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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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Key J.M. PROIX
:
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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

Code_Aster ®
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Titrate:
SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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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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SSLL11 - Treillis of pin jointed struts under concentrated loading
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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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SSLL11 - Treillis of pin jointed struts under concentrated loading
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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

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SSLL11 - Treillis of pin jointed struts under concentrated loading
Date:
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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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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

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SSLL11 - Treillis of pin jointed struts under concentrated loading
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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):
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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
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V3.01.011-E Page:
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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

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