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Code_Aster
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Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
1/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
Organization (S):
EDF/MTI/MN













Manual of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.011



SSLL11 - Lattice of pin jointed struts under load
specific




Summary:

This test makes it possible to check the elements of bar and beam for the structural analysis out of lattice. The lattice
considered is plane. Calculation is static, elastic, linear. The reference solution is analytical.

Three modelings make it possible to test the elements
POU_D_T
with and without rotulées connections, as well as
elements
BAR
.

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Code_Aster
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Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
2/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
1
Problem of reference
1.1 Geometry


X, U
y, v
With
B
C
D
L
L
L/2
L/2
L/2
F

Length L = 1 m
elements AC and BC surface A = 2. 10
­ 4
m
2
elements CD and data base surface A = 1. 10
­ 4
m
2


Co-ordinates of the points (in m):

WITH B
C D
X 0. 1.
0.5 2.
y 0. 0.
0.5 1.
Z 0. 0. 0. 0.


1.2
Material properties
E = 1.962 10
11
AP


1.3
Boundary conditions and loadings
The nodes A and B are articulated: U = v = 0
Vertical specific force in D: F = ­ 9.81 10
3
NR
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Code_Aster
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Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
3/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
2
Reference solution
2.1
Method of calculation used for the reference solution
The reference solution is that given in card SSLL11/89 of guide VPCS.
It is obtained by the method of displacements in [bib1].


2.2
Results of reference
Displacements of the points C and D.


2.3
Uncertainty on the solution
Analytical solution.


2.4 References
bibliographical
[1]
RAO (J.S.): The finite element method in engineering, problem 5.1, p. 275.
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Code_Aster
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Version
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Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
4/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
3 Modeling
With
3.1
Characteristics of modeling
Taking into account the twinges, the taking into account of the hinges modifies the results little. For
this modeling the hinges in A, B, C and D are rigidified (continuity of the 3 components
generalized efforts).
4 beams of full circular section: 4 meshs SEG2
elements AC and BC
radius R = 7.978845 10
­ 3
m
(surface A = 2. 10
­ 4
m
2
)
elements CD and data base
radius R = 5.641895 10
­ 3
m
(surface A = 1. 10
­ 4
m
2
)
Poisson's ratio:
= 0.3
Limiting conditions:
in all the nodes:
DDL_IMPO:
(ALL:“YES”
DZ: 0. , DRX: 0. , DRY: 0. )
(NODE: (A, B) DX: 0. , DY: 0. )

Name of the nodes:
Not A = A
Not C = C
Not B = B
Not D = D


3.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 4 SEG2


3.3 Functionalities
tested

Controls
Keys
AFFE_CARA_ELEM BEAM
NET
“CIRCLE”
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
ALL
[U4.25.01]
GROUP_NO
FORCE_NODALE
NODE
“MECHANICAL” AFFE_MODELE “POU_D_T'
[U4.22.01]
DEFI_MATERIAU ELAS
[U4.23.01]
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Code_Aster
®
Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
5/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
4
Results of modeling A
4.1 Values
tested

Not Displacement
(m)
Reference
Aster %
difference
U
C
2.6517 10
­ 4
2.6515
10
­ 4
0.00
C
V
C
0.8839 10
­ 4
0.88386
10
­ 4
0.00
U
D
3.47902 10
­ 3
3.4784
10
­ 3
­ 0.02
D
V
D
­ 5.60084 10
­ 3
­ 5.5994
10
­ 3
­ 0.03

4.2 Parameters
of execution
Version: 5.2
Machine: SGI/ORIGIN 2000 R10000
Overall dimension memory: 64 Mo
Time CPU To use:
2.1 seconds

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Code_Aster
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Version
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Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
6/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
5 Modeling
B
5.1
Characteristics of modeling
4 elements
POU_D_T
of full circular section: 4 meshs SEG2
elements AC and BC
radius R = 7.978845 10
­ 3
m
(surface A = 2. 10
­ 4
m
2
)
elements CD and data base
radius R = 5.641895 10
­ 3
m
(surface A = 1. 10
­ 4
m
2
)
Poisson's ratio:
= 0.3

Limiting conditions:
DDL_IMPO: (All:“YES”
DZ: 0. , DRX: 0. , DRY: 0. )

To treat the rotary joints, one creates as many nodes as of ends of bar.
C1
A1
B2
C2
C3
D3
D4
B4
· with the nodes
A1
,
B2
and
D4
DDL_IMPO: (DX: 0, D4: 0)
· with the nodes
C1, C2, C3
and
D3, D4
continuity
translations, by
LIAISON_DDL DX
and
DY
,
· no rotation is imposed.


5.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 4 SEG2


5.3 Functionalities
tested

Controls
Keys
AFFE_CARA_ELEM BEAM
NET
“CIRCLE”
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
NODE
[U4.25.01]
LIAISON_DDL
FORCE_NODALE
“MECHANICAL” AFFE_MODELE “POU_D_T'
[U4.22.01]
DEFI_MATERIAU ELAS
[U4.23.01]
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Code_Aster
®
Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
7/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
6
Results of modeling B
6.1 Values
tested

Not Displacement
(m)
Reference
Aster %
difference
U
C
2.6517 10
­ 4
2.6517
10
­ 4
0.00
C
V
C
0.8839 10
­ 4
0.8838
10
­ 4
­ 0.01
U
D
3.47902 10
­ 3
3.4790
10
­ 3
0
D
V
D
­ 5.60084 10
­ 3
­ 5.6003
10
­ 3
­ 0.01

6.2 Parameters
of execution
Version: 5.2
Machine: SGI/ORIGIN 2000 R10000
Overall dimension memory: 64 Mo
Time CPU To use: 3.7 seconds

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Code_Aster
®
Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
8/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
7 Modeling
C
7.1
Characteristics of modeling
4 elements
BAR
of full circular section: 4 meshs SEG2
elements AC and BC
radius R = 7.978845 10
­ 3
m
(surface A = 2. 10
­ 4
m
2
)
elements CD and data base
radius R = 5.641895 10
­ 3
m
(surface A = 1. 10
­ 4
m
2
)
Poisson's ratio:
= 0.3

Limiting conditions:
DDL_IMPO:
(
ALL:“YES”
DZ:
0.
)
(NODE: (A, B) DX: 0. , DY: 0. )


7.2
Characteristics of the mesh
A number of nodes: 4
A number of meshs and types: 4 SEG2


7.3 Functionalities
tested

Controls
Keys
AFFE_CARA_ELEM BARS
NET
“CIRCLE”
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
NODE
[U4.25.01]
FORCE_NODALE
[U4.23.02]
“MECHANICAL” AFFE_MODELE “BAR”
[U4.22.01]
DEFI_MATERIAU ELAS
[U4.23.01]

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Code_Aster
®
Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
9/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
8
Results of modeling C
8.1 Values
tested

Not Displacement
(m)
Reference
Aster %
difference
U
C
2.6517 10
­ 4
2.6517
10
­ 4
­ 0.002
C
V
C
0.8839 10
­ 4
0.8839
10
­ 4
­ 0.002
U
D
3.47902 10
­ 3
3.47902
10
­ 3
0
D
V
D
­ 5.60084 10
­ 3
­ 5.60035
10
­ 3
­ 0.009

8.2 Parameters
of execution
Version: 5.2
Machine: SGI/ORIGIN 2000 R10000
Overall dimension memory: 64 Mo
Time CPU To use: 2.4 seconds

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Code_Aster
®
Version
5.0
Titrate:
SSLL11 - Lattice of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
J.M. PROIX
Key
:
V3.01.011-E
Page:
10/10
Manual of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
9
Summary of the results
Results in conformity with the reference solution for three modelings:
·
model of beams,
·
model of linear beams + relations,
·
model of bars.