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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
Organization (S):
EDF/IMA/MN
Manual 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 bending
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 modelized using 20
right elements) and in addition right and curved elements.
The reference solution results from the file of validation of the code LICE. Results obtained with
Code_Aster
are very close (lower deviation than 2.10
4
for the modeling of 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).
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
1
Problem of reference
1.1 Geometry
y
Z
With
B
C
D
E
F
G
F
F
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 = 10
5
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 10
11
AP
= 0.3
= 7800. kg/m
3
= 10
6
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
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
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 the code LICE 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: < 10
3
(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 LICE. Card-index validation of module EFPOU
MPACO/B - Direction of the Studies and Search E.D.F (1988)
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
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
junction component
DIS_T
Limiting conditions:
DDL_IMPO:
(GROUP_NO:Beam
DX: 0. DRY: 0. DRZ: 0. )
(NODE:(A G)
DX: 0. DY: 0. DZ: 0. )
loading case 2
(NODE: With
DX: 0. DY: 1. DZ: 1. )
(only)
(NODE: G
DX: 0. DY:- 1. DZ: 1. )
loading case
1 FORCE_NODALE:(NODE:(C E) FZ = - 1000. )
loading case 3
AFFE_CHAM_NO (SIZE:“TEMP_R”
AFFE:(ALL:“yes” NOM_CMP:“TEMP” VALE_R: 100.)
loading case 4
GRAVITY:(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 mesh
A number of nodes: 7
A number of meshs and types: 6
SEG2
3.3 Functionalities
tested
Controls
Keys
AFFE_CARA_ELEM
BEAM
SECTION
“GENERAL”
[U4.24.01]
DISCRETE
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
NODE
TEMP_CALCULEE
GRAVITY
AFFE_MATERIAU
GROUP_MA
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“POU_C_T'
[U4.22.01]
“POU_D_T'
“DIS_T'
DEFI_MATERIAU
ELAS
[U4.23.01]
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
4
Results of modeling A
4.1 Values
tested
Case
Not
displacement
(m)
Reference
Aster
% diff
tolerance
B
v
B
8.120 10
3
8.1201 10
3
0.00
1. 10
3
1
W
B
1.000 10
2
1.0000 10
2
0.00
-
Forces
C
v
C
7.389 10
3
7.3895 10
3
0.00
-
nodal
D
W
D
2.553 10
2
2.5530 10
2
0.00
-
B
v
B
9.858 10
1
9.8585 10
1
0.00
1. 10
3
2
W
B
1.000
1.0000
0.00
-
Displacement
C
v
C
1.738 10
1
1.7382 10
1
0.01
-
imposed
D
W
D
1.812
1.8120
0.00
-
B
v
B
5.660 10
6
5.6597 10
6
0.01
1. 10
3
3
W
B
-
-
Dilation
C
v
C
1.305 10
4
1.3047 10
4
0.02
-
D
W
D
5.248 10
4
5.2480 10
4
0.00
-
B
v
B
3.111 10
3
3.1107 10
3
0.01
1. 10
3
4
W
B
4.552 10
3
4.5522 10
3
0.00
-
Gravity
C
v
C
1.180 10
3
1.1802 10
3
0.02
D
W
D
8.850 10
3
8.8504 10
3
0.00
4.2 Parameters
of execution
Version: 3.5.2
Machine: CRAY C90
Overall dimension memory:
8 megawords
Time CPU To use:
12 seconds
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
The arc of beam was modelized in a polygonal line of 2 * 20 SEG2
Limiting conditions:
DDL_IMPO:
(GROUP_NO:Npoutre
DX: 0. DRY: 0. DRZ: 0.)
(NODE:(A G)
DX: 0. DY: 0. DZ: 0. ) except for
loading case 2
(NODE: With
DX: 0. DY: 1. DZ: 1. )
(NODE: G
DX: 0. DY:- 1. DZ: 1. )
loading case 1
FORCE_NODALE:(NODE:(C D) Fz = - 1000. )
loading case
AFFE_CHAM_NO (SIZE:“TEMP_R”
AFFE:(ALL:'OUI' Nom_cmp:'TEMP' VALE_R:100.)
loading case 4
GRAVITY:(9.81 0. 0. - 1. )
Name of the nodes: WITH, B, C, D, E, F
5.2
Characteristics of the mesh
A number of nodes: 45
A number of meshs and types: 44
SEG2
5.3 Functionalities
tested
Controls
Keys
AFFE_CARA_ELEM
BEAM
SECTION
“GENERAL”
[U4.24.01]
DISCRETE
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
NODE
TEMP_CALCULEE
GRAVITY
AFFE_MATERIAU
GROUP_MA
[U4.23.02]
AFFE_MODELE
“MECHANICAL”
“POU_D_T'
GROUP_MA
[U4.22.01]
“DIS_T'
NET
DEFI_MATERIAU
ELAS
[U4.23.01]
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
6
Results of modeling B
6.1 Values
tested
Case
Not
displacement
(m)
Reference
Aster
% diff
tolerance
B
v
B
8.120 10
3
8.1209 10
3
0.01
1. 10
3
1
W
B
1.000 10
2
1.0000 10
2
0.00
-
Forces
C
v
C
7.389 10
3
7.3863 10
3
0.04
-
nodal
D
W
D
2.553 10
2
2.5528 10
2
0.01
-
B
v
B
9.858 10
1
9.8585 10
1
0.00
1. 10
3
2
W
B
1.000
1.0000
0.00
-
Displacement
C
v
C
1.738 10
1
1.7374 10
1
0.04
-
imposed
D
W
D
1.812
1.8121
0.
-
B
v
B
5.660 10
6
5.6612 10
6
0.02
1. 10
3
3
W
B
-
-
Dilation
C
v
C
1.305 10
4
1.3051 10
4
0.01
-
D
W
D
5.248 10
4
5.2484 10
4
0.01
-
B
v
B
3.111 10
3
3.1145 10
3
0.11
5. 10
3
4
W
B
4.552 10
3
4.5521 10
3
0.00
-
Gravity
C
v
C
1.180 10
3
1.1409 10
3
3.31
5. 10
2
D
W
D
8.850 10
3
8.8148 10
3
0.40
5. 10
3
6.2 Remarks
The modeling of the elbow by right elements requires a very fine mesh, for a precision
sufficient (in particular for a loading distributed).
6.3 Parameters
of execution
Version: 3.2.11
Machine: CRAY C90
Overall dimension memory:
8 megawords
Time CPU To use:
7.6 seconds
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
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/96/039 - Ind A
7
Summary of the results
Results obtained with
Code_Aster
coincide well with those of the code LICE (solution of
reference) in particular for modeling A (
POU_C_T
).
For modeling B, they are very close also (< 4 10
4
) except in the case of load of
gravity (3% of variation to the maximum) because of the dependence of the solution to the smoothness of
discretization.
This test thus validates the element
POU_C_T
.