Code_Aster
®
Version
5.0
Titrate:
SSNP111 - Passage of the points of Gauss to the nodes
Date:
21/02/02
Author (S):
X.DESROCHES, NR. RAHNI
Key
:
V6.03.111-A
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
Organization (S):
EDF/AMA, CS IF
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
V6.03.111 document
SSNP111 - Passage of the points of Gauss
with the nodes on quadratic elements
Summary:
It is about a test of static mechanics nonlinear.
The goal is to test, in the order CALC_ELEM, the matrices making it possible to place from the points
of integration to the nodes nodes. The treated case relates to a plane plate subjected on one of its faces to
a pressure varying linearly.
Code_Aster
®
Version
5.0
Titrate:
SSNP111 - Passage of the points of Gauss to the nodes
Date:
21/02/02
Author (S):
X.DESROCHES, NR. RAHNI
Key
:
V6.03.111-A
Page:
2/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
Plane rectangular plate.
NR
1
NR
2
= 40 mm
NR
1
NR
4
= 30 mm
1.2
Properties of materials
E = 200.000 MPa
= 0
Slope of the traction diagram C = 1930 Mpa
Elastic limit
181
=
y
Mpa
1.3
Boundary conditions and loadings mechanical
Face
2
1
NR
NR
: locked according to OX
Node
1
NR
: locked according to OY
Node
2
NR
: locked according to OY
Pressure varying linearly:
(
)
(
)
P
NR
P
NR
LMBO
LMBO
2
0
3
300
=
=
MPa
NR
1
NR
2
NR
3
NR
4
X
y
Code_Aster
®
Version
5.0
Titrate:
SSNP111 - Passage of the points of Gauss to the nodes
Date:
21/02/02
Author (S):
X.DESROCHES, NR. RAHNI
Key
:
V6.03.111-A
Page:
3/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Cumulated plastic deformation
P
is equal to:
C
P
y
L
-
=
with:
L
: stress with the node considered
y
: elastic limit
C
: slope of the traction diagram
The stresses are given by:
)
(
)
(
I
LMBO
I
xx
NR
P
NR
-
=
The plastic deformation is given by:
)
(
)
(
I
I
p
xx
NR
P
NR
=
2.2
Results of reference
One calculates with the nodes NR
2
and NR
3
the uniaxial stress, plastic deformation, as well as
cumulated plastic deformation.
Maybe for the problem considered:
NR
2
NR
3
xx
0 300
xx
0 6.1658
10
2
p
xx
0 6.1658
10
2
2.3
Uncertainty on the solution
Analytical solution.
2.4 References
bibliographical
[1]
LORENTZ E., PROIX J.M., VAUTIER I., VOLDOIRE F., WAECKEL F.: Initiation with
thermo plasticity in the code Aster. Manual of Reference of the course. EDF-DER, SCE IMA,
Dept. Mechanics and digital Models, HI-74/96/013/0
Code_Aster
®
Version
5.0
Titrate:
SSNP111 - Passage of the points of Gauss to the nodes
Date:
21/02/02
Author (S):
X.DESROCHES, NR. RAHNI
Key
:
V6.03.111-A
Page:
4/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
NR
1
NR
2
NR
3
NR
4
X
y
20 elements
5 elements
5 elements
5 elements
TRI6
QUA9
QUA8
3.2
Characteristics of the mesh
A number of nodes: 1072
A number of meshs and types:
100 QUAD9
100
QUAD8
200
TRIA6
3.3 Functionalities
tested
Controls
STAT_NON_LINE COMP_INCR
RELATION
VMIS_ISOT_LINE
CALC_ELEM OPTIONS
“SIEF_ELNO_ELGA”
“VARI_ELNO_ELGA”
“EPSP_ELNO”
Code_Aster
®
Version
5.0
Titrate:
SSNP111 - Passage of the points of Gauss to the nodes
Date:
21/02/02
Author (S):
X.DESROCHES, NR. RAHNI
Key
:
V6.03.111-A
Page:
5/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
4
Results of modeling A
4.1 Values
tested
Identification Increment
Reference
Aster Difference
Cumulated plastic deformation
Node NR
2
Node NR
3
10
0
6.1658 10
2
0
6.1230 10
2
0
0.6%
Plastic deformation
Node NR
2
Node NR
3
10
0
6.1658 10
2
1.46 10
5
6.1230 10
2
1.46 10
5
0.6%
Stresses
Node NR
2
Node NR
3
10
0
300
1.34
300.65
1.34
0.22%
Code_Aster
®
Version
5.0
Titrate:
SSNP111 - Passage of the points of Gauss to the nodes
Date:
21/02/02
Author (S):
X.DESROCHES, NR. RAHNI
Key
:
V6.03.111-A
Page:
6/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A
5
Summary of the results
The results coincide with the reference solution. They thus make it possible to rule on the validity of
matrices of passage of the points of gauss to the nodes nodes.