27- twisted or yielded thin Section linear

27- twisted or yielded thin Section linear

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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
Date : 21/11/2012 Page : 1/10
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SSLS27- Bored or yielded thin section
Summary:
The test, taken again guide VPCS, makes it possible to check the behavior of an clamped plane plate
subjected at its loose lead with two nodal forces of the same sign (bending) or of opposite sign (torsion).
The first loading constitutes an extension of the initial test for which a reference solution is given in [bib3].
5 modelizations are carried out: DKT, DST, DKQ, DSQ and Q4G.
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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
1
Reference problem
1.1
Geometry
z
Date : 21/11/2012 Page : 2/10
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:
52fb1123362d
y
D
C
C
C
E
b
A
x
L
Longueur Largeur Epaisseur Coordinates of the points (in
x
y
z
1.2
B
B
cas 1
cas 2
B
L = 12 m b = 1 m t = 0.05 m
m):
A
B
0.
- 0.5
0.
12.
- 0.5
0.
C
12.
0.5
0.
D
E
0.
0.5
0.
12.
0.
0.
Material properties
The elastic material properties considered are the following ones:
Young modulus: E=1.10 11 Pa
Poisson's ratio:  =0.25
1.3
Boundary conditions and loadings
Side AD clamped:
any point P such as
x P=0 ( u=v =w=0
 x = y= z =0 )
Loading: 2 loading cases
B and C : opposite forces parallel with the axis Z
2) in B and C : of the same forces directions parallel
with the axis Z
1)
in
F z = – 1 N F z =1 N
F z =1 N F z =1 N
B
C
B
C
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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
Date : 21/11/2012 Page : 3/10
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Clé : V3.03.027
2
Reference solution
2.1
Computation method used for the reference solution
•
:
52fb1123362d
Opposite forces perpendicular to the plate [bib1], [bib2]
The reference solution is that given in file SSLS 27/89 of guide VPCS:
Displacement of the point C : w=35.37 10−7 m
Resultant of the forces to fixed support ( AD ) according to DZ : RESULT Z =0
Time associated with the resultant with the forces to fixed support in the middle of
AD :
MOMENT X =−1
MOMENT Y =0
•
Of the same forces directions perpendicular to the plate [bib3]
The formulation in Euler beam gives a approached solution for a Poisson's ratio
 different.
F
2 L3
Displacement of all the nodes on the side BC : w 
6 E Iz
Resultant of the forces to fixed support ( AD ) according to DZ : RESULT Z =−2
Time associated with the resultant with the forces to fixed support in the middle of AD :
MOMENT X =0
MOMENT Y =24
2.2
Reference results
Displacement of the points B , C and E . Resultant with fixed support along
support compared to the axes X and Y in the middle of AD .
2.3
AD , time with fixed
Uncertainty on the solution
Analytical solution.
2.4
Bibliographical references
1)
J. ROBINSON «Element evaluation. With set of assessment shares and norm tests»
Proceedings of Finite Element Methods in the commercial Environment, Vol. 1, (October
1978).
2)
J.L. BATOZ, M.B. TAHAR «quadrilateral Evaluation of new thin punt boundary element»
International Journal for Numerical Methods in Engineering, Vol. 18, John Wiley & Sons
(1982).
3)
R.J. ROARK, W.C. YOUNG «Formulas for Stress and Strain» New York: Mc Graw- Hill, 5
° edition, p 96.
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)
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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
Date : 21/11/2012 Page : 4/10
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Clé : V3.03.027
:
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3
Modelization A
3.1
Characteristics of modelization
Shell element DKT
y
53
D
54
55
56
57
58
59
60
61
62
63
64
65
C
40
52
27
39
14
26
A
1
3
2
4
6
5
Cutting:
12 in length
Slenderness
transverse
longitudinal
7
9
8
4 in width:
10
11
12
13
96 meshes TRIA3
with symmetry by report centre
b /4t=5
L /12t=20
E
x
B
Ox
2 loading cases
1)
2)
Opposite forces
Of the same forces direction
Name of the nodes:
Not
Not
3.2
A=N1
B=N13
Not
Not
C= N65
D=N53
Not
E= N39
Characteristics of the mesh
Number of nodes: 65
Number of meshes and types: 96 TRIA3
3.3
Quantities tested and results
Loading
case
1
2
Not
B
E
C
B
E
C
Size and unit
displacement
displacement
displacement
displacement
displacement
displacement
DZ m
DZ m
DZ m
DZ m
DZ m
DZ m
Reference
Type of
reference
Tolerance
«ANALYTIQUE '
0.5%
0
«ANALYTIQUE '
1.0e -12
10- 6
«ANALYTIQUE '
0.5%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059
10- 3
«ANALYTIQUE '
1%
1.1059
10- 3
«ANALYTIQUE '
1%
- 3,537 10- 6
3,537
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
Date : 21/11/2012 Page : 5/10
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4
Modelization B
4.1
Characteristics of modelization
Shell element DST
y
D
53
54
55
56
57
58
59
60
61
62
63
64
65
C
40
52
27
39
14
26
A
1
3
2
4
6
5
Cutting:
12 in length
Slenderness
transverse
longitudinal
7
9
8
4 in width:
10
11
12
13
96 meshes TRIA3
with symmetry by report centre
E
x
B
Ox
b /4t=5
L /12t=20
2 loading cases
1)
2)
Opposite forces
Of the same forces direction
Name of the nodes:
Not
Not
4.2
A=N1
B=N13
Not
Not
C= N65
D=N53
Not
Not
E= N39
F =N27
Characteristics of the mesh
Number of nodes: 65
Number of meshes and types: 96 TRIA3
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)
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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
4.3
Date : 21/11/2012 Page : 6/10
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Quantities tested and results
Loading
case
1
2
Not
Size and unit
Reference
B
E
C
AD
F
F
B
E
C
AD
F
F
DZ m
displacement DZ m
displacement DZ m
Resulting force DZ  N 
Moment DRX  N.m 
Moment DRY  N.m 
displacement DZ m
displacement DZ m
displacement DZ m
Resulting force DZ  N 
Moment DRX  N.m 
Moment DRY  N.m 
- 3,537 10- 6
displacement
Type of
reference
Tolerance
«ANALYTIQUE '
0.5%
«ANALYTIQUE '
1.0e -12
«ANALYTIQUE '
0.5%
0
«ANALYTIQUE '
1.0e -8
-1
«ANALYTIQUE '
1.0e -6 %
0
«ANALYTIQUE '
1.0e -8
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
-2
«ANALYTIQUE '
1.0e -6 %
0
«ANALYTIQUE '
1.0e -8
24
«ANALYTIQUE '
1.0e -6 %
0
3,537 10- 6
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
Date : 21/11/2012 Page : 7/10
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Clé : V3.03.027
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52fb1123362d
5
Modelization C
5.1
Characteristics of modelization
Shell element DKT
y
D
C
E
x
A
B
Cutting:
12 in length
4 in width:
48 meshes QUAD4
with symmetry by report centre
Slenderness
transverse
longitudinal
b /4t=5
L /12t=20
Ox
2 loading cases
1)
2)
5.2
Opposite forces
Of the same forces direction
Characteristics of the mesh
Number of nodes: 65
Number of meshes and types: 48 QUAD4
5.3
Quantities tested and results
Loading
case
1
2
Not
B
E
C
B
E
C
Size and unit
displacement
displacement
displacement
displacement
displacement
displacement
DZ m
DZ m
DZ m
DZ m
DZ m
DZ m
Reference
Type of
reference
Tolerance
«ANALYTIQUE '
0.5%
«ANALYTIQUE '
1.0e -12
«ANALYTIQUE '
0.5%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
- 3,537 10- 6
0
3,537 10- 6
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)
Version
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Code_Aster
Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
Date : 21/11/2012 Page : 8/10
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Clé : V3.03.027
:
52fb1123362d
6
Modelization D
6.1
Characteristics of modelization
Shell element DST
y
D
C
E
x
A
B
Cutting:
12 in length
4 in width:
48 meshes QUAD4
with symmetry by report centre
Slenderness
transverse
longitudinal
b /4t=5
L /12t=20
Ox
2 loading cases
1)
2)
6.2
Opposite forces
Of the same forces direction
Characteristics of the mesh
Number of nodes: 65
Number of meshes and types: 48 QUAD4
6.3
Quantities tested and results
Loading
case
1
2
Not
B
E
C
B
E
C
Size and unit
displacement
displacement
displacement
displacement
displacement
displacement
DZ m
DZ m
DZ m
DZ m
DZ m
DZ m
Reference
Type of
reference
Tolerance
«ANALYTIQUE '
0.5%
«ANALYTIQUE '
1.0e -12
«ANALYTIQUE '
0.5%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
- 3,537 10- 6
0
3,537 10- 6
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)
Version
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Code_Aster
Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
Date : 21/11/2012 Page : 9/10
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Clé : V3.03.027
:
52fb1123362d
7
Modelization E
7.1
Characteristics of modelization
Shell element Q4G
y
D
C
E
x
A
B
Cutting:
12 in length
4 in width:
48 meshes QUAD4
with symmetry by report centre
Slenderness
transverse
longitudinal
b /4t=5
L /12t=20
Ox
2 loading cases
1)
2)
7.2
Opposite forces
Of the same forces direction
Characteristics of the mesh
Number of nodes: 65
Number of meshes and types: 48 QUAD4
7.3
Quantities tested and results
Loading
case
1
2
Not
B
E
C
B
E
C
Size and unit
displacement
displacement
displacement
displacement
displacement
displacement
DZ m
DZ m
DZ m
DZ m
DZ m
DZ m
Reference
Type of
reference
Tolerance
«ANALYTIQUE '
0.5%
«ANALYTIQUE '
1.0e -12
«ANALYTIQUE '
0.5%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
1.1059 10- 3
«ANALYTIQUE '
1%
- 3,537 10- 6
0
3,537 10- 6
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)
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Titre : SSLS27 - Plaque mince vrillée ou fléchie
Responsable : DE SOZA Thomas
8
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Date : 21/11/2012 Page : 10/10
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Summary of results
One finds the analytical results with very a good agreement which modelization takes account
transverse shear or not.
Warning : The translation process used on this website is a "Machine Translation". It may be imprecise and inaccurate in whole or in part and is
provided as a convenience.
Licensed under the terms of the GNU FDL (http://www.gnu.org/copyleft/fdl.html)