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7.2
Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, Key S. BAGUET
:
V3.03.105-D 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: V3.03.105

SSLS105 - Doubly gripped Hémisphère

Summary:

One treats the case of the hemisphere doubly gripped in linear elasticity, which makes it possible to evaluate the quality of
plane facets for the representation of a deep hull.

The values tested are the arrows at the points of application of the forces.

One has 3 modelings:

·
A: elements DKT
·
B: elements of COQUE_3D in QUAD9
·
C: elements SHB8

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

Code_Aster ®
Version
7.2
Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, Key S. BAGUET
:
V3.03.105-D Page:
2/8

1
Problem of reference

1.1 Geometry

Z
Z
C
C
y
B
B
y
2KN
With
With
2KN
X
X
Radius
R = 10. m
Thickness
T = 0.04 m


Co-ordinates of the points:

With
B
C
X 10.
0.
0.
y 0.
10.
0.
Z 0.
0.
10.

1.2
Material properties

E = 6.825 107 Pa, = 0.3

1.3
Boundary conditions and loadings

On a quarter of the hemisphere:

Not C
no displacement in Z
Side AC
symmetry compared to the xz plan
Side BC
symmetry compared to the yz plan
Side AB
free

Specific force in a: F = ­ 2. KN
Specific force in b: F = +2. KN

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

Code_Aster ®
Version
7.2
Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, Key S. BAGUET
:
V3.03.105-D Page:
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2
Reference solution

2.1
Method of calculation used for the reference solution

The reference solution is that given in the card “Test No LE3” of the tests of reference published
by NAFEMS [bib1].

2.2
Results of reference

Displacement of point A following X.

2.3 References
bibliographical

[1]
A. Morris. Dynamics Working Group - College off Aeronautics, Cranfield, the U.K. Free vibrations
benchmarks. NAFEMS - Test No LE3 - (1986).

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

Code_Aster ®
Version
7.2
Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, Key S. BAGUET
:
V3.03.105-D Page:
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3 Modeling
With

3.1
Characteristics of modeling

Element of hull DKT

Modeling of a quarter of the hemisphere in TRIA3.

Names of the nodes:



Not A
N03
Not B
N02
Not C
N01

3.2
Characteristics of the grid

A number of nodes: 734
A number of meshs and types: 1373 TRIA3

3.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL
TOUT


AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_NODALE
GROUP_NO
“MECHANICAL” AFFE_MODELE “DKT”
TOUT

DEFI_MATERIAU ELAS




4
Results of modeling A

4.1 Values
tested

Identification Reference Aster %
difference
Not A
­ 0.185 ­ 0.1838 ­ 0.66
displacement U
Not B
+0.185 +0.1839 ­ 0.59
displacement v
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
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:
V3.03.105-D Page:
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5 Modeling
B

5.1
Characteristics of modeling

Element of hull COQUE_3D MEC3QU9H

C
With
B
Modeling of a quarter of the hemisphere in QUAD9

Names of the nodes:



Not A
N01
Not B
N021
Not C
N041

5.2
Characteristics of the grid

A number of nodes: 256
A number of meshs and types: 75 QUAD9

5.3 Functionalities
tested

Commands




AFFE_CARA_ELEM HULL
TOUT


AFFE_CHAR_MECA DDL_IMPO
GROUP_NO


FORCE_NODALE
GROUP_NO
AFFE_MATERIAU ALL



“MECHANICAL” AFFE_MODELE “COQUE_3D”
TOUT

DEFI_MATERIAU ELAS




6
Results of modeling B

6.1 Values
tested

Identification Reference Aster %
difference
Not A
­ 0.185 ­ 0.1844
­ 0.32
displacement U
Not B
+0.185 +0.1844
­ 0.32
displacement v
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
03/11/03
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:
V3.03.105-D Page:
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7 Modeling
C

7.1
Characteristics of modeling

Element of hull COQUE_MASSIF SHB8
C2
C1
A1
B1
A2
B2


Modeling of a quarter of the hemisphere in SHB8

7.2
Characteristics of the grid

Case 1:
A number of nodes: 662
A number of meshs and types: 300 SHB8
Names of the nodes:




Not A1
N40
Not A2
N42

Not B1
N01
Not B2
N02

Not C1
N662
Not C2
N658

Case 2:
A number of nodes: 2522
A number of meshs and types: 1200 SHB8
Names of the nodes:




Not A1
N1239
Not A2
N1241

Not B1
N301
Not B2
N303

Not C1
N602
Not C2
N604

Case 3:
A number of nodes: 5582
A number of meshs and types: 2700 SHB8
Names of the nodes:




Not A1
N329
Not A2
N331

Not B1
N3439
Not B2
N3441

Not C1
N4760
Not C2
N4762


7.3 Functionalities
tested

Commands



MODI_MAILLAGE ORIE_SHB8
GROUP_MA ALL
AFFE_CHAR_MECA DDL_IMPO
GROUP_NO

FORCE_NODALE
GROUP_NO
AFFE_MATERIAU ALL


“MECHANICAL” AFFE_MODELE SHB8
TOUT
DEFI_MATERIAU ELAS


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

Code_Aster ®
Version
7.2
Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, Key S. BAGUET
:
V3.03.105-D Page:
7/8

8
Results of modeling C

8.1 Values
tested

Identification Reference Aster %
difference

Not A
­ 0.185 ­ 0.1490
­ 19.44
Cas¨ 1
displacement U
Not
B
+0.185 +0.1490
­ 19.44
displacement v

Not A
­ 0.185 ­ 0.1822
­ 1.49
Case 2
displacement U
Not
B
+0.185 +0.1822
­ 1.49
displacement v

Not A
­ 0.185 ­ 0.1845
­ 0.24
Case 3
displacement U
Not
B
+0.185 +0.1845
­ 0.24
displacement v

8.2 Notice

For this modeling, convergence is relatively slower than for the MEC3QU9H, it is necessary in
effect 1200 elements to obtain a relative error of about 1%. But time CPU is not
crippling (12s). This is undoubtedly due to the choice of the law of behavior specific to the element
SHB8: law of plane constraints, and nonnull rigidity in the direction of the normal to the element.
If one chose a law of elasticity in plane constraints, without modification, one one would obtain then
correct solution (0,2% of variation) as of the 1st case (300 elements). But this law would be then unsuited
for other tests, such that of the sphere under pressure (SSLS123).

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

Code_Aster ®
Version
7.2
Titrate:
SSLS105 - Doubly gripped Hémisphère


Date:
03/11/03
Author (S):
P. MASSIN, J.M. PROIX, Key S. BAGUET
:
V3.03.105-D Page:
8/8

9
Summary of the results

Severe test which requires a fine grid, in particular for element DKT. Results with the element
MEC3TR7H were not retained as test because it is necessary to have many elements
(1801) and thus a time of convergence much longer to obtain correct values by
report/ratio with other modelings (> 500 S for a relative error of about 4%).
For element SHB8, convergence is relatively slower than for the MEC3QU9H, it is necessary in
effect 1200 elements to obtain a relative error of about 1%. But time CPU is not
crippling (12s).

Results in conformity with the reference solution.
Handbook of Validation
V3.03 booklet: Linear statics of the plates and hulls
HT-66/03/008/A

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