Code_Aster
®
Version
4.0
Titrate:
SSNP305 Bars in compression
Date:
01/12/98
Author (S):
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.305-A
Page:
1/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
Organization (S):
EDF/IMA/MN, SAMTECH SA
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
Document: V6.03.305
SSNP305 - Element of bar in compression -
Appearance of a negative pivot
Summary:
This test of quasi-static mechanics linear 2D consists in charging an element of bar in compression. Of one
side, the element is fixed according to the degrees of translation on a node. Other side, the element is fixed according to
the second degree of translation on a node in order to modelize the slip along a line. With some
moment the stiffness becomes negative (= negative slope). This test is drawn from guide NAFEMS (analytical solution).
The structure will be charged by using a piloting by displacement.
The plate is modelized by 12 plane elements (MECPQU4). The material has a linear behavior and one
takes into account nonthe geometrical linearities. One uses the key word factor `
COMP_ELAS
'option `
GREEN
'.
Code_Aster
®
Version
4.0
Titrate:
SSNP305 Bars in compression
Date:
01/12/98
Author (S):
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.305-A
Page:
2/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
1
Problem of reference
1.1 Geometry
1.2
Material properties
Isotropic elastic material
E = 200000 MPa
= 0.0
1.3
Boundary conditions and loadings
Not a:
U
X
=0.
U
y
= 0.
Not b:
U
X
=0.
Loading by a force P on the point B. the force will be increased by using a piloting by
displacement of the point B.
L = 2500
L = 2500
To = 250
Code_Aster
®
Version
4.0
Titrate:
SSNP305 Bars in compression
Date:
01/12/98
Author (S):
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.305-A
Page:
3/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
2
Reference solution
2.1
Method of calculation used for the reference solution
Analytical solution.
2.2
Results of reference
Vertical displacement
(
)
=
-
Q
L
1
Deformation `
GREEN
'
(
)
P
EAQ
Q
= -
-
+
1
1
2
2
2
3
2
2 1
2.3 References
bibliographical
[1]
Benchmark tests for solution procedures for geometric non-linearity, NAFEMS, 1987
Code_Aster
®
Version
4.0
Titrate:
SSNP305 Bars in compression
Date:
01/12/98
Author (S):
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.305-A
Page:
4/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
3 Modeling
With
3.1
Characteristics of modeling A
P
N06
N07
L
early
E = 200000
E = 2nd 7
Modeling in plane stresses:
C_PLAN
The loading and the boundary conditions are modelized by:
DDL_IMPO:
(NODE: N7 DX: 0.)
(NODE: N1 DX: 0.
DY: 0.)
In order to respect the best possible behavior of bar, one prolongs the length of the bar and
one imposes on this surplus of matter a Young modulus of 2e7 MPa.
The other meshs are affected face value of 200000 MPa.
3.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs: 12 MECPQU4
3.3 Functionalities
tested
Controls
Keys
DEFI_MATERIAU
ELAS
[U4.23.01]
STAT_NON_LINE
COMP_ELAS
RELATION
`
ELAS
`
[U4.32.01]
DEFORMATION
`
GREEN
`
AFFE_CHAR_MECA_F
DDL_IMPO
[U4.25.01]
Code_Aster
®
Version
4.0
Titrate:
SSNP305 Bars in compression
Date:
01/12/98
Author (S):
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.305-A
Page:
5/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
4
Results of modeling A
4.1 Values
tested
Identification
Reference
Aster
% difference
FY (N7) with DX = - 250
1511441
1510290
0.076
FY (N7) with DX = - 500
2545584
2543930
0.065
FY (N7) with DX = - 750
3155464
3153710
0.055
FY (N7) with DX = - 1050
3401961
3400410
0.045
FY (N7) with DX = - 1500
2969848
2968840
0.034
FY (N7) with DX = - 2000
1697056
1696620
0.0256
FY (N7) with DX = - 2500
0
1.E-5
0
4.2 Remarks
The application of the loading is carried out with 100 increments.
4.3 Parameters
of execution
Version: 3.09
Machine:
System:
Overall dimension memory:
8 megawords
Time CPU To use:
170.29 seconds
Code_Aster
®
Version
4.0
Titrate:
SSNP305 Bars in compression
Date:
01/12/98
Author (S):
I. VAUTIER, L. LAMMERANT, H. DRION
Key:
V6.03.305-A
Page:
6/6
Manual of Validation
V6.03 booklet: Nonlinear statics of the plane systems
HI-75/98/040 - Ind A
5
Summary of the results
The results provided by Aster are in perfect agreement with the reference solution.