Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
1/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
Organization (S)
: EDF/IMA/MN
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
Document: V3.05.100
SSLX100 - Mix 3D - Hull - Beam in bending
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 bending, 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.
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
2/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
Z
y
X
O
D
C
C1
C2
M2
M4
M1
NR
L1
L2
L3
hull thickness 1
beam of section
rectangular
With
B
M
F = - 1.
Z
y
has
B
beam of section
rectangular
has
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 F
y
=-1 (load 1) or couples C
Z
=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
points P of AB
U (M) =
Z
(P). y + dx (P)
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
3/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution,
isostatic structure
.
The elastic arrow, elastic stresses and axial deformations and bending moment in all
not X-coordinate X are given by:
·
Charge n°1: force F
y
= 1
M
y
(X) = F
y
. L (1 - X/L)
(= E. I
Z
. U
y
“(X) in elasticity)
U
y
(X) = F
y
L. X
2
. (3 - X/L)/(6. E.I
Z
)
(in elasticity)
xx
(X, y) = F
y
. L (1 - X/L). y/(E.I
Z)
(in elasticity)
xx
(X, y) = - F
y
. L (1 - X/L). y/I
Z
(in elasticity)
·
Charge n°2: C couples
Z
=1 or rotation Dr.
Z
= C
Z
.L/(E.I
Z
)
M
y
(X) = C
Z
(= E. I
Z
. U
y
“(X) in elasticity)
U
y
(X) = C
Z
. X
2
. /(2. E.I
Z
)
(in elasticity)
xx
(X, y) = C
Z
. y/I
Z
(in elasticity)
xx
(X, y) = - C
Z
. y/(E.I
Z)
(in elasticity)
with:
L = L1 + L2 + L3 = 30 mm
I
Z
= A.H
3
/12 = 0.25 mm
4
Dr.
Z
= 0.0006
2.2
Results of reference
Axial arrows, stresses and deformations and bending moments in 4 points of the axis of the beam.
2.3
Uncertainty on the solution
Analytical solution.
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
4/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
Elements
HEXA20
,
DKT
and
POU_D_E
N13
N18
N17
N7
N1
N8
N2
N24
N6
N14
N20
N19
N9
N12
N5
N4
N3
N11
N10
N21
N22
N25
N23
N26
N23
N28
N29
Not NR --> N1
Not A --> N4
Not C --> N23
Not D --> N29
N15
N16
identical
HE1
T4
T3
T2
T1
S1
S2
Charge n°1: force F
y
Total embedding on the section out of O
3.2
Characteristics of the mesh
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
Controls
Keys
AFFE_MODELE
AFFE
MODELING
“3D”
[U4.22.01]
AFFE
MODELING
“DKT”
AFFE
MODELING
“POU_D_E”
AFFE_CARA_ELEM
HULL
[U4.24.01]
BEAM
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
LIAISON_GROUP
LIAISON_DDL
FORCE_NODALE
MECA_STATIQUE
[U4.31.01]
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
5/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
·
Charge n°1: force F
y
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
M
yN
(N1 node)
30.
M
yM
(N26 node)
20.
M
teststemyŕ
(N4 node)
20.
M
yC1
(N22 node)
10.
M
teststemyç
(N23 node)
10.
M
yD
(N29 node)
0.
4.2 Parameters
of execution
Version: 4.00.02
Machine: CRAY C98
System:
UNICOS 9.0
Overall dimension memory:
8 MW
Time CPU To use:
4 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
6/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
5 Modeling
B
5.1
Characteristics of modeling
Elements
HEXA20
,
DKT
and
POU_D_E
N13
N18
N17
N7
N1
N8
N2
N24
N6
N14
N20
N19
N9
N12
N5
N4
N3
N11
N10
N21
N22
N25
N23
N26
N27
N28
N29
Not NR --> N1
Not A --> N4
Not C --> N23
Not D --> N29
N15
N16
HE1
T4
T3
T2
T1
S1
S2
Charge n°1: force F
y
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 C
1
C
2
and C, introduced by
LIAISON_ELEM
:
“COQ_POU”
.
5.2
Characteristics of the mesh
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
Controls
Keys
AFFE_MODELE
AFFE
MODELING
“3D”
[U4.22.01]
AFFE
MODELING
“DKT”
AFFE
MODELING
“POU_D_E”
AFFE_CARA_ELEM
HULL
[U4.24.01]
BEAM
DISCRETE
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
“AVERAGE”
[U4.74.04]
RESULTANT
“DX” “DY” “DZ”
MOMENT
“DRX” “DRY” “DRZ”
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
7/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
6
Results of modeling B
6.1 Values
tested
·
Charge n°1: force F
y
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
M
Z
(not O)
30.
30.
0
M
Z
(not M)
20.
20.
0
M
Z
(point C)
10.
10.
0
M
Z
(N23 node)
10.
10.
0
M
Z
(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
Overall dimension memory:
8 MW
Time CPU To use:
4 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
8/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
7 Modeling
C
7.1
Characteristics of modeling
Elements
HEXA20
,
DKT
and
COQUE_C_PLAN
N13
N18
N17
N7
N1
N8
N2
N24
N6
N14
N20
N19
N9
N12
N5
N4
N3
N11
N10
N21
N22
N25
N23
N26
N23
N28
N29
Not NR --> N1
Not A --> N4
Not C --> N23
Not D --> N29
N15
N16
identical
HE1
T4
T3
T2
T1
S1
In N29: charge n°1: force F
y
, load n°2: C couples
Z
or rotation Dr.
Z
Displacements DY and DZ on the section 0 null on average (control
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 mesh
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
Controls
Keys
AFFE_MODELE
AFFE
MODELING
“3D”
[U4.22.01]
AFFE
MODELING
“DKT”
AFFE
MODELING
“COQUE_C_PLAN”
AFFE_CARA_ELEM
HULL
[U4.24.01]
BEAM
AFFE_CHAR_MECA
DDL_IMPO
[U4.25.01]
LIAISON_GROU
LIAISON_DDL
FORCE_NODALE
MECA_STATIQUE
[U4.31.01]
RECU_CHAMP
RESULT
NOM_CHAM
“DEPL”
[U4.62.01]
CALC_ELEM
RESULT
OPTION
“EFGE_ELNO_DEPL”
[U4.61.02]
“SIGM_ELNO_DEPL”
“EPSI_ELNO_DEPL”
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
9/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
8
Results of modeling C
8.1 Values
tested
Identification
Reference
Aster
(
= 0.3)
% difference
Charge 1:
force F
y
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
M
yN
(N8 node)
30.
n.c.
M
yM
(N26 node)
20.
n.c.
M
teststemyŕ
(N4 node)
20.
n.c.
M
yC1
(N22 node)
10.
n.c.
M
teststemyç
(N23 node)
10.
n.c.
M
yD
(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:
C couples
Z
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
M
yD
(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 element
Coque_C_Plan
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.I
Z
that is to say identical in all the model, the stresses are it too.
8.3 Parameters
of execution
Version: 4.02.12
Machine: CRAY C98
System:
UNICOS 9.0
Overall dimension memory:
8 MW
Time CPU To use:
16,2 seconds
Code_Aster
®
Version
4.0
Titrate:
SSLX100 Mixes 3D - Hull - Beam in bending
Date:
01/12/98
Author (S)
:
J.P. LEFEBVRE, F. VOLDOIRE
Key:
V3.05.100-B
Page:
10/10
Manual of Validation
V3.05 booklet: Linear statics of the assembled structures
HI-75/98/040 - Ind A
9
Summary of the results
·
The mesh 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 stresses and efforts give good results (modeling B). For
the element of hull 1D, the results are very good.