Code_Aster
®
Version
5.0
Titrate:
SSLL104 - Initial deformations in a right beam
Date:
14/09/00
Author (S):
J. Mr. PROIX, J. PELLET, L. VIVAN
Key
:
V3.01.104-B
Page:
1/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
Organization (S):
EDF/MTI/MN, CS IF
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.104
SSLL104 - Initial deformations in a beam
straight line
Summary:
This test validates the taking into account of the initial deformations in the elastic design of a right beam.
characteristics of calculation are:
·
analyze static,
·
linear behavior,
·
linear model,
·
1 only modeling testing the elements
POU_D_E
,
POU_D_T
and
POU_D_TG
,
·
the solution is analytical.
Code_Aster
®
Version
5.0
Titrate:
SSLL104 - Initial deformations in a right beam
Date:
14/09/00
Author (S):
J. Mr. PROIX, J. PELLET, L. VIVAN
Key
:
V3.01.104-B
Page:
2/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
B
With
X
Z
Y
X
A beam AB length
L
= 100 mm are located on trisecting trihedron (X, Y, Z):
coordinated bridge B are:
B
=
100
3
100
3
100
3
One defines also a point C medium of A, B.
The local reference mark (A, X, y, Z) results from the total reference mark (A, X, Y, Z) by the nautical angles
= °
= -
°
=
45
35 26
2
3
.
cos
1.2
Material properties
The material is elastic linear.
Young modulus E = 1.0 MPa (without influence on the result).
Poisson's ratio:
= 0
1.3
Boundary conditions and loadings
Embedding in a: DX = DY = DZ = DRX = DRY = DRZ = 0.
Loading: initial deformation in the local reference mark (A, X, y, Z)
·
strain according to X: EPX = 0.001
·
curvature according to Ay: KY = 0.002
·
curvature according to Az: KZ = 0.003
1.4
Characteristics of the section of beam
All the characteristics (surface, inertias,…) are taken equal to 1.
They are without influence on the result.
Code_Aster
®
Version
5.0
Titrate:
SSLL104 - Initial deformations in a right beam
Date:
14/09/00
Author (S):
J. Mr. PROIX, J. PELLET, L. VIVAN
Key
:
V3.01.104-B
Page:
3/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The solution is analytical. It is calculated in the local reference mark.
(
)
(
)
That is to say:
the displacement of the beam
generalized deformation of the beam
That is to say the solution:
then:
=
U
U v W
E
U
X
v
X
W
X
X
X
U X
X
X
v X
W X
X
y
Z
X
y
Z
xy
xz
X
y
Z
X
y
y
Z
Z
xy
Z
xz
y
=
=
=
= -
=
=
=
=
=
=
=
=
=
=
-
=
=
+
=
,
,
,
,
,
,
,
.
;
;
;
.
;
.
,
,
,
,
,
2
2
2
2
0
0
0
If one chooses
= EPX (= 0.001); = KY (= 0.002); = KZ (= 0.003) then
E E
init
-
= 0
efforts
are null. Balance is checked. In addition, the solution checks the C.L. (embedding in A). Thus it is
the solution of the problem arising.
2.2
Results of reference
The results expressed in the local reference mark are:
In b: Dx = 0.1; Dy = 15. ; Dz = 10. ; DRx = 0. ; DRy = 0.2; DRz = 0.3
Out of C: Dx = 0.05; Dy = 3.75. ; Dz = 2.5; DRx = 0. ; DRy = 0.1; DRz = 0.15
In the total reference mark, one finds at the points B and C:
()
(
)
()
(
)
()
(
)
()
(
)
()
(
)
()
()
DX B
DY B
DZ B
DRX B
DRY B
DRZ B
=
+
-
+
=
+
+
=
+
-
=
-
-
=
-
+
=
3
30 5
3
6
3 6 2 2
3
30 5
3
6 3 6 2 2
3
30 5
3
6
4 2
1
20
6 2 2
1
20
6 2 2
1
20 2 6
()
(
)
()
(
)
()
(
)
()
(
)
()
(
)
()
()
DX C
DY C
DZ C
DRX C
DRY C
DRZ C
=
+
-
+
=
+
+
=
+
-
=
-
-
=
-
+
=
3
60 5
3
24
3 6 2 2
3
60 5
3
24 3 6 2 2
3
60 5
3
24
4 2
1
40
6 2 2
1
40
6 2 2
1
40 2 6
2.3
Uncertainty on the solution
The solution is exact for the theory of the beams of Euler (or Timoshenko because it there not of
shearing). Torsion not intervening, the solution is also valid for the elements
POU_D_TG
.
Code_Aster
®
Version
5.0
Titrate:
SSLL104 - Initial deformations in a right beam
Date:
14/09/00
Author (S):
J. Mr. PROIX, J. PELLET, L. VIVAN
Key
:
V3.01.104-B
Page:
4/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
B
With
X
Z
Y
X
·
AB is cut out in 10 of the same elements length (10.). (Only one element would be sufficient).
·
3 identical calculations are successively made on this mesh with 3 modelings
different:
-
with 10 elements
POU_D_E
-
with 10 elements
POU_D_T
-
with 10 elements
POU_D_TG
3.2
Characteristics of the mesh
A number of nodes: 11
A number of meshs and types: 10 SEG2
3.3 Functionalities
tested
Controls
Key word factor
Key word argument
AFFE_CHAR_MECA
EPSI_INIT
EPX, KY, KZ
AFFE_MODELE MODELING
POU_D_E
AFFE_MODELE MODELING
POU_D_T
AFFE_MODELE MODELING
POU_D_TG
Code_Aster
®
Version
5.0
Titrate:
SSLL104 - Initial deformations in a right beam
Date:
14/09/00
Author (S):
J. Mr. PROIX, J. PELLET, L. VIVAN
Key
:
V3.01.104-B
Page:
5/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Modeling Identification Reference
Aster %
difference
POU_D_E
B DX
6.4664E+00
6.4664E+00
< 10
9
DY
1.4747E+01
1.4747E+01
< 10
9
DZ
8.1072E+00
8.1072E+00
< 10
9
DRX
2.6390E01
2.6390E01
< 10
9
DRY
1.8947E02
1.8947E02
< 10
9
DRZ
2.4495E01
2.4495E01
< 10
9
C DX
1.6022E+00
1.6022E+00
< 10
9
DY
3.7011E+00
3.7011E+00
< 10
9
DZ
2.0124E+00
2.0124E+00
< 10
9
DRX
1.3195E01
1.3195E01
< 10
9
DRY
9.4734E03
9.4734E03
< 10
9
DRZ
1.2247E01
1.2247E01
< 10
9
POU_D_T
B DX
6.4664E+00
6.4664E+00
< 10
9
DY
1.4747E+01
1.4747E+01
< 10
9
DZ
8.1072E+00
8.1072E+00
< 10
9
DRX
2.6390E01
2.6390E01
< 10
9
DRY
1.8947E02
1.8947E02
< 10
9
DRZ
2.4495E01
2.4495E01
< 10
9
C DX
1.6022E+00
1.6022E+00
< 10
9
DY 3.7011E+00
3.7011E+00
< 10
9
DZ 2.0124E+00
2.0124E+00
< 10
9
DRX
1.3195E01
1.3195E01
< 10
9
DRY 9.4734E03
9.4734E03
< 10
9
DRZ 1.2247E01
1.2247E01
< 10
9
POU_D_TG
B DX
6.4664E+00
6.4664E+00
< 10
9
DY
1.4747E+01
1.4747E+01
< 10
9
DZ
8.1072E+00
8.1072E+00
< 10
9
DRX
2.6390E01
2.6390E01
< 10
9
DRY
1.8947E02
1.8947E02
< 10
9
DRZ
2.4495E01
2.4495E01
< 10
9
C DX
1.6022E+00
1.6022E+00
< 10
9
DY
3.7011E+00
3.7011E+00
< 10
9
DZ
2.0124E+00
2.0124E+00
< 10
9
DRX
1.3195E01
1.3195E01
< 10
9
DRY
9.4734E03
9.4734E03
< 10
9
DRZ
1.2247E01
1.2247E01
< 10
9
4.2 Parameters
of execution
Version: 5.3
Machine: SGI Origin2000 - R12000
System:
IRIX 64
Overall dimension memory:
64 Mo
Time CPU To use: 3 seconds
Code_Aster
®
Version
5.0
Titrate:
SSLL104 - Initial deformations in a right beam
Date:
14/09/00
Author (S):
J. Mr. PROIX, J. PELLET, L. VIVAN
Key
:
V3.01.104-B
Page:
6/6
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/02/001/A
5
Summary of the results
As one could expect it, the results are very precise. They validate the good taking into account
initial strains and stresses in the elements of beam.
The test does not test the curved beams (
POU_C_T
) because one does not have reference solution.