Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
1/8
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.100
SSLL100 - Symmetrical Structure of beams
with an elbow
Summary:
This test in statics, linear elasticity makes it possible to validate the elements of rectangular beam and curves in inflection
plane, as well as the discrete elements. Four loadings are defined, of which some in local reference mark.
Two modelings make it possible to test on the one hand the right elements (the elbow is modelled using 20
right elements) and in addition right and curved elements.
The reference solution results from the file of validation of code POUX. Results obtained with
Code_Aster are very close (lower deviation than 2.104 for modeling to the arc of circle with POU_C_T,
a little higher variation (3%) for that with POU_D_T, which is due to a too coarse discretization).
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
2/8
1
Problem of reference
1.1 Geometry
F
F
Z
D
C
E
B
F
y
With
G
Symmetrical plane structure compared to the line y = 4.
Beams of section
circular
external diameter
of = 0.04 m
internal diameter
di = 0.01 m
Bend
of center
(y = 4 Z = 0)
and of radius = 2 2 m
Connection node-node
Kx = Kz = 105 NR/m
in the local reference mark
Co-ordinates of the points (in m):
With
B
C
D
E
F
G
X
0.
0.
0.
0.
0.
0.
0.
y
2.
0.
2.
4.
6.
8.
10.
Z
2.
0.
2.
2 2
2.
0.
2.
1.2
Material properties
E = 2.1 1011 Pa
= 0.3
= 7800. kg/m3
= 106 m/°C
1.3
Boundary conditions and loadings
Embedded points A and G
(v = W = 0)
(except in the case of load 2)
Loading:
1) loading concentrated out of C and E
F = 1000 NR
2) displacement imposed of A and G
Dx = 2 in local reference mark of meshs AB and GF
3) thermal expansion with T = 100°C
4) actual weight
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
3/8
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in the card of validation STA.MPACO/B of code POUX of
D.E.R [bib1].
2.2
Results of reference
Displacements of the points B, C and D.
2.3
Uncertainty on the solution
· modeling a: < 103 (finite element providing of the exact values to the nodes),
· B: a few % (numerical solution function of the discretization).
2.4 References
bibliographical
[1]
Computer code of structures of beam POUX. Card-index validation of module EFPOU
MPACO/B - Direction of Etudes and Recherches E.D.F (1988)
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
4/8
3 Modeling
With
3.1
Characteristics of modeling
6 meshs SEG2:
2 meshs CD, EC
curved beam
POU_C_T
2 meshs BC, EFF
right beam
POU_D_T
2 meshs AB, FG
connection element
DIS_T
Limiting conditions:
DDL_IMPO:
(GROUP_NO:Beam
DX: 0. DRY: 0. DRZ: 0. )
(NOEUD:(A G)
DX: 0. DY: 0. DZ: 0. )
loading case 2
(NOEUD: With
DX: 0. DY: 1. DZ: 1. )
(only)
(NOEUD: G
DX: 0. DY:- 1. DZ: 1. )
loading case 1 FORCE_NODALE:(NOEUD:(C E) FZ = - 1000. )
loading case 3 AFFE_CHAM_NO (GRANDEUR:“TEMP_R”
AFFE:(TOUT:“yes” NOM_CMP:“TEMP” VALE_R: 100.)
loading case 4 PESANTEUR:(9.81 0. 0. - 1. )
Name of the nodes: WITH, B, C, D, E, F
Name of the meshs: AB, BC, CD, OF, EFF, FG
3.2
Characteristics of the grid
A number of nodes: 7
A number of meshs and types: 6 SEG2
3.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
POUTRE
SECTION
“GENERALE”
[U4.24.01]
DISCRET
K_T_D_L
“LOCAL”
DEFI_ARC
ORIE_ARC
ORIENTATION
CARA
“VECT_Y”
AFFE_CHAM_NO
“TEMP_R”
“TEMP”
[U4.26.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_NODALE
NOEUD
TEMP_CALCULEE
PESANTEUR
AFFE_MATERIAU
GROUP_MA
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“POU_C_T'
[U4.22.01]
“POU_D_T'
“DIS_T'
DEFI_MATERIAU
ELAS
[U4.23.01]
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
5/8
4
Results of modeling A
4.1 Values
tested
Case
Not
displacement
Reference
Aster
% diff
tolerance
(m)
B
vB
8.120 103
8.1201 103
0.00
1. 103
1
wB
1.000 102
1.0000 102
0.00
-
Forces
C
vC
7.389 103
7.3895 103
0.00
-
nodal
D
wD
2.553 102
2.5530 102
0.00
-
B
vB
9.858 101
9.8585 101
0.00
1. 103
2
wB
1.000
1.0000
0.00
-
Displacement
C
vC
1.738 101
1.7382 101
0.01
-
imposed
D
wD
1.812
1.8120
0.00
-
B
vB
5.660 106
5.6597 106
0.01
1. 103
3
wB
-
-
Dilation
C
vC
1.305 104
1.3047 104
0.02
-
D
wD
5.248 104
5.2480 104
0.00
-
B
vB
3.111 103
3.1107 103
0.01
1. 103
4
wB
4.552 103
4.5522 103
0.00
-
Gravity
C
vC
1.180 103
1.1802 103
0.02
D
wD
8.850 103
8.8504 103
0.00
4.2 Parameters
of execution
Version: 3.5.2
Machine: CRAY C90
Obstruction memory:
8 megawords
Time CPU To use:
12 seconds
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
6/8
5 Modeling
B
5.1
Characteristics of modeling
The arc of beam was modelled in a polygonal line of 2 * 20 SEG2
Limiting conditions:
DDL_IMPO:
(GROUP_NO:Npoutre
DX: 0. DRY: 0. DRZ: 0.)
(NOEUD:(A G)
DX: 0. DY: 0. DZ: 0. ) except for
loading case 2
(NOEUD: With
DX: 0. DY: 1. DZ: 1. )
(NOEUD: G
DX: 0. DY:- 1. DZ: 1. )
loading case 1
FORCE_NODALE:(NOEUD:(C D) Fz = - 1000. )
loading case
AFFE_CHAM_NO (SIZE:“TEMP_R”
AFFE:(TOUT:'OUI' Nom_cmp:'TEMP' VALE_R:100.)
loading case 4
PESANTEUR:(9.81 0. 0. - 1. )
Name of the nodes: WITH, B, C, D, E, F
5.2
Characteristics of the grid
A number of nodes: 45
A number of meshs and types: 44 SEG2
5.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM
POUTRE
SECTION
“GENERALE”
[U4.24.01]
DISCRET
K_T_D_L
“LOCAL”
ORIENTATION
CARA
“VEC_Y”
AFFE_CHAM_NO
“TEMP_R”
“TEMP”
[U4.26.01]
AFFE_CHAR_MECA
DDL_IMPO
GROUP_NO
[U4.25.01]
FORCE_NODALE
NOEUD
TEMP_CALCULEE
PESANTEUR
AFFE_MATERIAU
GROUP_MA
[U4.23.02]
AFFE_MODELE
“MECANIQUE”
“POU_D_T'
GROUP_MA
[U4.22.01]
“DIS_T'
MAILLE
DEFI_MATERIAU
ELAS
[U4.23.01]
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
7/8
6
Results of modeling B
6.1 Values
tested
Case
Not
displacement
Reference
Aster
% diff
tolerance
(m)
B
vB
8.120 103
8.1209 103
0.01
1. 103
1
wB
1.000 102
1.0000 102
0.00
-
Forces
C
vC
7.389 103
7.3863 103
0.04
-
nodal
D
wD
2.553 102
2.5528 102
0.01
-
B
vB
9.858 101
9.8585 101
0.00
1. 103
2
wB
1.000
1.0000
0.00
-
Displacement
C
vC
1.738 101
1.7374 101
0.04
-
imposed
D
wD
1.812
1.8121
0.
-
B
vB
5.660 106
5.6612 106
0.02
1. 103
3
wB
-
-
Dilation
C
vC
1.305 104
1.3051 104
0.01
-
D
wD
5.248 104
5.2484 104
0.01
-
B
vB
3.111 103
3.1145 103
0.11
5. 103
4
wB
4.552 103
4.5521 103
0.00
-
Gravity
C
vC
1.180 103
1.1409 103
3.31
5. 102
D
wD
8.850 103
8.8148 103
0.40
5. 103
6.2 Remarks
The modeling of the elbow by right elements requires a very fine grid, for a precision
sufficient (in particular for a loading distributed).
6.3 Parameters
of execution
Version: 3.2.11
Machine: CRAY C90
Obstruction memory:
8 megawords
Time CPU To use:
7.6 seconds
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Code_Aster ®
Version
4.0
Titrate:
Symmetrical SSLL100 Structure of beams with an elbow
Date:
22/01/98
Author (S):
J.M. PROIX
Key:
V3.01.100-B Page:
8/8
7
Summary of the results
The results obtained with Code_Aster coincide well with those of code POUX (solution of
reference) in particular for modeling A (POU_C_T).
For modeling B, they are very close also (< 4 104) except in the case of load to
gravity (3% of variation to the maximum) because of the dependence of the solution to the smoothness of
discretization.
This test thus validates element POU_C_T.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A