Code_Aster
®
Version
4.0
Titrate:
SSLV114 Movements of solid body 2D and 3D
Date:
26/01/98
Author (S):
J. PELLET
Key:
V3.04.114-A
Page:
1/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
Document: V3.04.114
SSLV114 - Movements of solid body 2D and 3D
Summary:
This test validates (in 2D and 3D) the key word
LIAISON_SOLIDE
control
AFFE_CHAR_MECA
[U4.25.01].
This key word is used to rigidify an expressing whole of nodes by linear relations that displacements
“rigidified” nodes are dependant between them by the equation:
()
()
()
U
U
AM
M
With
With
=
+
.
This equation is valid only in small displacements.
The test problem the 2D and the 3D as well as the particular cases:
·
geometrically confused nodes (2D and 3D),
·
aligned nodes (in 3D).
Code_Aster
®
Version
4.0
Titrate:
SSLV114 Movements of solid body 2D and 3D
Date:
26/01/98
Author (S):
J. PELLET
Key:
V3.04.114-A
Page:
2/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
1
Problem of reference
1.1 Geometry
y
D
C
B
With
2e1, E2, E3
M
I
1
L
H
G
K
X
1
F
J
1
Z
O
NR
2
P
3
Q1, Q2, Q3
y
Problem 2D
3D problem
1.2
Material properties
E = 0
= 0
The finite elements present in this problem are only used to define the ddls carried by the nodes.
Their rigidity must be null.
1.3
Boundary conditions and loadings
In this problem, one defines “solid” groups of nodes:
·
in 2D:
-
WITH, B, C, D
-
E1, E2, E3
·
in 3D:
-
F, G, H, I, J, K, L, M
-
O, NR, P
-
Q1, Q2, Q3
For each one of these groups of nodes, one imposes partial displacements so that them
“solid” move while respecting:
()
()
()
()
()
()
()
()
()
()
in 2D:
translation:
rotation:
in 3D:
translation:
rotation:
T
T
T
T
T
With
E
With
E
F
NR
Q
F
NR
Q
=
=
=
=
=
=
=
=
=
=
1
2
3
1
0 01
1
2
3
4
1
0 001
0 002
0 003
.
.
.
.
.
.
.
.
.
Code_Aster
®
Version
4.0
Titrate:
SSLV114 Movements of solid body 2D and 3D
Date:
26/01/98
Author (S):
J. PELLET
Key:
V3.04.114-A
Page:
3/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
Selected displacements forced to lead to required displacements “solid” are:
2D
DX (A) = 2.
DX (E1) = 2.
DY (A) = 3.
DY (E1) = 3.
DY (B) = 3.001
(+DRZ (E1) = 0.001 for modeling B)
3D
DX (F, NR, Q1) = 2.
DY (F, NR, Q1) = 3.
DZ (F, NR, Q1) = 4.
DY (J, O) = 2.002
DY (J, O) = 2.999
DX (I) = 1.997
+ DRZ (NR) = 0.003
for modeling B
DRX (Q1) = 0.001
DRY (Q1) = 0.002
DRZ (Q1) = 0.003
2
Reference solution
2.1
Method of calculation used for the reference solution
The movement of the “solids” being imposed, the reference solution (in displacement) is it
imposed movement.
The reference solution is thus exact (in small rotations).
2.2
Results of reference
()
()
()
()
()
In 2D:
In 3D:
U
U
U
U
U
C
E
L
P
Q
=
=
=
=
=
1 999
3 001
2
2
3
1 999
3 002
3 999
1 998
3 001
4 000
3
2
3
4
.
.
;
.
.
.
.
.
;
.
.
.
;
.
.
.
2.3
Uncertainty on the solution
Exact solution.
Code_Aster
®
Version
4.0
Titrate:
SSLV114 Movements of solid body 2D and 3D
Date:
26/01/98
Author (S):
J. PELLET
Key:
V3.04.114-A
Page:
4/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
The finite elements affected on the meshs of the mesh are those of modelings D_PLAN and 3D.
ddls carried by the nodes is thus:
DX, DY in 2D,
DX, DY, DZ in 3D
3.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 1
QUAD4
, 1
HEXA8
, 8
SEG2
3.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
LIAISON_SOLIDE
[U4.25.01]
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
DX (C)
1.999
1.999
² 10
12
DY (C)
3.001
3.001
² 10
12
2D DX (E2)
2.000
2.000
² 10
12
DY (E2)
3.000
3.000
² 10
12
DX (L)
1.999
1.999
² 10
12
3D DY (L)
3.002
3.002
² 10
12
DZ (L)
3.999
3.999
² 10
12
DX (P)
1.998
1.998
² 10
12
DY (P)
3.001
3.001
² 10
12
DZ (P)
4.000
4.000
² 10
12
DX (Q3)
2.000
2.000
² 10
12
DY (Q3)
3.000
3.000
² 10
12
DZ (Q3)
4.000
4.000
² 10
12
4.2 Parameters
of execution
Version: 3.04
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
5 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV114 Movements of solid body 2D and 3D
Date:
26/01/98
Author (S):
J. PELLET
Key:
V3.04.114-A
Page:
5/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
The finite elements affected on the meshs of the mesh are those of modelings
D_PLAN
,
COQUE_C_PLAN
, 3D and
POU_D_E
.
·
the nodes 2D carry the ddls DX, DY
(+ DRZ for B and E1),
·
the nodes 3D carry ddls DX, DY, DZ
(+DRX, DRY, DRZ for I, NR and Q1).
5.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 1 QUAD4, 1 HEXA8, 10 SEG2
5.3 Functionalities
tested
Controls
Keys
AFFE_CHAR_MECA
LIAISON_SOLIDE
[U4.25.01]
6
Results of modeling B
6.1 Values
tested
Identification
Reference
Aster
% difference
DX (C)
1.999
1.999
² 10
12
DY (C)
3.001
3.001
² 10
12
2D DX (E2)
2.000
2.000
² 10
12
DY (E2)
3.000
3.000
² 10
12
DX (L)
1.999
1.999
² 10
12
3D DY (L)
3.002
3.002
² 10
12
DZ (L)
3.999
3.999
² 10
12
DX (P)
1.998
1.998
² 10
12
DY (P)
3.001
3.001
² 10
12
DZ (P)
4.000
4.000
² 10
12
DX (Q3)
2.000
2.000
² 10
12
DY (Q3)
3.000
3.000
² 10
12
DZ (Q3)
4.000
4.000
² 10
12
6.2 Parameters
of execution
Version: 3.04
Machine: CRAY C90
System:
UNICOS 8.0
Overall dimension memory:
8 MW
Time CPU To use:
5 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLV114 Movements of solid body 2D and 3D
Date:
26/01/98
Author (S):
J. PELLET
Key:
V3.04.114-A
Page:
6/6
Manual of Validation
V3.04 booklet: Linear statics of the voluminal structures
HI-75/96/017 - Ind A
7
Summary of the results
The results are excellent (
² 10
12
).