Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
1/8

Organization (S): EDF-R & D/AMA

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.105

SSLL105 - Elastic Flambement 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.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
2/8

1
Problem of reference

1.1 Geometry

Y
L
With
Z
B
Section:
X
B
L
T
C
P
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
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
3/8

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 traditional case test (HM-77/94/079).
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
4/8

3 Modeling
With

3.1
Characteristics of modeling

20 elements POU_D_E

3.2
Characteristics of the grid

A number of nodes: 21

A number of meshs and types: 20 SEG2

3.3 Functionalities
tested

Commands




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

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
5/8

5 Modeling
B

5.1
Characteristics of modeling

20 elements POU_D_T

5.2
Characteristics of the grid

A number of nodes: 21

A number of meshs and types: 20 SEG2

5.3 Functionalities
tested

Commands




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

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
6/8

7 Modeling
C

7.1
Characteristics of modeling

20 elements POU_D_TG

7.2
Characteristics of the grid

A number of nodes: 21

A number of meshs and types: 20 SEG2

7.3 Functionalities
tested

Commands




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 Aster calculation of the reference [bib1].

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
7/8

9 Modeling
D

9.1
Characteristics of modeling

20 elements POU_D_E

9.2
Characteristics of the grid

A number of nodes: 21

A number of meshs and types: 20 SEG2

9.3 Functionalities
tested

Commands




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

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLL105 - Elastic Flambement of a structure in L

Date:
28/10/03
Author (S):
J.M. PROIX, G. DEVESA Key
:
V3.01.105-B Page:
8/8

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 warping since the results of
modeling C (POU_D_TG) are slightly different from the others, while remaining with less than 2% of
reference.

Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HT-66/03/008/A

Outline document