure
symmetry 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.

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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, $ν$

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)	$d_{X}$ $d_{X}$ [m]	5.90E-005	5.89E-005	5.72E-005	-3.10
(B)	$d_{X}$ $d_{X}$ [m]	5.90E-005	5.90E-005	5.72E-005	-3.05
(C)	$d_{X}$ $d_{X}$ [m]	5.90E-005	5.90E-005	5.71E-005	-3.14
(D)	$d_{X}$ $d_{X}$ [m]	5.90E-005	5.89E-005	5.72E-005	-3.05
(A)	$σ_{X X}$ $σ_{X X}$ [Mpa]	-6.00E+001	-5.72E+001	-5.61E+001	-6.45
(B)	$σ_{X X}$ $σ_{X X}$ [Mpa]	-6.00E+001	-6.04E+001	-6.00E+001	-0.02
(C)	$σ_{X X}$ $σ_{X X}$ [Mpa]	-6.00E+001	-5.92E+001	-5.12E+001	-14.63
(D)	$σ_{X X}$ $σ_{X X}$ [Mpa]	-6.00E+001	-5.94E+001	-5.99E+001	-0.19
(A)	$σ_{Y Y}$ $σ_{Y Y}$ [Mpa]	1.00E+002	9.79E+001	1.02E+002	1.51
(B)	$σ_{Y Y}$ $σ_{Y Y}$ [Mpa]	1.00E+002	9.92E+001	1.00E+002	0.00
(C)	$σ_{Y Y}$ $σ_{Y Y}$ [Mpa]	1.00E+002	1.00E+002	1.03E+002	3.49
(D)	$σ_{Y Y}$ $σ_{Y Y}$ [Mpa]	1.00E+002	9.96E+001	9.99E+001	-0.06
(A)	$ϵ_{X X}$ $ϵ_{X X}$	-4.50E-004	-4.33E-004	-4.53E-004	0.71
(B)	$ϵ_{X X}$ $ϵ_{X X}$	-4.50E-004	-4.49E-004	-4.68E-004	3.98
(C)	$ϵ_{X X}$ $ϵ_{X X}$	-4.50E-004	-4.47E-004	-4.35E-004	-3.36
(D)	$ϵ_{X X}$ $ϵ_{X X}$	-4.50E-004	-4.47E-004	-4.67E-004	3.86
(A)	$ϵ_{Y Y}$ $ϵ_{Y Y}$	5.90E-004	5.75E-004	5.71E-004	-3.14
(B)	$ϵ_{Y Y}$ $ϵ_{Y Y}$	5.90E-004	5.88E-004	5.72E-004	-3.05
(C)	$ϵ_{Y Y}$ $ϵ_{Y Y}$	5.90E-004	5.90E-004	5.71E-004	-3.26
(D)	$ϵ_{Y Y}$ $ϵ_{Y Y}$	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

Last updated: January 29th, 2019

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Hollow Cylinder in Plain Strain Condition

Overview

Geometry

Analysis type and Domain

Simulation Setup

Results

References

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