Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
1/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
Organization (S):
EDF-R & D/AMA
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.105
SSLL105 - Elastic buckling of a structure
in L
Summary:
An L-shaped structure made up of two slim beams of mean rectangular section is subjected
with a force at an end, and is embedded at the other end. One seeks the critical loads
elastic buckling associated the positive and negative values of the force. The field of the test is:
·
linear elastic mechanics,
·
buckling of beams,
·
The first 3 modelings relate to (
POU_D_E
,
POU_D_T
,
POU_D_TG
).
·
The fourth modeling tests the criterion of buckling in the nonlinear operator of statics.
Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
2/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
1
Problem of reference
1.1 Geometry
L
X
P
C
L
Y
B
With
Z
B
Section:
T
Geometrical characteristics:
L = 240 mm
B = 30 mm
T = 0.6 mm
1.2
Material properties
E = 71240 MPa
= 0.3
1.3
Boundary conditions and loadings
·
C.L. : embedding in A
·
Loading:
F
X
= P
-
case 1:
P
= 1 NR
-
case 2:
P
= +1 NR
Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
3/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
2
Reference solution
2.1
Method of calculation used for the reference solution
Average of codes (8 results in [bib1]).
2.2
Results of reference
Values of the critical load for the two loading cases.
2.3
Uncertainty on the solution
2% (maximum variation compared to the average of results used).
2.4 References
bibliographical
[1]
G. DEVESA: Processing of great displacements in the element of angle with 7 ddl
established in Code_Aster validation by a conventional case test (HM-77/94/079).
Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
4/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
3 Modeling
With
3.1
Characteristics of modeling
20 elements
POU_D_E
3.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 20 SEG2
3.3 Functionalities
tested
Controls
CALC_MATR_ELEM “RIGI_GEOM”
4
Results of modeling A
4.1 Values
tested
Loading case
Reference
Aster %
difference
1 1.088
1.090
0.19
2 0.680
0.6813
0.19
Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
5/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
5 Modeling
B
5.1
Characteristics of modeling
20 elements
POU_D_T
5.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 20 SEG2
5.3 Functionalities
tested
Controls
CALC_MATR_ELEM “RIGI_GEOM”
6
Results of modeling B
6.1 Values
tested
Loading case
Reference
Aster %
difference
1 1.088
1.090
0.19
2 0.680
0.6813
0.19
Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
6/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
7 Modeling
C
7.1
Characteristics of modeling
20 elements
POU_D_TG
7.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 20 SEG2
7.3 Functionalities
tested
Controls
CALC_MATR_ELEM “RIGI_GEOM”
8
Results of modeling C
8.1 Values
tested
Loading case
Reference
Aster %
difference
1 1.088
1.0918
0.35
2 0.680
0.688
1.2
8.2 Remarks
The results of this modeling differ slightly from the others and are identical to those obtained
by calculation Aster of the reference [bib1].
Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
7/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
9 Modeling
D
9.1
Characteristics of modeling
20 elements
POU_D_E
9.2
Characteristics of the mesh
A number of nodes: 21
A number of meshs and types: 20 SEG2
9.3 Functionalities
tested
Controls
STAT_NON_LINE CRIT_FLAMB
10 Results of modeling D
10.1 Values
tested
Loading case
Reference
Aster %
difference
1 1.088
1.0866
0.12
2 0.680
0.67983
0.025
Code_Aster
®
Version
7.2
Titrate:
SSLL105 - Elastic buckling of a structure in L
Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA
Key
:
V3.01.105-B
Page:
8/8
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A
11 Summary of the results
The results of 4 modelings are very close to the reference solution which is an average
results of 8 codes. One notes a small effect due to the roll since the results of
modeling C (
POU_D_TG
) are slightly different from the others, while remaining with less than 2% of
reference.