Code_Aster
®
Version
5.0
Titrate:
SSNL115 - Beam cantilever in pure bending
Date:
03/05/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.115-A
Page:
1/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
Organization (S):
EDF/ERMEL/PEL
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.115
SSNL115 - Beam cantilever in pure bending
Summary:
This test makes it possible to check the calculation of the internal variables to nodes “VARI_ELNO_ELGA” then values
averages with nodes “VARI_NOEU_ELGA” starting from the “VARI_ELGA”. This test relates to the following elements:
POU_D_TG, POU_D_T, POU_D_E.
Code_Aster
®
Version
5.0
Titrate:
SSNL115 - Beam cantilever in pure bending
Date:
03/05/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.115-A
Page:
2/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
1
Problem of reference
1.1 Geometry
N1
N2
N3
2000
2000
Z
F
F
X
Length of the bar: 4000.0mm
1.2
Properties of material
Elastic characteristics:
E = 2.1E+05 MPa, NAKED = 0.3, RHO = 7.85E-06 kg/mm
3
, ALPHA = 6.7E-06/°C
Plastic characteristics:
ECRO_LINE
:
D_SIGM_EPSI = 1.05E+05 MPa, SY = 240.0 MPa
ECRO_FLEJOU
:
EP = 1.05E+05 MPa, KNOWN = 360.0 MPa, SY = 240.0 MPa, THEN = 0.65,
VMIS_POUTRE
:
NP = 2.2344E+05 NR, MEY = 3.336336E+06 NR
mm
, MPY = 5.258208E+06
N.mm,
CAY = 8.100000E-01, CBY = 3.000000E-03, MEZ = 1.490016E+06 N.mm,
MPZ = 2.650968E+06 N.mm, CAZ = 8.100000E-01, CBZ = 3.000000E-03,
MPX = 5.474160E+05 N.mm
Mechanical characteristics of the beam: BEAM: SECTION = “GENERAL”,
With (mm
2
) IY
(mm
4
) IZ
(mm
4
) JX
(mm
4
) JG
(mm
6
) IZR2
(mm
5
)
9.3100E+02 6.88087E+05 1.76294E+05 1.52060E+04 5.60390E+06 7.95527E+06
AY
AZ
EY (mm)
EZ (mm)
IYR2 (mm
5
)
1.1702E+00 1.1964E+00 2.3446E+01 0.0000E+00 0.0000E+00
1.3
Boundary conditions and loadings
With the node N1 blocking of all the DDL: DX, DY, DZ, DRX, DRY, DRZ
Force imposed on the nodes N2 and N3 following axis X: F = 500N.
Code_Aster
®
Version
5.0
Titrate:
SSNL115 - Beam cantilever in pure bending
Date:
03/05/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.115-A
Page:
3/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
2
Reference solution
2.1 Method
For the following models of beams: POU_D_TG, POU_D_T, POU_D_E, the diagram of integration
fact on a finite element of type “SEG2” with 3 points of integration [R3.01.00] [R3.01.01] [R3.08.01].
following figure represents a “SEG2” with the position of the points of integration.
- 1
1
0
- G
G
G1
G2
G3
N1
N2
with:
G
=
3
5
The function allowing to calculate the values with the nodes starting from the values at the points of integration
is degree 2. The following expression makes it possible to calculate the value interpolated with a X-coordinate
, to leave
values known at the point of integration.
V (
) =
V
V
V
G
G
G
G
G
G
G
G
G
1
3
2
2
1
1
1
2
1
.
.
.
.
.
.
-
+
-
+
+
+
with V
g1
, V
g2
, V
g3
values known at the points of integration.
One finds although V (
G
) = V
g1
, V (0) = V
g3
, V (
G
) = V
g2
. The following figure shows an example
of interpolation realized with the preceding function.
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
- 1.00
- 0.80
- 0.60
- 0.40
- 0.20
0.00
0.20
0.40
0.60
0.80
1.00
Values at the points of integration
Function of interpolation
2.2
Sizes and results of reference
Calculation of the variables intern with nodes “VARI_ELNO_ELGA” then average values with the nodes
“VARI_NOEU_ELGA” starting from the “VARI_ELGA”.
2.3
Uncertainties on the solution
None on the values interpolated with the nodes starting from the values known at the points integration.
Code_Aster
®
Version
5.0
Titrate:
SSNL115 - Beam cantilever in pure bending
Date:
03/05/02
Author (S):
J.L. FLEJOU
Key
:
V6.02.115-A
Page:
4/4
Manual of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HR-17/02/019/A
3 Modeling
With
3.1
Characteristics of modeling and the mesh
The mesh consists of 2 linear elements: “POU_D_TG”
3.2 Functionalities
tested
Controls
CALC_ELEM OPTION
VARI_ELNO_ELGA
CALC_NO OPTION VARI_NOEU_ELGA
4
Results of modeling A
4.1 Values
tested
·
The V7 variable at the points of integration G1, G2, G3 for the two meshs.
These values are obtained directly after a STAT_NON_LINE. They are the data
of input of the functionality to be tested.
VARI_ELGA
V7 at the G1 point
V7 at the G3 point
V7 at the G2 point
Net M1
8.32692E-01
6.01116E-01
3.69098E-01
Net m2
2.67395E-01
1.51149E-01
4.04224E-02
·
The V7 variable with the N1 nodes, N2 and N3.
The theoretical values are obtained using the function of interpolation. Values of
Code_Aster are obtained after a CALC_ELEM, option “VARI_ELNO_ELGA”.
VARI_ELNO_ELGA
Theoretical value
Code_Aster
% Relative Error
Net M1, V7 with the N1 node
8.99996E-01
8.99996E-01
< 1.0E-04
Net M1, V7 with the node N2
3.01499E-01
3.01498E-01
< 1.0E-04
Net m2, V7 with the node N2
3.02259E-01
3.02259E-01
< 1.0E-04
Net m2, V7 with the N3 node
9.23832E-03
9.23854E-03
2.4E-03
·
The V7 variable with the N1 nodes, N2 and N3.
The “VARI_NOEU_ELGA” are the averages of the “VARI_ELNO_ELGA” calculated with the nodes, they
are obtained for Code_Aster by a CALC_NO.
VARI_NOEU_ELGA
Theoretical value
Code_Aster
% Relative Error
V7 with the N1 node
8.99996E-01
8.99996E-01
< 1.0E-04
V7 with the node N2
3.01879E-01
3.01879E-01
< 1.0E-04
V7 with the N3 node
9.23832E-03
9.23854E-03
2.38E-03
5 Synthesis
The results show the correct operation of the passage of the variables of the points of Gauss with
nodes.