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

Organization (S): EDF/AMA, CS IF
Handbook 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.

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A

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

1
Problem of reference

1.1 Geometry

Plane rectangular plate.

N4
N3
N1N2 = 40 mm
N1N4 = 30 mm
y

X
N1
N2

1.2
Properties of materials

E = 200.000 MPa
= 0

Slope of the traction diagram C = 1930 Mpa
Elastic limit
y
= 181 Mpa

1.3
Boundary conditions and loadings mechanical

Face NR NR: blocked according to OX
1
2
Node NR: blocked according to OY
1
Node NR: blocked according to OY
2

Pressure varying linearly:

P (N2)
LMBO
= 0

P (NR)
LMBO
3 = 300 MPa

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A

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

2
Reference solution

2.1
Method of calculation used for the reference solution

The cumulated plastic deformation P is equal to:
y
-
P
L
=

C
with: : constraint with the node considered
L
y
: elastic limit
C: slope of the traction diagram

The constraints are given by:
(NR) = - P (NR)
xx
I
LMBO
I


The plastic deformation is given by:
p
(NR) = P (NR)
xx
I
I

2.2
Results of reference

One calculates in the nodes N2 and N3 the uniaxial constraint, the plastic deformation, as well as
cumulated plastic deformation.
Maybe for the problem considered:


N2
N3

0 ­ 300
xx

0 ­ 6.1658
10­2
xx
p

0 6.1658
10­2
xx

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 Aster code. Handbook of Référence of the course. EDF-DER, SCE IMA,
Dept. Numerical mechanics and Modèles, HI-74/96/013/0

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A

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

3 Modeling
With

3.1
Characteristics of modeling

N4
N3
TRI6
5 elements
y
QUA8
5 elements
X
QUA9
5 elements
N1
20 elements
N2


3.2
Characteristics of the grid

A number of nodes: 1072
A number of meshs and types:
100 QUAD9
100
QUAD8
200
TRIA6

3.3 Functionalities
tested

Commands



STAT_NON_LINE COMP_INCR
RELATION
VMIS_ISOT_LINE
CALC_ELEM OPTIONS
“SIEF_ELNO_ELGA”

“VARI_ELNO_ELGA”
“EPSP_ELNO”

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A

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

4
Results of modeling A

4.1 Values
tested

Identification Increment
Reference
Aster Difference
Cumulated plastic deformation




Node N2
10
0
0
0
N3 node
6.1658 10­2
6.1230 10­2
0.6%
Plastic deformation




Node N2
10
0
­ 1.46 10­5
­ 1.46 10­5
N3 node
­ 6.1658 10­2
­ 6.1230 10­2
­ 0.6%
Constraints




Node N2
10
0
­ 1.34
­ 1.34
N3 node
­ 300
­ 300.65
0.22%

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A

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

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.

Handbook of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HT-66/02/001/A

Outline document