Code_Aster ®
Version
4.0
Titrate:
SSNP05 Plaque in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-A Page:
1/6
Organization (S): 1EDF/IMA/MN
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.005
SSNP05 - Plaque in traction-shearing:
viscoelasticity of Lemaître
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 3D) for one
nonradial loading. This test is drawn from guide VPCS of the SFM.
The plate is modelled by a voluminal element (HEXA8).
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:
SSNP05 Plaque in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-A Page:
2/6
1
Problem of reference
1.1 Geometry
Square plate
C
B
D
D
D
D
D
D
With
y
X
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
On 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:
SSNP05 Plaque in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-A Page:
3/6
2
Reference solution
2.1
Method of calculation used for the reference solution
Calculation carried out with various codes of finite elements using various explicit algorithms,
semi-implicit or implicit.
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 0.01%.
2.4 References
bibliographical
[1]
Card-index SSNP05/89 of Commission VPCS
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Code_Aster ®
Version
4.0
Titrate:
SSNP05 Plaque in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-A Page:
4/6
3 Modeling
With
3.1
Characteristics of modeling
Z
N07
N05
N08
N06
y
N03
N01
N04
N02
X
The loading and the boundary conditions are modelled by:
DDL_IMPO: (NOEUD: N04, DX: 0., DY:0.)
DDL_IMPO: (NOEUD: N08, DX: 0., DY:0., DZ:0.)
DDL_IMPO: (NOEUD: N02, DX: 0.)
DDL_IMPO: (NOEUD: N06, DX: 0.)
1
1
FORCE_NODALE: (NOEUD: (N01 N03 N05 N07), FX: -
()
T, FY: -
()
T)
D
D
4
4
1
FORCE_NODALE: (NOEUD: (N03 N04 N07 N08), FX: -
()
T)
D
4
1
FORCE_NODALE: (NOEUD: (N02 N04 N06 N08), FY:
()
T)
D
4
1
FORCE_NODALE: (NOEUD: (N01 N02 N05 N06), FX:
()
T)
D
4
3.2
Characteristics of the grid
A number of nodes:
8
A number of meshs and types:
1 HEXA8
3.3 Functionalities
tested
Commands
Key
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:
SSNP05 Plaque in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-A Page:
5/6
4
Results of modeling A
4.1 Values
tested
Variables
Moments (S)
Reference
Aster
% difference
v
30
2.465 104
2.457 104
0.333%
xx
v
30
2.135 104
2.128 104
0.333%
xy
v
3630
2.867 103
2.876 103
0.316%
xx
v
3630
2.483 103
2.491 103
0.326%
xy
v
3660
2.879 103
2.889 103
0.337%
xx
v
3660
2.565 103
2.562 103
0.101%
xy
v
3720
2.879 103
2.889 103
0.337%
xx
v
3720
3.272 103
3.271 103
0.037%
xy
4.2 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
Obstruction memory:
8 MW
Time CPU To use:
39.37 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:
SSNP05 Plaque in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-A Page:
6/6
5
Summary of the results
The precision necessary for this test was fixed at 0.5% instead of 0.1% not not to lengthen time too much
of calculation. However, one checks that by refining the discretization in time, the error made compared to
the reference solution tends towards zero.
Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A