Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
1/8

Organization (S): EDF/AMA, SAMTECH
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.141

SSNV141 - Spherical Calotte pinch

Summary:

One presents in this case-test a geometrical nonlinear quasi static calculation of segment of a sphere pinch. It
allows to test modeling COQUE_3D into nonlinear geometrical and the algorithm of update of
great rotations 3D (key Mot GREEN_GR of operator STAT_NON_LINE). This popular example in analysis
linear watch capacity of the element of hull to representing well the inflection without extension and them
movements of rigid body. Moreover the thinness of the hull compared to its radius of curvature allows
to test the processing of blocking in transverse shearing. Deformations obtained by Code_Aster
different from 0.1 to 1.25% compared to those of Code the SAMCEF software, taken for reference.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
2/8

1
Problem of reference

1.1 Geometry
Z
18°
P4
P3
H = 0.04
R = 10
F
F
P7
P6
F
F
X
y
1
P
P2
P5


Cap pinch:

In P1 F = Fex
In P6 F = - Fex
In P2 F = - Fey
In P7 F = Fey
With F > 0



1.2
Material properties

Elastic behavior:

E = 6.825 × 107
.
; = 0 3
.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
3/8

1.3
Boundary conditions and loadings

One seeks the successive states of balance under the loading

F (T) = T

applied into 1
P
P6
P2
P7

Because of the geometrical and physical symmetry of the problem, only the quarter P P P P
1 2 3 4 is modelled,

by taking account of the conditions of symmetry. These conditions eliminate 5 movements from body
rigid. The last movement of rigid body is eliminated by blocking displacement according to Z. with
not P5,

C.L. :
P5:
DZ=0
Symmetry:
P2P3:
DY=0.
DRX=0.
DRZ=0.
P4P1:
DX=0.

DRY=0. DRZ=0.

One is interested particularly in displacements of items 1
P and 3
P following the directions of
loading.

2
Reference solution

This solution [bib4] is that which is obtained with software the SAMCEF software [bib1]. Modeling is based
on a theory of hull in resulting efforts with a Co-rotational formulation [bib3] and one
discretization DSQ [bib2].

20 elements
20 elements
20 elements
20 elements


The grid considered is 20 × 20 elements quadrilateral.

The strategy of Newton with level of force imposed illustrates a difficulty of convergence. One pushes
calculation to F = 100.

2.1 References
bibliographical

[1]
The SAMCEF software, Manuel of reference V7.1 Volume Eléments, 1998
[2]
J-L. Batoz, G.Dhatt, “Modélisation of Structures by Eléments Finis:Hulls”, Hermčs,
Paris, 1992
[3]
Crisfield Mr. A., “Non-linear Finite Element Analysis off Solids and Structures”, Volume 1:
Essentials, John Wiley, Chichester, 1994
[4]
PH. JETTEUR, Cinématique Non Linéaire of Coques. Report/ratio SAMTECH, Contract
PP/GC-134/96, 1998
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
4/8

3 Modeling
With

3.1
Characteristics of modeling

Element MEC3QU9H (voluminal hull)
Modeling COQUE_3D

10 elements
10 elements
10 elements
10 elements


3.2
Characteristics of the grid

A number of nodes: 441

A number of meshs and types: 100 QUAD9

3.3 Functionalities
tested

· Modeling COQUE_3D into nonlinear geometrical.
· The static algorithm of update of great rotations GREEN_GR of STAT_NON_LINE.

STAT_NON_LINE:
(
COMP_ELAS:
(
RELATION
: “elas”
COQUE_NCOU
: 1
DEFORMATION: “green_gr”
)
)
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
5/8

4
Results of modeling A

4.1 Values
tested

The incremental analysis is carried out in the interval of pseudo-time [0: 100.] in 10 steps of load.

History of horizontal displacement DX at the P1 point

Moment
Force F
Aster
Reference
% difference

020. 020.
+1.486E+00
+1.484E+00
+0.107
050. 050.
+2.571E+00
+2.578E+00
- 0.262
100. 100.
+3.362E+00
+3.390E+00
- 0.827

History of horizontal displacement DY at the P2 point

Moment
Force F
Aster
Reference
% difference

020. 020.
­ 1.816E+00
­ 1.799E+00
+0.954
050. 050.
­ 3.779E+00
- 3.759E+00
+0.543
100. 100.
­ 5.780E+00
- 5.802E+00
- 0.300

4.2 Remarks

One uses as value for COEF_RIGI_DRZ: 0.001.

One presents the curve displacement ­ load at the requested points.


EDF
Department Mecanique and Modeles Numeriques
Electricity
HEMISPHERE GRIPS. CURVES DEPLACEMENT-CHARGE
from France
4
them displacements are about
size of the hemisphere (R=10)
- Contrary to the linear solution,
the modules of displacements are
2
different
0
T
NR
E
M
E
AC
- 2
PL
COURBE DX (F) in P1
OF
COURBE DY (F) in P2
- 4
- 6
- 8
0
20
40
60
80
100
CHARGE
agraf 16/02/99 (c) EDF/DER 1992-1998

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
6/8

5 Modeling
B

5.1
Characteristics of modeling

Element MEC3TR7H (voluminal hull)
Modeling COQUE_3D


10 segments
20 segments
20 segments
20 segments


5.2
Characteristics of the grid

A number of nodes: 1541

A number of meshs and type: 734 TRIA7

5.3 Functionalities
tested

· Modeling COQUE_3D into nonlinear geometrical.
· The static algorithm of update of great rotations GREEN_GR of STAT_NON_LINE.

STAT_NON_LINE:
(
COMP_ELAS:
(
RELATION
: “elas”
COQUE_NCOU
: 1
DEFORMATION: “green_gr”
)
)
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
7/8

6
Results of modeling B

6.1 Values
tested

The incremental analysis is carried out in the interval of pseudo-time [0: 100.] in 10 steps of load.

History of horizontal displacement DX at the P1 point

Moment
Force F
Aster
Reference
% difference

020. 020.
+1.486E+00
+1.479E+00
- 0.345
050. 050.
+2.559E+00
+2.578E+00
- 0.748
100. 100.
+3.348E+00
+3.390E+00
- 1.250

History of horizontal displacement DY at the P2 point

Moment
Force F
Aster
Reference
% difference

020. 020.
­ 1.801E+00
­ 1.799E+00
+0.09
050. 050.
­ 3.739E+00
- 3.759E+00
- 0.528
100. 100.
­ 5.731E+00
- 5.802E+00
- 1.222

6.2 Remarks

One uses as value for COEF_RIGI_DRZ: 0.001.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Code_Aster ®
Version
6.0
Titrate:
SSNV141 - Spherical Calotte pinch


Date:
19/08/02
Author (S):
P. MASSIN, Key Mr. Al MIKDAD
:
V6.04.141-B Page:
8/8

7
Summary of the results

H
The facts of the case correspond to a thin hull
= 0 4
. %. It is necessary
R
to increase the value of the COEF_RIGI_DRZ which allots a rigidity around the normal of the elements
of hull which is worth by defect 10­5 the smallest rigidity of inflection around the directions in the plan of
the hull in order to be able to increase the value of the swing angle which one can reach.
values of this coefficient until 10­3 remain licit.

The Code_Aster solution is close to the reference solution the SAMCEF software for two modelings.

This test thus shows the correct operation of modeling COQUE_3D in great displacements
and great rotations, without revealing of blocking in shearing.

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A

Outline document