Code_Aster
®
Version
4.0
Titrate:
SSNP101 Plates in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Organization (S):
EDF/IMA/MN
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.101
SSNP101 - Plate 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 modelized by an element 2D (QUAD4).
Results obtained by
Code_Aster
are very close to the reference solution.
Code_Aster
®
Version
4.0
Titrate:
SSNP101 Plates in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A
Page:
2/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
1
Problem of reference
1.1 Geometry
Square plate
D
D
D
D
D
C
D
B
With
y
X
The problem is independent
dimensions of the plate
1.2
Material properties
E = 178.600 MPa
= 0.3
Viscoelastic relation of behavior of Lemaître
(
)
(
)
N
K
K
m
m
=
=
=
=
=
-
11
1
3 28410
3045
1
0 17857
5 6
4
.
.
.
1.3
Boundary conditions and loadings
In a: U
X
= U
y
= 0
On side AB: U
X
= 0
Loading below:
Ways OA and AB, of duration 30 seconds,
Time of hold in A and 3600 second old B.
B
420
With (210, 210)
0
3
D
MPa
(
)
D
MPa
(
)
Code_Aster
®
Version
4.0
Titrate:
SSNP101 Plates in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A
Page:
3/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
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 aid
test SSNP05A.
2.2
Results of reference
v
xx
and
v
xy
at the moment T = 30 S, T = 3630 S, T = 3660 S and T = 3720 S
2.3
Uncertainty on the solution
Uncertainty lower than 0.5%.
Code_Aster
®
Version
4.0
Titrate:
SSNP101 Plates in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A
Page:
4/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
3 Modeling
With
3.1
Characteristics of modeling
N02
N03
y
N01
N04
X
The loading and the boundary conditions are modelized by:
DDL_IMPO: (NODE: N04, DX: 0., DY:0.)
DDL_IMPO: (NODE: N03, DX: 0.)
FORCE_NODALE: (NODE; (N01 N02), FX:
()
-
1
2
T
D
, FY:
()
-
1
2
T
D
)
FORCE_NODALE: (NODE; (N01 N04), FX:
()
-
1
2
T
D
)
FORCE_NODALE: (NODE; (N03 N04), FY:
()
1
2
T
D
)
FORCE_NODALE: (NODE; (N02 N03), FX:
()
1
2
T
D
)
where
()
D
T
and
()
D
T
are the higher definite positive functions [§1.3].
3.2
Characteristics of the mesh
A number of nodes:
4
A number of meshs and types:
1 QUAD4
3.3 Functionalities
tested
Controls
Key
AFFE_MODELE
AFFE
MODELING
D_PLAN
[U4.22.01]
DEFI_MATERIAU
LEMAITRE
NR
[U4.23.01]
UN_SUR_K
UN_SUR_M
AFFE_CHAR_MECA
FORCE_NODALE
NODE
[U4.25.01]
STAT_NON_LINE
COMP_INCR
RELATION
LEMAITRE
[U4.32.01]
CALC_ELEM
OPTION
EPSI_ELNO_DEPL
[U4.61.01]
Code_Aster
®
Version
4.0
Titrate:
SSNP101 Plates in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A
Page:
5/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
4
Results of modeling A
4.1 Values
tested
Variables
Moments (S)
Reference
Aster
% difference
v
xx
30
1.7620 10
4
1.7623 10
4
0.017%
v
xy
30
1.81585 10
4
1.81582 10
4
0.002%
v
xx
3630
1.9030 10
3
1.9033 10
3
0.018%
v
xy
3630
2.0789 10
3
2.0791 10
3
0.012%
v
xx
3660
1.9130 10
3
1.9125 10
3
0.024%
v
xy
3660
2.1906 10
3
2.1904 10
3
0.011%
v
xx
3720
1.8740 10
3
1.8741 10
3
0.004%
v
xy
3720
3.1813 10
3
3.1814 10
3
0.005%
4.2 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
39.07 seconds
Code_Aster
®
Version
4.0
Titrate:
SSNP101 Plates in traction-shearing
Date:
24/08/99
Author (S):
PH. BONNIERES
Key:
V6.03.101-A
Page:
6/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
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
).