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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
Key J.M. PROIX
:
V3.01.011-E Page:
1/10
Organization (S): EDF/MTI/MN
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
Document: V3.01.011
SSLL11 - Treillis 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 elements POU_D_T with and without rotulées connections, as well as
elements BARRE.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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Author (S):
Key J.M. PROIX
:
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1
Problem of reference
1.1 Geometry
D
F
C
L
L/2
With
B
y, v
L/2
L/2
L
X, U
Length L = 1 m
elements AC and BC surface A = 2. 104 m2
elements CD and data base surface A = 1. 104 m2
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 1011 Pa
1.3
Boundary conditions and loadings
The nodes A and B are articulated: U = v = 0
Vertical specific force in D: F = 9.81 103 NR
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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Author (S):
Key J.M. PROIX
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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.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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3 Modeling
With
3.1
Characteristics of modeling
Taking into account the twinges, the taking into account of the articulations modifies the results little. For
this modeling the articulations 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 103 m
(surface A = 2. 104 m2)
elements CD and data base
radius R = 5.641895 103 m
(surface A = 1. 104 m2)
Poisson's ratio:
= 0.3
Limiting conditions:
in all the nodes:
DDL_IMPO:
(TOUT:“OUI”
DZ: 0. , DRX: 0. , DRY: 0. )
(NOEUD: (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 grid
A number of nodes: 4
A number of meshs and types: 4 SEG2
3.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM BEAM
MAILLE
“CERCLE”
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
TOUT
[U4.25.01]
GROUP_NO
FORCE_NODALE
NOEUD
“MECHANICAL” AFFE_MODELE “POU_D_T'
[U4.22.01]
DEFI_MATERIAU ELAS
[U4.23.01]
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
Code_Aster ®
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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
Key J.M. PROIX
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V3.01.011-E Page:
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4
Results of modeling A
4.1 Values
tested
Not Reference Displacement
Aster %
difference
(m)
CPU
2.6517 104 2.6515
104
0.00
C
Vc
0.8839 104 0.88386
104
0.00
uD
3.47902 103 3.4784
103
0.02
D
VD
5.60084 103 5.5994
103
0.03
4.2 Parameters
of execution
Version: 5.2
Machine: SGI/ORIGIN 2000 R10000
Obstruction memory: 64 Mo
Time CPU To use:
2.1 seconds
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
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SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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Author (S):
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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 103 m
(surface A = 2. 104 m2)
elements CD and data base
radius R = 5.641895 103 m
(surface A = 1. 104 m2)
Poisson's ratio:
= 0.3
Limiting conditions:
DDL_IMPO: (All:“OUI”
DZ: 0. , DRX: 0. , DRY: 0. )
To treat the rotary joints, one creates as many nodes as of ends of bar.
D3
· with the nodes
C3
A1, B2 and D4
C1
D4
DDL_IMPO: (DX: 0, D4: 0)
· with the C1 nodes, C2, C3 and D3, D4 continuity
C2
translations, by LIAISON_DDL DX and DY,
· no rotation is imposed.
A1
B4
B2
5.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 4 SEG2
5.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM BEAM
MAILLE
“CERCLE”
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
NOEUD
[U4.25.01]
LIAISON_DDL
FORCE_NODALE
“MECHANICAL” AFFE_MODELE “POU_D_T'
[U4.22.01]
DEFI_MATERIAU ELAS
[U4.23.01]
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
Code_Aster ®
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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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Author (S):
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6
Results of modeling B
6.1 Values
tested
Not Reference Displacement
Aster %
difference
(m)
CPU
2.6517 104 2.6517
104
0.00
C
Vc
0.8839 104 0.8838
104
0.01
uD
3.47902 103 3.4790
103
0
D
VD
5.60084 103 5.6003
103
0.01
6.2 Parameters
of execution
Version: 5.2
Machine: SGI/ORIGIN 2000 R10000
Obstruction memory: 64 Mo
Time CPU To use: 3.7 seconds
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
Key J.M. PROIX
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V3.01.011-E Page:
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7 Modeling
C
7.1
Characteristics of modeling
4 elements BARRE of full circular section: 4 meshs SEG2
elements AC and BC
radius R = 7.978845 103 m
(surface A = 2. 104 m2)
elements CD and data base
radius R = 5.641895 103 m
(surface A = 1. 104 m2)
Poisson's ratio:
= 0.3
Limiting conditions:
DDL_IMPO:
(
TOUT:“OUI”
DZ:
0.
)
(NOEUD: (A, B) DX: 0. , DY: 0. )
7.2
Characteristics of the grid
A number of nodes: 4
A number of meshs and types: 4 SEG2
7.3 Functionalities
tested
Commands
Keys
AFFE_CARA_ELEM BARS
MAILLE
“CERCLE”
[U4.24.01]
AFFE_CHAR_MECA DDL_IMPO
NOEUD
[U4.25.01]
FORCE_NODALE
[U4.23.02]
“MECHANICAL” AFFE_MODELE “BAR”
[U4.22.01]
DEFI_MATERIAU ELAS
[U4.23.01]
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
Key J.M. PROIX
:
V3.01.011-E Page:
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8
Results of modeling C
8.1 Values
tested
Not Reference Displacement
Aster %
difference
(m)
CPU
2.6517 104 2.6517
104
0.002
C
Vc
0.8839 104 0.8839
104
0.002
uD
3.47902 103 3.47902
103
0
D
VD
5.60084 103 5.60035
103
0.009
8.2 Parameters
of execution
Version: 5.2
Machine: SGI/ORIGIN 2000 R10000
Obstruction memory: 64 Mo
Time CPU To use: 2.4 seconds
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
Code_Aster ®
Version
5.0
Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
16/02/00
Author (S):
Key J.M. PROIX
:
V3.01.011-E Page:
10/10
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.
Handbook of Validation
V3.01 booklet: Linear statics of the linear structures
HI-75/01/010/A
Outline document