Code_Aster ®
Version
4.0
Titrate:
SSNP101 Plaque in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A Page:
1/6
Organization (S): EDF/IMA/MN
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.101
SSNP101 - Plaque in traction-shearing:
viscoelasticity of Lemaître (D_PLAN)
Summary:
This test of nonlinear quasi-static mechanics consists in charging in traction-shearing a square plate.
One thus validates the relation of nonlinear behavior of viscoelasticity of Lemaître in plane deformations
for a nonradial loading.
The plate is modelled by an element 2D (QUAD4).
The results obtained by Code_Aster are very close to the reference solution.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP101 Plaque in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A Page:
2/6
1
Problem of reference
1.1 Geometry
Square plate
C
B
D
D
D
D
D
D
With
y
The problem is independent
X
dimensions of the plate
1.2
Material properties
E = 178.600 MPa
= 0.3
Viscoelastic relation of behavior of Lemaître
1
-
1
N = 11
= 328410 4
.
(K =
)
3045
= 017857
.
(m = 5. )
6
K
m
1.3
Boundary conditions and loadings
In a: ux = uy = 0
On side AB: ux = 0
Loading below:
Ways OA and AB, of duration 30 seconds,
Time of maintenance in A and 3600 second old B.
3D MPa
(
)
B
420
With (210, 210)
D MPa
(
)
0
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP101 Plaque in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation 3D Aster carried out with an element HEXA8 of which all the nodes have a displacement imposed no one
according to OZ. That makes it possible to constitute a reference for the case of the plane deformations (in the plan
(OX, OY)), where one does not have an analytical solution or results of other computer codes.
Operation in 3D of the non-linear viscoelasticity of Lemaître itself was validated with the assistance
test SSNP05A.
2.2
Results of reference
v and at the moment T = 30 S, T = 3630 S, T = 3660 S and T = 3720 S
xx
vxy
2.3
Uncertainty on the solution
Uncertainty lower than 0.5%.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP101 Plaque in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
y
N02
N03
N01
N04
X
The loading and the boundary conditions are modelled by:
DDL_IMPO: (NOEUD: N04, DX: 0., DY:0.)
DDL_IMPO: (NOEUD: N03, DX: 0.)
1
1
FORCE_NODALE: (NOEUD; (N01 N02), FX: -
()
T, FY: -
()
T)
D
D
2
2
1
FORCE_NODALE: (NOEUD; (N01 N04), FX: -
()
T)
D
2
1
FORCE_NODALE: (NOEUD; (N03 N04), FY:
()
T)
D
2
1
FORCE_NODALE: (NOEUD; (N02 N03), FX:
()
T)
D
2
where ()
D T and
()
D T are the higher definite positive functions [§1.3].
3.2
Characteristics of the grid
A number of nodes:
4
A number of meshs and types:
1 QUAD4
3.3 Functionalities
tested
Commands
Key
AFFE_MODELE
AFFE
MODELISATION
D_PLAN
[U4.22.01]
DEFI_MATERIAU
LEMAITRE
NR
[U4.23.01]
UN_SUR_K
UN_SUR_M
AFFE_CHAR_MECA
FORCE_NODALE
NOEUD
[U4.25.01]
STAT_NON_LINE
COMP_INCR
RELATION
LEMAITRE
[U4.32.01]
CALC_ELEM
OPTION
EPSI_ELNO_DEPL
[U4.61.01]
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP101 Plaque in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
Variables
Moments (S)
Reference
Aster
% difference
v
30
1.7620 104
1.7623 104
0.017%
xx
v
30
1.81585 104
1.81582 104
0.002%
xy
v
3630
1.9030 103
1.9033 103
0.018%
xx
v
3630
2.0789 103
2.0791 103
0.012%
xy
v
3660
1.9130 103
1.9125 103
0.024%
xx
v
3660
2.1906 103
2.1904 103
0.011%
xy
v
3720
1.8740 103
1.8741 103
0.004%
xx
v
3720
3.1813 103
3.1814 103
0.005%
xy
4.2 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
39.07 seconds
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP101 Plaque in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A Page:
6/6
5
Summary of the results
One cannot use the viscoelastic model of LEMAITRE (nor those of Zircaloy: ZIRC_CYRA2, and
ZIRC_EPRI) in 2D forced plane (C_PLAN).
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A