Code_Aster
®
Version
4.0
Titrate:
SSNP05 Plates in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-A
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/96/043 - Ind A
Organization (S): 1
EDF/IMA/MN
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.005
SSNP05 - Plate 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 modelized by a voluminal element (HEXA8).
Results obtained by
Code_Aster
are very close to the reference solution.
Code_Aster
®
Version
4.0
Titrate:
SSNP05 Plates in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-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
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
On 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:
SSNP05 Plates in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-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 carried out with various codes of finite elements using various explicit algorithms,
semi-implicit or implicit.
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 0.01%.
2.4 References
bibliographical
[1]
Card-index SSNP05/89 of Commission VPCS
Code_Aster
®
Version
4.0
Titrate:
SSNP05 Plates in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-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
Z
X
y
N07
N05
N06
N08
N03
N01
N02
N04
The loading and the boundary conditions are modelized by:
DDL_IMPO: (NODE: N04, DX: 0., DY:0.)
DDL_IMPO: (NODE: N08, DX: 0., DY:0., DZ:0.)
DDL_IMPO: (NODE: N02, DX: 0.)
DDL_IMPO: (NODE: N06, DX: 0.)
FORCE_NODALE: (NODE: (N01 N03 N05 N07), FX:
()
-
1
4
T
D
, FY:
()
-
1
4
T
D
)
FORCE_NODALE: (NODE: (N03 N04 N07 N08), FX:
()
-
1
4
T
D
)
FORCE_NODALE: (NODE: (N02 N04 N06 N08), FY:
()
1
4
T
D
)
FORCE_NODALE: (NODE: (N01 N02 N05 N06), FX:
()
1
4
T
D
)
3.2
Characteristics of the mesh
A number of nodes:
8
A number of meshs and types:
1 HEXA8
3.3 Functionalities
tested
Controls
Key
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:
SSNP05 Plates in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-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
2.465 10
4
2.457 10
4
0.333%
v
xy
30
2.135 10
4
2.128 10
4
0.333%
v
xx
3630
2.867 10
3
2.876 10
3
0.316%
v
xy
3630
2.483 10
3
2.491 10
3
0.326%
v
xx
3660
2.879 10
3
2.889 10
3
0.337%
v
xy
3660
2.565 10
3
2.562 10
3
0.101%
v
xx
3720
2.879 10
3
2.889 10
3
0.337%
v
xy
3720
3.272 10
3
3.271 10
3
0.037%
4.2 Parameters
of execution
Version: 3.02.11
Machine: CRAY C90
Overall dimension memory:
8 MW
Time CPU To use:
39.37 seconds
Code_Aster
®
Version
4.0
Titrate:
SSNP05 Plates in traction-shearing: viscoelasticity of Lemaître
Date:
01/09/99
Author (S):
PH. BONNIERES
Key:
V6.03.005-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
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.