Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
1/10
Organization (S): EDF/IMA/MN
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
Document: V3.05.100
SSLX100 - Mélange 3D - Coque - Poutre in inflection
Summary:
This test makes it possible to validate for a linear elastic design:
· a mixture of various mechanical models: model 3D (element HEXA20), model of hull
(element DKT) and model of beam (elements POU_D_E, or elements COQUE_C_PLAN),
· linear relations between degrees of freedom.
The test is based on the elastic analytical solution of a beam in inflection, the reduced number of elements for
the various models leads to a poor solution, which is however improved clearly with employment of
boundary conditions appropriate to the theory of the beams.
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
2/10
1
Problem of reference
1.1 Geometry
y
hull thickness 1
beam of section
M2
rectangular
B
C2
has
O
C
D
M
X
M1
With
C1
F = - 1.
NR
M4
L1
L2
L3
Z
y
Z
B
has
beam of section
rectangular
L1 = L2 = L3 = 10 mm
B = 1 mm
= 3 mm have
1.2
Material properties
E = 200.000 MPa
= 0.3
= 0.0 make it possible to avoid the variation of orthogonal curvature induced by the effect Poisson in
plates, which causes a difference between the theories of beams and plates, out of average fiber.
1.3
Boundary conditions and loadings
· force Fy=-1 (load 1) or couples Cz=1 (load 2)
· defined or applied to neutral fiber
· embedding of the section X = 0
· continuity of displacements of translation on AB
· continuity of displacements of translation out of C
· equality of displacements of rotation around Z on C1-C2
· for the points M of the section (M1 m2 M4) displacements of translation U (M) depend
linearly displacement of rotation Z of the points P of AB
U (M) = ­ Z (P). y + dx (P)
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
3/10
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution, isostatic structure.
The elastic arrow, elastic constraints and axial deformations and bending moment in all
not X-coordinate X are given by:
· Charge n°1: force Fy = ­ 1
My (X) = Fy. L (1 - X/L)
(= E. Iz. uy " (X) in elasticity)
uy (X) = Fy L. x2. (3 - X/L)/(6. E.Iz)
(in elasticity)

(in elasticity)
xx (X, y) = ­ Fy. L (1 - X/L). y/(E.Iz)

(in elasticity)
xx (X, y) = - Fy. L (1 - X/L). y/Iz
· Charge n°2: Cz=1 or rotation drz couples = Cz.L/(E.Iz)
My (X) = Cz
(= E. Iz. uy " (X) in elasticity)
uy (X) = Cz. x2. /(2. E.Iz)
(in elasticity)

(in elasticity)
xx (X, y) = ­ Cz. y/Iz

(in elasticity)
xx (X, y) = - Cz. y/(E.Iz)
with:
L = L1 + L2 + L3 = 30 mm
Iz = A. h3/12 = 0.25 mm4
drz = 0.0006
2.2
Results of reference
Axial arrows, constraints and deformations and bending moments in 4 points of the axis of the beam.
2.3
Uncertainty on the solution
Analytical solution.
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
4/10
3 Modeling
With
3.1
Characteristics of modeling
Elements HEXA20, DKT and POU_D_E
N19
N18
N17
N25
N20
N16
N24
T4
N15
N13
N14
N12
N11
N26
T3
S1
S2
HE1
N10
N23
N23
N9
N28
N29
T2
N5
T1
N7
identical
N8
N6
N4
N1
N21
N22
N2
N3
Not NR --> N1
Not A --> N4
Not C --> N23
Not D --> N29
Charge n°1: force Fy
Total embedding on the section out of O
3.2
Characteristics of the grid
A number of nodes: 28
A number of meshs and types: 1 HEXA20, 4 TRIA3/DKT, 2 SEG2/POU_D_E
3.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
AFFE
MODELISATION
“3D”
[U4.22.01]
AFFE
MODELISATION
“DKT”
AFFE
MODELISATION
“POU_D_E”
AFFE_CARA_ELEM
COQUE
[U4.24.01]
POUTRE
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
LIAISON_GROUP
LIAISON_DDL
FORCE_NODALE
MECA_STATIQUE
[U4.31.01]
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
5/10
4
Results of modeling A
4.1 Values
tested
· Charge n°1: force Fy
Identification
Reference
Aster
% difference
one (N1 node)
0.
0.
0.
uM (N26 node)
­ 0.0267
­ 0.0231
­ 13.5
uA (N4 node)
­ 0.0267
­ 0.0230
­ 13.8
uC1 (N22 node)
­ 0.0933
­ 0.0855
­ 8.4
CPU (N23 node)
­ 0.0933
­ 0.0856
­ 8.3
uD (N29 node)
­ 0.18
­ 0.1686
­ 6.4
MyN (N1 node)
­ 30.
MyM (N26 node)
­ 20.
MyA (N4 node)
­ 20.
MyC1 (N22 node)
­ 10.
MyC (N23 node)
­ 10.
MyD (N29 node)
0.
4.2 Parameters
of execution
Version: 4.00.02
Machine: CRAY C98
System:
UNICOS 9.0
Obstruction memory:
8 MW
Time CPU To use:
4 seconds
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
6/10
5 Modeling
B
5.1
Characteristics of modeling
Elements HEXA20, DKT and POU_D_E
N19
N18
N17
N25
N20
N16
N24
N15
T4
N13
N14
N12
N11
N26
T3
S1
HE1
S2
N10
N23
N27
N9
N28
N29
T2
N5
T1
N7
N8
N6
N4
N1
N21
N22
N2
N3
Not NR --> N1
Not A --> N4
Not C --> N23
Not D --> N29
Charge n°1: force Fy
Embedding on the section out of O carried out by a connection 3d_POUTRE between the face N1 N13 N19 N7 and
a discrete element located on the origin.
Additional relation, compared to modeling A, between C1 C2 and C, introduced by
LIAISON_ELEM: “COQ_POU”.
5.2
Characteristics of the grid
A number of nodes: 29
A number of meshs and types: 1 HEXA20, 4 TRIA3/DKT, 2 SEG2/POU_D_E, 1 POI1/DIS_TR,
1 QUAD8, 2 SEG2/BORD_DKT
5.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
AFFE
MODELISATION
“3D”
[U4.22.01]
AFFE
MODELISATION
“DKT”
AFFE
MODELISATION
“POU_D_E”
AFFE_CARA_ELEM
COQUE
[U4.24.01]
POUTRE
DISCRET
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
LIAISON_GROU
LIAISON_ELEM
OPTION
“3d_POU”
FORCE_NODALE
“COQ_POU”
MECA_STATIQUE
OPTION
“SIEF_ELGA_DEPL”
[U4.31.01]
“EFGE_ELNO_DEPL”
POST_RELEVE_T
ACTION
OPERATION
“MOYENNE”
[U4.74.04]
RESULTANTE
“DX” “DY” “DZ”
MOMENT
“DRX” “DRY” “DRZ”
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
7/10
6
Results of modeling B
6.1 Values
tested
· Charge n°1: force Fy
Identification
Reference
Aster
% difference
one (N1 node)
0.
­ 3.81 E18
0.
uM (N26 node)
­ 0.0267
­ 0.0260
­ 2.6
uA (N4 node)
­ 0.0267
­ 0.0259
­ 2.9
uC1 (N22 node)
­ 0.0933
­ 0.0928
­ 0.5
CPU (N23 node)
­ 0.0933
­ 0.0929
­ 0.4
uD (N29 node)
­ 0.18
­ 0.1804
+0.2
Mz (not O)
­ 30.
­ 30.
0
Mz (not M)
­ 20.
­ 20.
0
Mz (point C)
­ 10.
­ 10.
0
Mz (N23 node)
­ 10.
­ 10.
0
Mz (N29 node)
0.
0.
0
6.2 Remarks
The moments resulting at the points O, M and C are obtained by POST_RELEVE (moment resulting from
nodal forces on the edges A B and C1 C2).
6.3 Parameters
of execution
Version: 4.00.02
Machine: CRAY C98
System:
UNICOS 9.0
Obstruction memory:
8 MW
Time CPU To use:
4 seconds
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
8/10
7 Modeling
C
7.1
Characteristics of modeling
Elements HEXA20, DKT and COQUE_C_PLAN
N19
N18
N17
N25
N20
N16
N24
T4
N15
N13
N14
N12
N11
N26
T3
S1
HE1
N10
N23
N23
N9
N28
N29
T2
N5
T1
N7
identical
N8
N6
N4
N1
N21
N22
N2
N3
Not NR --> N1
Not A --> N4
Not C --> N23
Not D --> N29
In N29: charge n°1: force Fy, load n°2: Cz or rotation drz couples
Displacements DY and DZ on section 0 null on average (command LIAISON_DDL).
Note:
As the width of the beam is a=3mm, the Young modulus is multiplied by 3 in
material of Coque_C_Plan.
7.2
Characteristics of the grid
A number of nodes: 29
A number of meshs and types: 1 HEXA20, 4 TRIA3/DKT, 1 SEG3/COQUE_C_PLAN
7.3 Functionalities
tested
Commands
Keys
AFFE_MODELE
AFFE
MODELISATION
“3D”
[U4.22.01]
AFFE
MODELISATION
“DKT”
AFFE
MODELISATION
“COQUE_C_PLAN”
AFFE_CARA_ELEM
COQUE
[U4.24.01]
POUTRE
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
LIAISON_GROU
LIAISON_DDL
FORCE_NODALE
MECA_STATIQUE
[U4.31.01]
RECU_CHAMP
RESULTAT
NOM_CHAM
“DEPL”
[U4.62.01]
CALC_ELEM
RESULTAT
OPTION
“EFGE_ELNO_DEPL”
[U4.61.02]
“SIGM_ELNO_DEPL”
“EPSI_ELNO_DEPL”
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
9/10
8
Results of modeling C
8.1 Values
tested
Identification
Reference
Aster (= 0.3)
% difference
Charge 1: force Fy
one (N8 node)
0.
5.97 10-5
0.00
uM (N26 node)
­ 0.0267
­ 0.02528
­ 5.30
uA (N4 node)
­ 0.0267
­ 0.02519
­ 5.64
uC1 (N22 node)
­ 0.0933
­ 0.09136
­ 2.08
CPU (N23 node)
­ 0.0933
­ 0.09148
­ 1.95
uD (N29 node)
­ 0.18
­ 0.1766
- 1.90
MyN (N8 node)
­ 30.
n.c.
MyM (N26 node)
­ 20.
n.c.
MyA (N4 node)
­ 20.
n.c.
MyC1 (N22 node)
­ 10.
n.c.
MyC (N23 node)
­ 10.
n.c.
MyD (N28 node)
- 5.
- 5.0012
0.025
xx (X, H/2) (N28 node)
- 30.0000
- 30.0007
0.025
xx (X, H/2) (N28 node)
­ 5.0 10-5
5.0012 10-5
0.025
Charge 2: Cz couples
one (N1 node)
0.
­ 2.28 10-6
0.00
uM (N26 node)
­ 0.0010
­ 0.001005
0.451
uA (N4 node)
­ 0.0010
­ 0.000998
- 0.224
uC1 (N22 node)
­ 0.0040
­ 0.003998
- 0.052
CPU (N23 node)
­ 0.0040
­ 0.004005
0.117
uD (N29 node)
­ 0.0090
­ 0.009005
0.058
MyD (N28 node)
1.0
0.99952
- 0.048
xx (X, H/2) (N28 node)
6.0000
5.9971
- 0.048
xx (X, H/2) (N28 node)
1.0 10-5
0.9995 10-5
- 0.048
8.2 Remarks
The calculation of the efforts and the moment in the Coque_C_Plan element is carried out with the node N28 medium
so that the interpolation is correct; knowing that the Young modulus is triple so that the product E. Iz
that is to say identical in all the model, the constraints are it too.
8.3 Parameters
of execution
Version: 4.02.12
Machine: CRAY C98
System:
UNICOS 9.0
Obstruction memory:
8 MW
Time CPU To use:
16,2 seconds
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A

Code_Aster ®
Version
4.0
Titrate:
SSLX100 Mélange 3D - Coque - Poutre in inflection
Date: 01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B Page:
10/10
9
Summary of the results
· The grid is very coarse in elements 3D and plate. The test deserves a modeling more
fine, since the results are influenced by the way of describing the conditions
of embedding out of O. the modeling A led to an error of 14% to the maximum,
· however that with a good taking into account of these conditions, the solution is clearly
better (modeling B led to an error of 3% maximum).
· The comparisons of the constraints and efforts give good results (modeling B). For
the element of hull 1D, the results are very good.
Handbook of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A