Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
1/8

Organization (S): EDF-R & D/AMA, INSA LYON
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
Document: V3.03.124
SSLS124 - Poutre in inflection with various
twinges

Summary:

This test represents a calculation quasi-static of a beam in inflection, embedded at an end, and subjected to
a vertical force at the other end. This test makes it possible to validate for a linear elastic design, and four
values of twinge (variable thicknesses) in each of two modelings:

· Finite elements SHB8 for a regular grid (modeling A)
· Finite elements SHB8 for a nonregular grid (modeling B)

Displacements obtained are compared with the elastic analytical solution of a beam in inflection. This test
allows to assemble the limits of the elements in term of twinge, on the one hand, and to show their good
convergence for a very irregular grid, in addition.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
2/8

1
Problem of reference

1.1 Geometry
Z
C
y
O
H
L
F
With
X
B
L


L= length 100 m, width l=10 Mr.
Thickness: case 1 h=10 m, cases 2 h=1 m, cases 3 h=0.1 m, cases 4 h=0.05 m, cases 5 h=0.02 m

1.2
Material properties

E = 2. 1011 Pa
= 0.3

1.3
Boundary conditions and loadings

Embedded on side OC: U = v = W = 0, X = y = Z = 0

At end AB, a load uniformly distributed of resultant:
Force parallel with axis Z; Fz = 1 NR

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
3/8

2
Reference solution

2.1
Method of calculation used for the reference solution

The results of reference are obtained by the theory of the elastic beams.

Vertical displacement at end AB is given by:
Uy = F.L3/3.E.Iz

With
Iz = l.h3/12

2.2
Results of reference

Displacement of points A and B following Z.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
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3 Modeling
With

3.1
Characteristics of modeling

Element SHB8

Z
X
y


Cutting: a regular grid is considered in this modeling.

Regular grid:

10 meshs SHB8: 1 according to the width, 10 according to the length, 1 according to the thickness
thickness: case 1 h=10 m, cases 2 h=1 m, cases 3 h=0.1 m, cases 4 h=0.05 m, cases 5 h=0.02 m

Boundary conditions:

In all the nodes on the side OC: blocked displacement following X
in C1: blocked displacement following Y and Z
in C2: blocked displacement following Y
in O1: blocked displacement following Z

Loading:
in A2: nodal force according to X: FX = 0,5
in B2: nodal force following Y: FY = 0,5

Name of the nodes:

Not O1
N40
Not O2
N44
Not A1
N03
Not A2
N01
Not B1
N04
Not B2
N02
Not C1
N43
Not C2
N39

3.2
Characteristics of the grid

A number of nodes: 44
A number of meshs and types: 11 SHB8
In the case of the regular grid, each element is a perfect square on side length 10m

3.3 Functionalities
tested

Commands



MODI_MAILLAGE ORIE_SHB8
GROUP_MA
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

FORCE_NODALE
GROUP_NO
AFFE_MODELE AFFE
MODELISATION
:
SHB8
MECA_STATIQUE SOLVEUR
NPREC

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
5/8

4
Results of modeling A

4.1 Values
tested

Regular grid:

Thickness
Not
Size in unit
Reference
Aster
% difference
Case 1
A2
displacement W (m)
2. 10­9
2.008 10­9
+0.41
H = 10m
B2
displacement W (m)
2. 10­9
2.008 10­9
+0.41
Case 2
A2
displacement W (m)
2. 10­6
1.995 10­6
­ 0.27
H = 1m
B2
displacement W (m)
2. 10­6
1.995 10­6
­ 0.27
Case 3
A2
displacement W (m)
2. 10­3
1.994 10­3
­ 0.28
H = 0.1m
B2
displacement W (m)
2. 10­3
1.994 10­3
­ 0.28
Case 4
A2
displacement W (m)
1.6 10­2
1.597 10­2
­ 0.2
H = 0.05m
B2
displacement W (m)
1.6 10­2
1.595 10­2
­ 0.3
Case 5
A2
displacement W (m)
0.25
2.380 10­1
+4.8
H = 0.02m
B2
displacement W (m)
0.25
2.416 10­1
+3.4

4.2 Remarks

For the strong twinges, (case 3, 4, 5), it is necessary to increase the number of decimals
lost with the resolution, using key word NPREC. This does not prevent from obtaining a correct solution
(at least for cases 3 and 4).

The twinges are (ratio H/min (I, L/10)) :

Case 1: 1
Case 2: 0.1
Case 3: 0.01
Case 4: 0.005
Case 5: 0.002
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
6/8

5 Modeling
B

5.1
Characteristics of modeling

Element SHB8



Cutting: an irregular grid is considered in this modeling.

Not-regular grid:

10 meshs SHB8: 1 according to the width, 10 according to the length, 1 according to the thickness
thickness: case 1 h=10 m, cases 2 h=1 m, cases 3 h=0.1 m, cases 4 h=0.05 m, cases 5 h=0.02 m

Boundary conditions:

In all the nodes on the side OC: blocked displacement following X
in C1: blocked displacement following Y and Z
in C2: blocked displacement following Y
in O1: blocked displacement following Z

Loading:
in A2: nodal force according to X: FX = 0,5
in B2: nodal force following Y: FY = 0,5

Names of the nodes:

Not O1
N40
Not O2
N44
Not A1
N03
Not A2
N01
Not B1
N04
Not B2
N02
Not C1
N43
Not C2
N39

5.2
Characteristics of the grid

A number of nodes: 44
A number of meshs and types: 11 SHB8

5.3 Functionalities
tested

Commands



MODI_MAILLAGE ORIE_SHB8
GROUP_MA
TOUT
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

FORCE_NODALE
GROUP_NO
AFFE_MODELE AFFE
MODELISATION
:
SHB8
MECA_STATIQUE SOLVEUR
NPREC


Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
7/8

6
Results of modeling B

6.1 Values
tested

Not-regular grid:

Thickness
Not
Size in unit
Reference
Aster
% difference
Case 1
A2
displacement W (m)
2. 10­9
1.939 10­9
­ 3.03
H = 10m
B2
displacement W (m)
2. 10­9
1.921 10­9
­ 3.94
Case 2
A2
displacement W (m)
2. 10­6
1.925 10­6
­ 3.73
H = 1m
B2
displacement W (m)
2. 10­6
1.907 10­6
­ 4.64
Case 3
A2
displacement W (m)
2. 10­3
1.925 10­3
­ 3.75
H = 0.1m
B2
displacement W (m)
2. 10­3
1.907 10­3
­ 4.65
Case 4
A2
displacement W (m)
1.6 10­2
1.542 10­2
­ 3.60
H = 0.05m
B2
displacement W (m)
1.6 10­2
1.528 10­2
­ 4.51
Case 5
A2
displacement W (m)
0.25
2.479 10­1
­ 0.83
H = 0.02m
B2
displacement W (m)
0.25
2.45710­1
­ 1.72

6.2 Remarks

For the strong twinges, (case 3, 4, 5), it is necessary to increase the number of decimals
lost with the resolution, using key word NPREC. This does not prevent from obtaining a correct solution
(at least for cases 3 and 4).

The twinges are (ratio H/min (I, L/10)) :

Case 1: 1
Case 2: 0.1
Case 3: 0.01
Case 4: 0.005
Case 5: 0.002

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

Code_Aster ®
Version
7.2
Titrate:
SSLS124 - Poutre in inflection with various twinges

Date
:
06/11/03
Author (S):
J.M. PROIX, Key S. BAGUET
:
V3.03.124-A Page:
8/8

7
Summary of the results

In the case of the regular grid, from good solutions are obtained. The quality of the solution declines
nevertheless when the twinge of the element (side ratio/thickness) reached 200.

In the case of the not-regular grid, whatever the twinge of the element, one tends to underestimate
the rigidity of the beam from approximately 4%.

This test can be supplemented by a modeling 3D and to be applied to the elements of COQUE_3D
MEC3QU9H like with elements DKT.

Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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