Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
1/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
Organization (S):
EDF/AMA, SAMTECH
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
Document: V6.04.141
SSNV141 - Segment of a sphere 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 Word
GREEN_GR
of the operator
STAT_NON_LINE
). This popular example in analysis
linear watch capacity of the element of hull to representing well the bending 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.
Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
2/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
1
Problem of reference
1.1 Geometry
X
y
Z
°
18
04
.
0
=
H
F
10
=
R
1
P
2
P
3
P
4
P
5
P
F
F
F
6
P
7
P
Cap pinch:
In
In
In
In
P F
Fe
P F
Fe
P F
Fe
P F
Fe
X
X
y
y
1
6
2
7
=
= -
= -
=
With
F
>
0
1.2
Material properties
Elastic behavior:
E
=
×
=
6.825 10
0 3
7
.
;
.
Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
3/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
1.3
Boundary conditions and loadings
One seeks the successive states of balance under the loading
()
F T
T
=
applied in
7
2
6
1
P
P
P
P
Because of the geometrical and physical symmetry of the problem, only the quarter
P P P P
1 2 3 4
is modelized,
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 locking following displacement
Z
. with
not
P
5
,
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 the points
3
1
P
P
and
according to 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].
elements
20
elements
20
elements
20
elements
20
The mesh considered is of
20 20
×
quadrilateral elements.
The strategy of Newton with level of force imposed illustrates a difficulty of convergence. One pushes
calculation until
100
=
F
.
2.1 References
bibliographical
[1]
The SAMCEF software, Manual of reference V7.1 Elements Volume, 1998
[2]
J-L. Batoz, G.Dhatt, “Modeling of the Structures by Finite elements:Hulls”, Hermès,
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, Nonlinear Kinematics of the Hulls. Report/ratio SAMTECH, Contract
PP/GC-134/96, 1998
Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
4/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
3 Modeling
With
3.1
Characteristics of modeling
Element MEC3QU9H (voluminal hull)
Modeling COQUE_3D
elements
10
elements
10
elements
10
elements
10
3.2
Characteristics of the mesh
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”
)
)
Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
5/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
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 pitches 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.
CHARGE
OF
PL
AC
E
M
E
NR
T
EDF
Electricity
from France
Mechanical department and Numerical Models
HEMISPHERE GRIPS. CURVES DEPLACEMENT-CHARGE
agraf 16/02/99 (c) EDF/DER 1992-1998
CURVE DX (F) in P1
CURVE DY (F) in P2
them displacements are about
size of the hemisphere (R=10)
- Contrary to the linear solution,
the modules of displacements are
different
- 8
- 6
- 4
- 2
0
2
4
0
20
40
60
80
100
Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
6/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
5 Modeling
B
5.1
Characteristics of modeling
Element MEC3TR7H (voluminal hull)
Modeling COQUE_3D
segments
20
segments
10
segments
20
segments
20
5.2
Characteristics of the mesh
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”
)
)
Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
7/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
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 pitches 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.
Code_Aster
®
Version
6.0
Titrate:
SSNV141 - Segment of a sphere pinch
Date:
19/08/02
Author (S):
P. MASSIN, Mr. Al MIKDAD
Key
:
V6.04.141-B
Page:
8/8
Manual of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HT-66/02/001/A
7
Summary of the results
The facts of the case correspond to a thin hull
H
R
=
0 4%
.
. It is necessary
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 10
5
the smallest rigidity of bending 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 up to 10
3
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.