Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 1/22
Organization (S): EDF-R & D/AMA
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.106
SSLL106 - Right Tuyau
Summary:
This test allows a simple checking of the right pipe sections in static mechanics of the structures
linear.
The model is linear.
For each modeling, 6 types of loading are applied at the end: a traction, 2 efforts
edges, 2 moments bending and a torsion. One applies moreover one internal pressure, a linear force
distributed and a thermal expansion.
The values tested are displacements, the efforts with the nodes, and the constraints and deformations at the points
of Gauss. The reference solution is analytical (RDM).
Two modelings (A and B) make it possible to test element TUYAU with 3 modes of Fourier (modeling
TUYAU_3M)
: modeling A uses MECA_STATIQUE, modeling B uses STAT_NON_LINE
(elastic behavior).
Two modelings (C and D) make it possible to test element TUYAU with 6 modes of Fourier (modeling
TUYAU_6M).
Two modelings (E and F) make it possible to test element TUYAU with 3 modes of Fourier and 4 nodes
(modeling TUYAU_3M).
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 2/22
1
Problem of reference
1.1 Geometry
Right beam length L, directing vector (4, 3, 0).
y
B
X
Y
3
0.032
L
Z
0.04
O
X
O
4
L =5
Z
Section of the pipe
Tubular section of external radius has = 0.04m, of radius interns B = 0.032m, thickness E = 0.008 m
1.2
Material properties
E = 2. 1011 Pa = 0.3
density =7800 kg/m3, thermal dilation coefficient
5
10
=
1.3
Boundary conditions and loadings
· Embedding out of O
· 6 elementary Loadings at the end B
-
in reference mark (X, y, Z) related to the beam:
Fx = 5.102 NR MX = 5.102 Nm
Fy = 5.102 NR My = 5.102 Nm
Fz = 5.102 NR Mz = 5.102 Nm
-
maybe, in the total reference mark (X, Y, Z):
-
1 loading of traction: FX = 4.102 NR and FY = 3.102 NR
-
2 sharp efforts:in the plan (oxy) FX = 3.102 NR and FY = 4.102 NR and in the plan
(oyz) FZ = 5.102 NR
-
1 torque: MX = 4.102 Nm and MY = 3.102 Nm
-
2 sharp efforts:in the plan (oxy) MX = 3.102 Nm and MY = 4.102 Nm and in the plan
(oyz) MZ = 5.102 Nm
· Internal pressure: P=107 Pa
· Gravity, with g=10m/s ², in the direction - Z
· Linear loading, Fz=-141.146 NR/m (what corresponds to the load due to gravity:
Fz=mg)
· Thermal dilation: Temp = 100°C
1.4
Notation of the characteristics of cross sections
The geometrical characteristics of the cross sections are noted:
S:
surface of the section
I, I
y
Z:
geometrical moments of inertia compared to the principal axes of inertia of
section
Jx:
constant of torsion
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 3/22
2
Reference solution
2.1
Method of calculation used for the reference solution
· Analytical solution [bib1]: displacements out of B in the reference mark (Oxyz) related to the beam.
L
Traction simple U = F
X
X E S
(F L3
2
y
)
L Fy
Pure bending
uy =
=
3rd I
Z
2nd I
Z
Z
F 3
L2 F
Pure bending
Z L
Z
U =
= -
Z
y
3rd I
2nd I
y
y
MR. L
Torsion
X
X = G Jx
Mr. L2
MR. L
y
y
Pure inflection
uz = -
=
2nd I
y
E I
y
y
M
2
M
Pure inflection
Z L
Z L
U y =
= +
2nd I
Z
Z
E I Z
P
has 2
b2
+ B has
Pressure
U =
R (
1 -) + (1 +)
=
R
calculated in R
E b2 - a2
R 2
2
in fact U v
arie enters
-
7 1
, 2 10 6 in R = B
R
and
-
7 7
, 8 10 6 in R = has
Here, the values are obtained with:
S =
- 3 m2 Iy = Iz =
- 6 m4 J =
-
1809557 10
118707 10
2 37414
.
10 6 m4
.
.
X
L = 5 m
For the generalized deformations of beam, one obtains, by the law of behavior:
Fx
simple
Traction
Ex = ES
Fy
Fy (L - X)
simple
Inflection
xy =
Z =
GS
I.E.(internal excitation) Z
Z
F
Fz (L - X)
simple
Inflection
=
xz = GS
y
I.E.(internal excitation) y
M X
Torsion
X = GJx
M y
pure
Inflection
y = EIy
M Z
pure
Inflection
Z = + EIz
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 4/22
Loading of gravity and linear loading:
2
pL
If p indicates the distributed load, the moment in the beginning is worth: M (O) =
and of following displacement
2
pL4
Z at the end B is worth: U (B) =
Z
8EI
The thermal loading of dilation led to an axial displacement (in the local direction X):
U (B) = L
X
(T)
The deformations of free dilation of the surface of the pipe are simply, in local reference mark:
= =
xx
(T
yy
)
Finally to validate the calculation of the matrix of mass, a modal analysis of the first 12 modes
clean (with embedding out of O) must give, for the modes of inflection:
2
I.E.(internal excitation)
F
I
=
I
L
S
Lambdai mode
Frequency
1 1,87510407
2,9030234
2 4,69409113 18,192937
3 7,85475744 50,9407506
4 10,9955407
99,8235399
5 14,1371684
165,015464
6 17,2787596
246,504532
7 20,4203522
344,291453
8 23,5619449
458,376195
9 26,7035376
588,758758
10 29,8451302
735,43914
11 32,9867229
898,417343
12 36,1283155
1077,69337
2.2
Results of reference
· Displacement at the point B, efforts, constraints and deformations in the vicinity of the point O.
· Deformation generalized.
· Eigen frequencies
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
Handbook of validation, test SSLL102 Poutre embedded subjected to unit efforts
[V3.01.102]
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 5/22
3 Modeling
With
3.1
Characteristics of modeling
10 elements TUYAU.
3.2
Characteristics of the grid
10 meshs SEG3. The beam is directed according to the vector (4, 3, 0).
3.3 Functionalities
tested
Commands
AFFE_MODELE MODELING
TUYAU
AFFE_CARA_ELEM BEAM
SECTION RINGS
MACRO_ELAS_MULT
OPTION
SIEF_ELGA_DEPL
OPTION
EPSI_ELGA_DEPL
OPTION
EFGE_ELNO_DEPL
Notice on the contents of the fields:
Fields at the points of Gauss for element TUYAU
, EPSI_ELGA_DEPL and
SIEF_ELGA_DEPL, which provide the strains and the stresses to the points of integration
in the local reference mark of the element, are organized in the following way:
The values are stored:
· for each point of Gauss in the length, (n=1, 3)
· for each point of integration in the thickness, (n=1, 2NCOU+1=7)
· for each point of integration on the circumference, (n=1, 2NSECT+1=33)
· 6 components of strain or stresses:
EPXX EPYY EPZZ EPXY EPXZ EPYZ or SIXX SIYY SIZZ SIXY
SIXZ SIYZ
where X indicates the direction given by the two nodes nodes of
the element, Y represents the angle describing the circumference and Z
represent the radius. EPZZ and EPYZ corresponding to,
in
rr
R
case of the deformations and SIZZ and SIYZ corresponding to,
in
rr R
the case of the constraints is taken equal to zero.
(for MECA_STATIQUE or MACRO_ELAS_MULT, the number of layers is fixed, and equal to 3, and
the number of sectors is equal to 16).
EFGE_ELNO_DEPL represents the efforts generalized with the 3 nodes in the traditional way: NR,
VY, VZ, MT, MFY, MFZ.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 6/22
4
Results of modeling A
4.1 Values
tested
Loading case
Size
Reference
Aster %
difference
FX = 4.102
DX
5.53E06
5.52E06
0.04
FY = 3.102 DY
4.14E06
4.14E06
0.04
FX = 3.102 DRZ
2.63E02
2.63E02
0.04
FY = 4.102 DX
5.27E02
5.26E02
0.056
DY
7.02E02
7.02E02
0.056
FZ = 5.102 DRX
1.58E02
1.58E02
0.04
DRY
2.11E02
2.11E02
0.039
DZ
8.78E02
8.77E02
0.056
MX = 4.102 DRX
1.10E02
1.10E02
0
MY = 3.102 DRY
8.21E03
8.21E03
0
MX = 3.102 DRX
6.32E03
6.32E03
0.04
MY = 4.102 DRY
8.42E03
8.42E03
0.04
DZ
2.63E02
2.63E02
0.04
MZ = 5.102 DRZ
1.05E02
1.05E02
0.039
DX
1.58E02
1.58E02
0.04
DY
2.11E02
2.11E02
0.039
7: pressure
WO
7.38E06
7.16E06
2.946
8: gravity
DZ
4.646 E-02 4.642
E-02
0.09
9: charge distributed
DZ
4.646 E-02 4.642
E-02
0.09
Loading case
Field
Net Point Component Reference
Aster %
difference
1
EFGE_ELNO_DEPL
M18 1 NR
5.00E+02
5.01E+02 0.136
1
EPSI_ELGA_DEPL
M18 1 EPXX 1.38E06
1.38E06
0.031
1
SIEF_ELGA_DEPL
M18 1 SIXX 2.76E+05
2.73E+05
1.159
4
EFGE_ELNO_DEPL
M18 1 MT
5.00E+02
5.00E+02 0
4
EPSI_ELGA_DEPL
M18 1 EPXY 8.77E05 8.76E05
0.102
4
EPSI_ELGA_DEPL
M18 693 EPXY 1.09E04 1.10E04 0.049
4
SIEF_ELGA_DEPL
M18 1 SIXY 6.75E+06 6.74E+06
0.159
4
SIEF_ELGA_DEPL
M18 693 SIXY
8.42E+06 8.42E+06 0.049
5
EFGE_ELNO_DEPL
M18 1 MFY 5.00E+02
5.01E+02 0.123
5
EPSI_ELGA_DEPL
M18 479 EPXX
6.74E05
6.74E05 0.046
5
SIEF_ELGA_DEPL
M18 479 SIXX
1.35E+07
1.33E+07 1.288
6
EFGE_ELNO_DEPL
M18 1 MFZ 5.00E+02
5.01E+02 0.123
6
EPSI_ELGA_DEPL
M18 471 EPXX
6.74E05
6.74E05 0.046
6
SIEF_ELGA_DEPL
M18 471 SIXX
1.35E+07
1.33E+07 1.288
7
EPSI_ELGA_DEPL
M18 1 EPYY 2.28E04
2.24E04
1.716
7
EPSI_ELGA_DEPL
M18 693 EPYY
1.78E04
1.79E04 0.741
7
SIEF_ELGA_DEPL
M18 1 SIYY 4.56E+07
4.53E+07
0.641
7
SIEF_ELGA_DEPL
M18 693 SIYY
3.56E+07
3.54E+07 0.371
8
EFGE_ELNO_DEPL
M1 1 MFY
1764.3
1728
2
9
EFGE_ELNO_DEPL
M1 1 MFY
1764.3
1728
2
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 7/22
Generalized deformations DEGE_ELNO_DEPL:
Loading case
Loadings
Size
Reference
Aster %
difference
1 FX = 4.102
EPXX
1.38155E-06
1.38155E-06
0.04
FY = 3.102
2 FX = 3.102 GAXY 3.5920E-06 4.7415E06 32
FY = 4.102 KZ
1.0530E02 1.04E02 1.2
3 FZ = 5.102 GAXZ 3.5920E-06 4.7415E06
32
KY
1.0530E02
1.04E02
1.2
4 MX = 4.102 GAT 2.73783E-03 2.73783E-03 0
MY = 3.102
5 MX = 3.102 KY
2.1060E-03 2.1052E-03 0.04
MY = 4.102
6 MZ = 5.102 KZ
2.1060E-03 2.1052E-03
0.04
Fréquenc
Reference
Aster %
difference
E clean
1 2.90229
2.90378
0.05
2 2.90229
2.
90378
0.05
3 18.18967
18.2047
0.08
4 18.18967
18.2047
0.08
5 50.99367
51.006 0.02
6 50.99367
51.006 0.02
7 99.81783
100.0478
0.2
8 99.81783
100.0478
0.2
9 157.0190
157.0185 0.001
10 164.9922
165.606 0.3
11 164.9922
165.606 0.3
12 253.185 247.82 2
4.2 Remarks
The values of shearings corresponding to the shearing action are not precise for this
modeling. This is due to the functions of interpolation of command 2 of this element, for displacements
of beam and rotations of beams. As transverse shearings of beam are obtained
by:
duy
= -
, and that for the pure bending, rotations vary like polynomials of command 2,
xy
Z
dx
but displacements, like polynomials of command 3, which is badly approached by the functions
of interpolation. The derivative of displacements is thus not precise.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 8/22
5 Modeling
B
5.1
Characteristics of modeling
10 elements TUYAU, calculation with STAT_NON_LINE.
5.2
Characteristics of the grid
10 meshs SEG3. The beam is directed according to the vector (4, 3, 0).
5.3 Functionalities
tested
Commands
AFFE_MODELE
MODELISATION
TUYAU
AFFE_CARA_ELEM BEAM
SECTION RINGS
STAT_NON_LINE COMP_INCR
RELATION ELAS
COMP_INCR
TUYAU_NCOU
3
COMP_INCR
TUYAU_NSEC
16
OPTION
SIEF_ELNO_ELGA
Notice on the contents of the fields:
Stress fields at the points of Gauss for element TUYAU, SIEF_ELGA, in
the local reference mark of the element, are organized in the following way:
The values are stored:
· for each point of Gauss in the length, (n=1, 3)
· for each point of integration in the thickness, (n=1, 2NCOU+1)
· for each point of integration on the circumference, (n=1, 2NSECT+1)
· 6 components of strain or stresses:
EPXX EPYY EPZZ EPXY EPXZ EPYZ or SIXX SIYY SIZZ SIXY
SIXZ SIYZ
where X indicates the direction given by the two nodes nodes of
the element, Y represents the angle describing the circumference and Z
represent the radius. EPZZ and EPYZ corresponding to,
in
rr
R
case of the deformations and SIZZ and SIYZ corresponding to,
in
rr R
the case of the constraints is taken equal to zero.
(in STAT_NON_LINE, the number of layers is variable, as well as the number of sectors.
One uses here 3 layers and 16 sectors by analogy with modeling A).
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 9/22
6
Results of modeling B
6.1 Values
tested
Loading case
Size
Reference
Aster %
difference
1 DX
5.53E06
5.52E06
0.04
1 DY
4.14E06
4.14E06
0.04
2 DRZ
2.63E02
2.63E02
0.04
2 DX
5.27E02
5.26E02
0.056
2 DY
7.02E02
7.02E02
0.056
3 DRX
1.58E02
1.58E02
0.04
3 DRY
2.11E02
2.11E02
0.039
3 DZ
8.78E02
8.77E02
0.056
4 DRX
1.10E02
1.10E02
0
4 DRY
8.21E03
8.21E03
0
5 DRX
6.32E03
6.32E03
0.04
5 DRY
8.42E03
8.42E03
0.04
5 DZ
2.63E02
2.63E02
0.04
6 DRZ
1.05E02
1.05E02
0.039
6 DX
1.58E02
1.58E02
0.04
6 DY
2.11E02
2.11E02
0.039
7 WO
7.38E06
7.16E06
2.946
Loading case
Field
Net
Not Component Reference
Aster %
difference
1
SIEF_ELGA
M18 Z SIXX 2.76E+05
2.73E+05
1.159
1
SIEF_ELNO_ELGA
M18 1 NR 5.00E+02
5.01E+02 0.136
4
SIEF_ELGA
M18 1 SIXY 6.75E+06
6.74E+06
0.159
4
SIEF_ELGA
M18 693
SIXY 8.42E+06
8.42E+06 0.049
4
SIEF_ELNO_ELGA
M18 1 MT 5.00E+02
5.00E+02 0
5
SIEF_ELGA
M18 479
SIXX 1.35E+07
1.33E+07 1.288
5
SIEF_ELNO_ELGA
M18 1 MFY 5.00E+02
5.01E+02 0.123
6
SIEF_ELGA
M18 471
SIXX 1.35E+07
1.33E+07 1.288
6
SIEF_ELNO_ELGA
M18 1 MFZ 5.00E+02
5.01E+02 0.123
7
SIEF_ELGA
M18 1 SIYY 4.56E+07
4.53E+07
0.641
7
SIEF_ELGA
M18 693
SIYY 3.56E+07
3.54E+07 0.371
Generalized deformations DEGE_ELNO_DEPL:
Loading case
Loadings
Size
Reference
Aster %
difference
1 FX = 4.102
EPXX
1.38155E-06 1.38155E-06
0.04
FY = 3.102
2 FX = 3.102 GAXY 3.5920E-06
4.7415E06
32
FY = 4.102 KZ 1.0530E02
1.04E02
1.2
3 FZ = 5.102 GAXZ
3.5920E-06
4.7415E06
32
KY
1.0530E02
1.04E02
1.2
4 MX = 4.102 GAT 2.73783E-03
2.73783E-03
0
MY = 3.102
5 MX = 3.102 KY
2.1060E-03
2.1052E-03
0.04
MY = 4.102
6 MZ = 5.102 KZ 2.1060E-03
2.1052E-03
0.04
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 10/22
6.2 Remarks
The values of shearings corresponding to the shearing action are not precise for this
modeling. This is due to the functions of interpolation of command 2 of this element, for displacements
of beam and rotations of beams. As transverse shearings of beam are obtained
by:
duy
= -
, and that for the pure bending, rotations vary like polynomials of command 2,
xy
Z
dx
but displacements, like polynomials of command 3, which is badly approached by the functions
of interpolation. The derivative of displacements is thus not precise.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 11/22
7 Modeling
C
7.1
Characteristics of modeling
10 elements TUYAU_6M.
7.2
Characteristics of the grid
10 meshs SEG3. The beam is directed according to the vector (4, 3, 0).
7.3 Functionalities
tested
Commands
AFFE_MODELE MODELING
TUYAU_6M
AFFE_CARA_ELEM BEAM
SECTION RINGS
MACRO_ELAS_MULT
OPTION
SIEF_ELGA_DEPL
OPTION
EPSI_ELGA_DEPL
OPTION
EFGE_ELNO_DEPL
Notice on the contents of the fields:
Fields at the points of Gauss for element TUYAU
, EPSI_ELGA_DEPL and
SIEF_ELGA_DEPL, which provide the strains and the stresses to the points of integration
in the local reference mark of the element, are organized in the following way:
The values are stored:
· for each point of Gauss in the length, (n=1, 3)
· for each point of integration in the thickness, (n=1, 2NCOU+1=7)
· for each point of integration on the circumference, (n=1, 2NSECT+1=33)
· 6 components of strain or stresses:
EPXX EPYY EPZZ EPXY EPXZ EPYZ or SIXX SIYY SIZZ SIXY
SIXZ SIYZ
where X indicates the direction given by the two nodes nodes of
the element, Y represents the angle describing the circumference and Z
represent the radius. EPZZ and EPYZ corresponding to,
in
rr
R
case of the deformations and SIZZ and SIYZ corresponding to,
in
rr R
the case of the constraints is taken equal to zero.
(for MECA_STATIQUE or MACRO_ELAS_MULT, the number of layers is fixed, and equal to 3, and
the number of sectors is equal to 16).
EFGE_ELNO_DEPL represents the efforts generalize with the 3 nodes in the traditional way: NR,
VY, VZ, MT, MFY, MFZ.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 12/22
8
Results of modeling C
8.1 Values
tested
Loading case
Size
Reference
Aster %
difference
1 FX = 4.102
DX
5.53E06
5.52E06
0.04
1 FY = 3.102 DY
4.14E06
4.14E06
0.04
2 FX = 3.102 DRZ
2.63E02
2.63E02
0.04
2 FY = 4.102 DX
5.27E02
5.26E02
0.056
2
DY
7.02E02
7.02E02
0.056
3 FZ = 5.102 DRX
1.58E02
1.58E02
0.04
3
DRY
2.11E02
2.11E02
0.039
3
DZ
8.78E02
8.77E02
0.056
4 MX = 4.102 DRX
1.10E02
1.10E02
0
4 MY = 3.102 DRY
8.21E03
8.21E03
0
5 MX = 3.102 DRX
6.32E03
6.32E03
0.04
5 MY = 4.102 DRY
8.42E03
8.42E03
0.04
5
DZ
2.63E02
2.63E02
0.04
6 MZ = 5.102 DRZ
1.05E02
1.05E02
0.039
6
DX
1.58E02
1.58E02
0.04
6
DY
2.11E02
2.11E02
0.039
7: pressure
WO
7.38E06
7.16E06
2.946
8: gravity
DZ
4.646 E-02 4.642
E-02
0.09
9: charge distributed
DZ
4.646 E-02 4.642
E-02
0.09
Loading case
Field
Net Point Component Reference
Aster %
difference
1
EFGE_ELNO_DEPL
M18 1 NR
5.00E+02
5.01E+02 0.136
1
EPSI_ELGA_DEPL
M18 1 EPXX 1.38E06
1.38E06
0.031
1
SIEF_ELGA_DEPL
M18 1 SIXX 2.76E+05
2.73E+05
1.159
4
EFGE_ELNO_DEPL
M18 1 MT
5.00E+02
5.00E+02 0
4
EPSI_ELGA_DEPL
M18 1 EPXY 8.77E05 8.76E05
0.102
4
EPSI_ELGA_DEPL
M18 693
EPXY 1.09E04 1.10E04 0.049
4
SIEF_ELGA_DEPL
M18 1 SIXY 6.75E+06 6.74E+06
0.159
4
SIEF_ELGA_DEPL
M18 693
SIXY 8.42E+06 8.42E+06 0.049
5
EFGE_ELNO_DEPL
M18 1 MFY 5.00E+02
5.01E+02 0.123
5
EPSI_ELGA_DEPL
M18 479
EPXX
6.74E05
6.74E05 0.046
5
SIEF_ELGA_DEPL
M18 479
SIXX
1.35E+07
1.33E+07 1.288
6
EFGE_ELNO_DEPL
M18 1 MFZ 5.00E+02
5.01E+02 0.123
6
EPSI_ELGA_DEPL
M18 471
EPXX
6.74E05
6.74E05 0.046
6
SIEF_ELGA_DEPL
M18 471
SIXX
1.35E+07
1.33E+07 1.288
7
EPSI_ELGA_DEPL
M18 1 EPYY 2.28E04
2.24E04
1.716
7
EPSI_ELGA_DEPL
M18 693
EPYY
1.78E04
1.79E04 0.741
7
SIEF_ELGA_DEPL
M18 1 SIYY 4.56E+07
4.53E+07
0.641
7
SIEF_ELGA_DEPL
M18 693
SIYY
3.56E+07
3.54E+07 0.371
8
EFGE_ELNO_DEPL
M1 1 MFY
1764.3
1728
2
9
EFGE_ELNO_DEPL
M1 1 MFY
1764.3
1728
2
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 13/22
Generalized deformations DEGE_ELNO_DEPL:
Loading case
Loadings
Size
Reference
Aster %
difference
1 FX = 4.102
EPXX
1.38155E-06 1.38155E-06
0.04
FY = 3.102
2 FX = 3.102 GAXY 3.5920E-06
4.7415E06
32
FY = 4.102 KZ 1.0530E02
1.04E02
1.2
3 FZ = 5.102 GAXZ
3.5920E-06
4.7415E06
32
KY
1.0530E02
1.04E02
1.2
4 MX = 4.102 GAT 2.73783E-03
2.73783E-03
0
MY = 3.102
5 MX = 3.102 KY
2.1060E-03
2.1052E-03
0.04
MY = 4.102
6 MZ = 5.102 KZ 2.1060E-03
2.1052E-03
0.04
Fréquenc
Reference
Aster %
difference
E clean
1 2.90229 2.90378
0.05
2 2.90229 2.
90378
0.05
3 18.18967 18.2047 0.08
4 18.18967 18.2047 0.08
5 50.99367 51.006 0.02
6 50.99367 51.006 0.02
7 99.81783 100.0478 0.2
8 99.81783 100.0478 0.2
9 157.0190 157.0185 0.001
10 164.9922
165.606
0.3
11 164.9922
165.606
0.3
12 253.185
247.82
2
8.2 Remarks
The values of shearings corresponding to the shearing action are not precise for this
modeling. This is due to the functions of interpolation of command 2 of this element, for displacements
of beam and rotations of beams. As transverse shearings of beam are obtained
by:
duy
= -
, and that for the pure bending, rotations vary like polynomials of command 2,
xy
Z
dx
but displacements, like polynomials of command 3, which is badly approached by the functions
of interpolation. The derivative of displacements is thus not precise.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 14/22
9 Modeling
D
9.1
Characteristics of modeling
10 elements TUYAU_6M, calculation with STAT_NON_LINE.
9.2
Characteristics of the grid
10 meshs SEG3. The beam is directed according to the vector (4, 3, 0).
9.3 Functionalities
tested
Commands
AFFE_MODELE
MODELISATION
TUYAU_6M
AFFE_CARA_ELEM BEAM
SECTION
CERCLE
STAT_NON_LINE COMP_INCR
RELATION ELAS
COMP_INCR
TUYAU_NCOU
3
COMP_INCR
TUYAU_NSEC
16
OPTION
SIEF_ELNO_ELGA
Notice on the contents of the fields:
Stress fields at the points of Gauss for element TUYAU, SIEF_ELGA, in
the local reference mark of the element, are organized in the following way:
The values are stored:
· for each point of Gauss in the length, (n=1, 3)
· for each point of integration in the thickness, (n=1, 2NCOU+1)
· for each point of integration on the circumference, (n=1, 2NSECT+1)
· 6 components of strain or stresses:
EPXX EPYY EPZZ EPXY EPXZ EPYZ or SIXX SIYY SIZZ SIXY
SIXZ SIYZ
where X indicates the direction given by the two nodes nodes of
the element, Y represents the angle describing the circumference and Z
represent the radius. EPZZ and EPYZ corresponding to,
in
rr
R
case of the deformations and SIZZ and SIYZ corresponding to,
in
rr R
the case of the constraints is taken equal to zero.
(in STAT_NON_LINE, the number of layers is variable, as well as the number of sectors.
One uses here 3 layers and 16 sectors by analogy with modeling A).
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 15/22
10 Results of modeling D
10.1 Values
tested
Loading case
Size
Reference
Aster %
difference
1 DX
5.53E06
5.52E06
0.04
1 DY
4.14E06
4.14E06
0.04
2 DRZ
2.63E02
2.63E02
0.04
2 DX
5.27E02
5.26E02
0.056
2 DY
7.02E02
7.02E02
0.056
3 DRX
1.58E02
1.58E02
0.04
3 DRY
2.11E02
2.11E02
0.039
3 DZ
8.78E02
8.77E02
0.056
4 DRX
1.10E02
1.10E02
0
4 DRY
8.21E03
8.21E03
0
5 DRX
6.32E03
6.32E03
0.04
5 DRY
8.42E03
8.42E03
0.04
5 DZ
2.63E02
2.63E02
0.04
6 DRZ
1.05E02
1.05E02
0.039
6 DX
1.58E02
1.58E02
0.04
6 DY
2.11E02
2.11E02
0.039
7 WO
7.38E06
7.16E06
2.946
Loading case
Field
Net
Not Component Reference
Aster %
difference
1
SIEF_ELGA
M18 Z SIXX 2.76E+05
2.73E+05
1.159
1
SIEF_ELNO_ELGA
M18 1 NR 5.00E+02
5.01E+02 0.136
4
SIEF_ELGA
M18 1 SIXY 6.75E+06
6.74E+06
0.159
4
SIEF_ELGA
M18 693
SIXY 8.42E+06
8.42E+06 0.049
4
SIEF_ELNO_ELGA
M18 1 MT 5.00E+02
5.00E+02 0
5
SIEF_ELGA
M18 479
SIXX 1.35E+07
1.33E+07 1.288
5
SIEF_ELNO_ELGA
M18 1 MFY 5.00E+02
5.01E+02 0.123
6
SIEF_ELGA
M18 471
SIXX 1.35E+07
1.33E+07 1.288
6
SIEF_ELNO_ELGA
M18 1 MFZ 5.00E+02
5.01E+02 0.123
7
SIEF_ELGA
M18 1 SIYY 4.56E+07
4.53E+07
0.641
7
SIEF_ELGA
M18 693
SIYY 3.56E+07
3.54E+07 0.371
Generalized deformations DEGE_ELNO_DEPL:
Loading case
Loadings
Size
Reference
Aster %
difference
1 FX = 4.102
EPXX
1.38155E-06 1.38155E-06
0.04
FY = 3.102
2 FX = 3.102 GAXY 3.5920E-06
4.7415E06
32
FY = 4.102 KZ 1.0530E02
1.04E02
1.2
3 FZ = 5.102 GAXZ
3.5920E-06
4.7415E06
32
KY
- 1.0530E02
- 1.04E02
1.2
4 MX = 4.102 GAT 2.73783E-03
2.73783E-03
0
MY = 3.102
5 MX = 3.102 KY
2.1060E-03
2.1052E-03
0.04
MY = 4.102
6 MZ = 5.102 KZ 2.1060E-03
2.1052E-03
0.04
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 16/22
10.2 Remarks
The values of shearings corresponding to the shearing action are not precise for this
modeling. This is due to the functions of interpolation of command 2 of this element, for displacements
of beam and rotations of beams. As transverse shearings of beam are obtained
by:
duy
= -
, and that for the pure bending, rotations vary like polynomials of command 2,
xy
Z
dx
but displacements, like polynomials of command 3, which is badly approached by the functions
of interpolation. The derivative of displacements is thus not precise.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 17/22
11 Modeling
E
11.1 Characteristics of modeling
8 elements TUYAU with 3 modes of Fourier and 4 nodes
11.2 Characteristics of the grid
8 meshs SEG4. The beam is directed according to the vector (4, 3, 0).
11.3 Functionalities
tested
Commands
AFFE_MODELE MODELING
TUYAU
AFFE_CARA_ELEM BEAM
SECTION
CERCLE
MACRO_ELAS_MULT
OPTION
SIEF_ELGA_DEPL
OPTION
EPSI_ELGA_DEPL
OPTION
EFGE_ELNO_DEPL
CREA_MAILLAGE OPTION
SEG3_4
Notice on the contents of the fields:
Fields at the points of Gauss for element TUYAU
, EPSI_ELGA_DEPL and
SIEF_ELGA_DEPL, which provide the strains and the stresses to the points of integration
in the local reference mark of the element, are organized in the following way:
The values are stored:
· for each point of Gauss in the length, (n=1, 3)
· for each point of integration in the thickness, (n=1, 2NCOU+1=7)
· for each point of integration on the circumference, (n=1, 2NSECT+1=33)
· 6 components of strain or stresses:
EPXX EPYY EPZZ EPXY EPXZ EPYZ or SIXX SIYY SIZZ SIXY
SIXZ SIYZ
where X indicates the direction given by the two nodes nodes of
the element, Y represents the angle describing the circumference and Z
represent the radius. EPZZ and EPYZ corresponding to,
in
rr
R
case of the deformations and SIZZ and SIYZ corresponding to,
rr R
in the case of the constraints are taken equal to zero.
(for MECA_STATIQUE or MACRO_ELAS_MULT, the number of layers is fixed, and equal to 3, and
the number of sectors is equal to 16).
EFGE_ELNO_DEPL represents the efforts generalize with the 3 nodes in the traditional way: NR,
VY, VZ, MT, MFY, MFZ.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 18/22
12 Results of modeling E
12.1 Values
tested
Loading case
Size
Reference
Aster %
difference
FX = 4.102
DX
5.53E06
5.52E06
0.04
FY = 3.102 DY 4.14E06
4.14E06
0.04
FX = 3.102 DRZ 2.63E02 2.63E02
0.04
FY = 4.102 DX
5.27E02
5.264E02
0.02
DY
7.02E02
7.019E02
0.02
FZ = 5.102 DRX
1.58E02
1.58E02
0.04
DRY
2.11E02
2.11E02
0.04
DZ
8.78E02
8.77E02
0.02
MX = 4.102 DRX
1.10E02
1.10E02
0
MY = 3.102 DRY
8.21E03
8.21E03
0
MX = 3.102 DRX
6.32E03
6.32E03
0.04
MY = 4.102 DRY
8.42E03
8.42E03
0.04
DZ
2.63E02
2.63E02
0.04
MZ = 5.102 DRZ
1.05E02
1.05E02
0.039
DX
1.58E02
1.58E02
0.04
DY
2.11E02
2.11E02
0.039
7: pressure
WO
7.38E06
7.16E06
2.946
8: gravity
DZ
4.646 E-02 4.644
E-02 0.04
9: charge distributed
DZ
4.646 E-02 4.644
E-02 0.04
Loading case
Field
Net
Not Component Reference
Aster %
difference
1
EFGE_ELNO_DEPL
M18 1 NR
5.00E+02
5.01E+02
0.136
1
EPSI_ELGA_DEPL
M18 1 EPXX 1.38E06
1.38E06
0.031
1
SIEF_ELGA_DEPL
M18 1 SIXX 2.76E+05
2.73E+05
1.159
4
EFGE_ELNO_DEPL
M18 1 MT 5.00E+02
5.00E+02
0
4
EPSI_ELGA_DEPL
M18 1 EPXY
8.77E05 8.76E05
0.102
4
EPSI_ELGA_DEPL
M18 693
EPXY 1.09E04 1.10E04 0.049
4
SIEF_ELGA_DEPL
M18 1 SIXY 6.75E+06 6.74E+06
0.159
4
SIEF_ELGA_DEPL
M18 693
SIXY 8.42E+06 8.42E+06 0.049
5
EFGE_ELNO_DEPL
M18 1 MFY 5.00E+02
5.01E+02
0.123
5
EPSI_ELGA_DEPL
M18 479
EPXX 6.74E05
6.74E05 0.046
5
SIEF_ELGA_DEPL
M18 479
SIXX
1.35E+07
1.33E+07 1.288
6
EFGE_ELNO_DEPL
M18 1 MFZ 5.00E+02
5.01E+02
0.123
6
EPSI_ELGA_DEPL
M18 471
EPXX 6.74E05
6.74E05 0.046
6
SIEF_ELGA_DEPL
M18 471
SIXX
1.35E+07
1.33E+07 1.288
7
EPSI_ELGA_DEPL
M18 1 EPYY 2.28E04
2.24E04
1.716
7
EPSI_ELGA_DEPL
M18 693
EPYY 1.78E04
1.79E04 0.741
7
SIEF_ELGA_DEPL
M18 1 SIYY 4.56E+07
4.53E+07
0.641
7
SIEF_ELGA_DEPL
M18 693
SIYY
3.56E+07
3.54E+07 0.371
8
EFGE_ELNO_DEPL
M1 1 MFY
1764.3
1760
0.2
9
EFGE_ELNO_DEPL
M1 1 MFY
1764.3
1760
0.2
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 19/22
Generalized deformations DEGE_ELNO_DEPL:
Loading case
Loadings
Size
Reference
Aster %
difference
1 FX = 4.102
EPXX
1.38155E-06
1.38155E-06
0.04
FY = 3.102
2 FX = 3.102 GAXY 3.5920E-06 4.7415E06 1.1
FY = 4.102 KZ
1.0530E02
1.04E02 0.05
3 FZ = 5.102 GAXZ 3.5920E-06
4.7415E06 1.1
KY
1.0530E02
1.04E02
0.05
4 MX = 4.102 GAT 2.73783E-03
2.73783E-03
0
MY = 3.102
5 MX = 3.102 KY
2.1060E-03 2.1052E-03 0.04
MY = 4.102
6 MZ = 5.102 KZ
2.1060E-03 2.1052E-03
0.04
Fréquenc
Reference
Aster %
difference
E clean
1 2.90229
2.90303
0.02
2 2.90229
2.90303
0.02
3 18.18967
18.171 0.1
4 18.18967
18.171 0.1
5 50.99367
50.781 0.4
6 50.99367
50.781 0.4
7 99.81783
99.923 0.6
8 99.81783
99.923 0.6
9 157.0190
157.0185 0.001
12.2 Remarks
The values of shearings corresponding to the shearing action are precise for this modeling.
This is due to the functions of interpolation of command 3 of this element, for displacements of beam and
rotations of beams.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 20/22
13 Modeling
F
13.1 Characteristics of modeling
1 elements TUYAU_3M with 4 nodes, calculation with STAT_NON_LINE.
13.2 Characteristics of the grid
1 meshs SEG4. The beam is directed according to the vector (4, 3, 0).
13.3 Functionalities
tested
Commands
AFFE_MODELE
MODELISATION
TUYAU
AFFE_CARA_ELEM BEAM
SECTION RINGS
STAT_NON_LINE COMP_INCR
RELATION ELAS
COMP_INCR
TUYAU_NCOU
3
COMP_INCR
TUYAU_NSEC
16
OPTION
SIEF_ELNO_ELGA
CREA_MAILLAGE OPTION
SEG3_4
Notice on the contents of the fields:
Stress fields at the points of Gauss for element TUYAU, SIEF_ELGA, in
the local reference mark of the element, are organized in the following way:
The values are stored:
· for each point of Gauss in the length, (n=1, 3)
· for each point of integration in the thickness, (n=1, 2NCOU+1)
· for each point of integration on the circumference, (n=1, 2NSECT+1)
· 6 components of strain or stresses:
EPXX EPYY EPZZ EPXY EPXZ EPYZ or SIXX SIYY SIZZ SIXY
SIXZ SIYZ
where X indicates the direction given by the two nodes nodes of
the element, Y represents the angle describing the circumference and Z
represent the radius. EPZZ and EPYZ corresponding to,
in
rr
R
case of the deformations and SIZZ and SIYZ corresponding to,
in
rr R
the case of the constraints is taken equal to zero.
(in STAT_NON_LINE, the number of layers is variable, as well as the number of sectors.
One uses here 3 layers and 16 sectors by analogy with modeling A).
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 21/22
14 Results of modeling F
14.1 Values
tested
Loading case
Size
Reference
Aster %
difference
1 DX
5.53E06
5.52E06 0.04
1 DY
4.14E06
4.14E06 0.04
2 DRZ
2.63E02
2.63E02 0.04
2 DX
5.27E02
5.26E02 0.02
2 DY
7.02E02
7.02E02 0.02
3 DRX
1.58E02
1.58E02 0.04
3 DRY
2.11E02
2.11E02 0.02
3 DZ
8.78E02
8.77E02 0.04
4 DRX
1.10E02
1.10E02 0
4 DRY
8.21E03
8.21E03 0
5 DRX
6.32E03
6.32E03 0.04
5 DRY
8.42E03
8.42E03 0.04
5 DZ
2.63E02
2.63E02 0.04
6 DRZ
1.05E02
1.05E02 0.04
6 DX
1.58E02
1.58E02 0.04
6 DY
2.11E02
2.11E02 0.04
7 WO
7.38E06
7.167E06 3.3
Loading case
Field
Net
Not Component Reference
Aster %
difference
1
SIEF_ELGA
M18 Z SIXX 2.76E+05
2.73E+05
1.159
1
SIEF_ELNO_ELGA
M18 1 NR 5.00E+02
5.01E+02 0.136
4
SIEF_ELGA
M18 1 SIXY 6.75E+06
6.74E+06
0.159
4
SIEF_ELGA
M18 693
SIXY 8.42E+06
8.42E+06 0.049
4
SIEF_ELNO_ELGA
M18 1 MT 5.00E+02
5.00E+02 0
5
SIEF_ELGA
M18 479
SIXX 1.35E+07
1.33E+07 1.288
5
SIEF_ELNO_ELGA
M18 1 MFY 5.00E+02
5.01E+02 0.123
6
SIEF_ELGA
M18 471
SIXX 1.35E+07
1.33E+07 1.288
6
SIEF_ELNO_ELGA
M18 1 MFZ 5.00E+02
5.01E+02 0.123
7
SIEF_ELGA
M18 1 SIYY 4.56E+07
4.53E+07
0.641
7
SIEF_ELGA
M18 693
SIYY 3.56E+07
3.54E+07 0.371
Generalized deformations DEGE_ELNO_DEPL:
Loading case
Loadings
Size
Reference
Aster %
difference
1 FX = 4.102
EPXX
1.38155E-06 1.38155E-06
0.04
FY = 3.102
2 FX = 3.102 GAXY 3.5920E-06
4.7415E06
21
FY = 4.102 KZ 1.0530E02
1.04E02
0.04
3 FZ = 5.102 GAXZ
3.5920E-06
4.7415E06
21
KY
1.0530E02
1.04E02
0.04
4 MX = 4.102 GAT 2.73783E-03
2.73783E-03
0
MY = 3.102
5 MX = 3.102 KY
2.1060E-03
2.1052E-03
0.04
MY = 4.102
6 MZ = 5.102 KZ 2.1060E-03
2.1052E-03
0.04
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Code_Aster ®
Version
7.2
Titrate:
SSLL106 - Right Tuyau
Date:
05/01/04
Author (S):
J. Mr. PROIX
Key: V3.01.106-B Page: 22/22
14.2 Remarks
The values of shearings corresponding to the shearing action are not precise for this
modeling. This is due to the weak discretization for this modeling (only one element).
15 Summary of the results
This test makes it possible to check the correct operation of element TUYAU (3 modes and 6 modes of Fourier)
in linear elasticity, with operators MECA_STATIQUE and STAT_NON_LINE, for the whole of
loadings applicable to this element.
The variations compared to the analytical reference solution (solution in assumption of beam) are very
weak for displacements (0,04% to 0,06%), except for the loading of pressure where the variation of 3%
is due to the fact that Wo represents an average radial displacement. Actually this radial displacement varies
in the thickness. The variation on the strains and the stresses (~
- 1%) are more important than that
on displacements but remains acceptable taking into account the fact that these values are calculated in
points of integration located in the thickness of the pipe.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Outline document