Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
1/14

Organization (S): EDF/MTI/MN, EDF/UTO/LOCATED, SAMTECH

Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
V6.04.115 document

SSNV115 - Tôle undulated in behavior
nonlinear

Summary:

This problem validates the elastoplastic law of behavior with criterion of Von Mises with linear work hardening
isotropic for modelings of plates [R3.07.03] and voluminal hulls [R3.07.04] where effects of
membrane and of inflection are also important.

The geometry of the model respects 3 constraints:

·
the thickness is low to respect the assumption of the thin hulls,
·
the problem must be in plane deformation according to OZ,
·
the curvature according to OY is selected so that the “inflection” and the “membrane” are both
significant.

There is no analytical solution. Modeling A (2D D_PLAN) is used as reference. The test does not have
physical significance and the values of displacements obtained are very important compared to
dimensions of the initial structure. This test is thus rather a test of not-regression and comparison
inter-modelings.

The results (in displacement) differ from 2 to 3% between modelings plates and the reference 2D. This variation
is reduced to 0.5% between modelings voluminal hulls and the reference 2D.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
2/14

1
Problem of reference

1.1 Geometry
y
B
D
With
C
X
X
01
Z
y seen of “crosses”

R
R
H
With
C
X
X
R
R


0


Characteristics of the hull:

·
thickness H = 0.05 mm,
·
radius of curvature R = 1 mm,
·
L= width AB = CD = 0.1 mm,
·
position of the first center of curvature: 0 = (0, - R) and OA = R = 01
. ,
·
the angle is selected so that the surface upper of the hull than item X is with
(y = 0), i.e. aligned with A and C,

1 H
cos = 1 - 4 R


H
·
position of the second center of curvature: 0 2 cos, -
and 0
1
R
R
, X
R


.
2
=

1.2
Material properties

E = 2.000 MPa
= 0.3
One uses an elastoplastic law of behavior with criterion of Von Mises with work hardening
isotropic linear: y = 100 MPa AND: 200 MPa.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
3/14

1.3
Boundary conditions and loadings

·
on AB: embedding: DX = DY = DZ = DRX = DRY = DRZ = 0,
·
on all the hull: deformation planes according to OZ => DZ = DRX = DRY = 0,
·
on CD: linear effort (by unit of length OZ) according to OX given by: fx = 50 NR/mm It is
equivalent with a pressure of pX = fx/H = 100 MPa being exerted on the side CD,
·
the loading is applied gradually to the structure. The way of loading is
cut out in 10 equal increments.

fx 5.
0.
1. T

2
Reference solution

2.1
Method of calculation used for the reference solution

Modeling A (2D D_PLAN) is used as reference for modelings of hull.

2.2
Results of reference

Displacements according to OX and OY of item X in Misters.

2.3
Uncertainty on the solution

The experiment shows that if one doubles the number of elements in the two directions, the result varies
of less than 2%.

The selected criteria of convergence must also make it possible to reach the precision estimated for
this calculation 2D: (2 or 3%).

3 Bibliography

[1]
F. VOLDOIRE, C. SEVIN:Axisymmetric thermoelastic hulls and 1D. Documentation of
Reference of Code_Aster [R3.07.02].
[2]
P. MASSIN: Elements of plate DKT, DST, DKQ, DSQ and Q4. Documentation of
Reference of Code_Aster [R3.07.03].
[3]
P. MASSIN, A. LAULUSA: Elements of three-dimensional hull. Documentation of
Reference of Code_Aster [R3.07.04].
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
4/14

4 Modeling
With

4.1
Characteristics of modeling

Discretization: 20 X 4 elements QUAD8 with modeling D_PLAN.

Boundary conditions:

y
H
bout1
0
bout2
X
0:
DX = DY = 0.
bout1: DX = 0.


Name of the nodes: not X = group_no X = N148

Loading: linear force (by unit of length OZ) FX distributed on the group_ma bout2
FX = 5./H = 100. This loading is equivalent to a pressure of 100 MPa.

4.2
Characteristics of the grid

A number of nodes:
289
A number of meshs and type:
80 QUAD8

4.3 Functionalities
tested

Commands


STAT_NON_LINE COMP_INCR RELATION
“VMIS_ISOT_LINE”

5
Results of modeling A

5.1 Values
tested

With the sequence number 10

Identification
Aster (mm)
DX (X) with T = 1.
0.02743
DY (X) with T = 1.
­ 0.2804

5.2 Parameters
of execution

Version:
5.02.22


Machine:
Origin 2000
System:
UNICOS 8
Obstruction memory:
100 Mo
Time CPU To use:
12.5 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
5/14

6 Modeling
B

6.1
Characteristics of modeling

B
X
Fx
D
With
C
Fx
Z


One seeks a movement independent of Z; only one “line” of triangular elements is thus enough.

Cutting: 20 quadrangles => 40 triangles DKT. Modeling DKT.

The thickness of the elements is divided into 17 layers for nonlinear calculation [R3.07.03]. Each
layer comprises 3 points of integration in higher skin of layer, in the middle of each layer and
in lower skin of layer. The model here studied thus includes/understands 15 points of integration in
the thickness of the plate.

Boundary conditions:



AB (GROUP_NO: bout1): DX = DY = DZ = DRX = DRY = DRZ = 0


TOUT: “OUI”: DZ = DRX = DRY = 0

Loading: nodal forces out of C and D FX = p Lh/2 = 0.25 NR.
X

6.2
Characteristics of the grid

A number of nodes:
42
A number of meshs and type:
40 TRIA3

6.3 Functionalities
tested

Commands


AFFE_MODELE
MODELISATION
DKT
AFFE_CARA_ELEM HULL
EPAIS
STAT_NON_LINE COMP_INCR RELATION
“VMIS_ISOT_LINE”
“COQUE_NCOU”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
6/14

7
Results of modeling B

7.1 Values
tested

With the sequence number 10 = 1 is T.

Identification Référence Aster (mm)
% difference
DX (X)
0.02743 0.02681 ­ 2.275
DY (X)
­ 0.2804 ­ 0.2886
2.937
FX (A)
­ 0.25 ­ 0.249 ­ 0.054

Note:

If one further increases the number of layers for integration in the thickness, the relative error
on DX (X) passes in lower part of 2%. For 19 layers one finds an error of 1.29% thus. That
on DY (X) remains unchanged.

7.2 Parameters
of execution

Version:
5.02.22


Machine:
Origin 2000
System:
UNICOS 8
Obstruction memory:
100 Mo
Time CPU To use:
13.7 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
7/14

8 Modeling
C

8.1
Characteristics of modeling

Z
B
X
Fx
D
With
C
Fx
Z


One seeks a movement independent of Z; only one “line” of quadrangular elements is enough
thus.

Cutting: 40 quadrangles DKQ. Modeling DKT.

The thickness of the elements is divided into 7 layers for nonlinear calculation [R3.07.03], in order to
to have a very high degree of accuracy on the state of stresses in the thickness of the plate. Each layer
comprise 3 points of integration in higher skin of layer, in the middle of each layer and in skin
lower of layer. The model studied here thus includes/understands 15 points of integration in the thickness of
the plate.

Boundary conditions:



AB (GROUP_NO: bout1): DX = DY = DZ = DRX = DRY = DRZ = 0


TOUT: “OUI”: DZ = DRX = DRY = 0

Loading: nodal forces out of C and D FX = p Lh/2 = 0.25 NR.
X

8.2
Characteristics of the grid

A number of nodes:
82
A number of meshs and type:
40 QUA4

8.3 Functionalities
tested

Commands


AFFE_MODELE
MODELISATION
DKT
AFFE_CARA_ELEM HULL
EPAIS
STAT_NON_LINE COMP_INCR RELATION
“VMIS_ISOT_LINE”
“COQUE_NCOU”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
8/14

9
Results of modeling C

9.1 Values
tested

With the sequence number 10 is, T = 1.

Identification Référence Aster (mm)
% difference
DX (X)
0.02743 0.0270
­ 1.44
DY (X)
­ 0.2804 ­ 0.288
2.966
FX (A)
­ 0.25 ­ 0.25
0

Note:

If one further increases the number of layers for integration in the thickness the relative error
on DX (X) passes in lower part of 1%. That on DY (X) remains unchanged.

9.2 Parameters
of execution

Version:
5.02.20


Machine:
Origin 2000
System:
UNICOS 8.0
Obstruction memory:
100 Mo
Time CPU To use:
15.9 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
9/14

10 Modeling
D

10.1 Characteristics of modeling

Z
B
X
D
With
E
C
Z


One seeks a movement independent of Z; only one “line” of quadrangular elements is enough
thus.

Cutting: 8 quadrangles MEC3QU9H. Modélisation COQUE_3D.

The thickness of the elements is divided into 3 layers for nonlinear calculation [R3.07.04]. Each
layer comprises 3 points of integration in higher skin of layer, in the middle of each layer and
in lower skin of layer. The model here studied thus includes/understands 7 points of integration in
the thickness of the plate.

Boundary conditions:



AB (GROUP_NO: AB): DX = DY = DZ = DRX = DRY = DRZ = 0


TOUT: “OUI”: DZ = DRX = DRY = 0

Loading: two types of loading are applied:
·
nodal forces out of C and D and E (node medium on the side CD) FX (C) = FX (D) =pxLh/6 =0.08333N.

FX (E) =2pxLh/3=0.33N.
·
force distributed on the side CD FX = 5N/Misters.

10.2 Characteristics of the grid

A number of nodes:
43 external + 8 interns
A number of meshs and types:
8 QUA9 + 1 SEG3

10.3 Functionalities
tested

Commands


AFFE_MODELE
MODELISATION
COQUE_3D
AFFE_CARA_ELEM HULL
EPAIS

A_CIS
AFFE_CHAR_MECA
FORCE_NODALE


FORCE_ARETE
STAT_NON_LINE COMP_INCR RELATION
“VMIS_ISOT_LINE”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
10/14

11 Results of modeling D

11.1 Values
tested

With the sequence number 10 = 1 is T. The results are identical with FORCE_NODALE or
FORCE_ARETE.

Identification Référence Aster (mm)
% difference
DX (X)
0.02743 0.02762
0.701
DY (X)
­ 0.2804 ­ 0.2807
0.091

11.2 Parameters
of execution

Version:
5.02.20


Machine:
Origin 2000
System:
UNICOS 8.0
Obstruction memory:
100 Mo
Time CPU To use:
45.7 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
11/14

12 Modeling
E

12.1 Characteristics of modeling

Z
B
X
D
With
X E
teststemxç
Z


One seeks a movement independent of Z; only one “line” of quadrangular elements is enough
thus.

Cutting: 12 triangles MEC3TR7H. Modélisation COQUE_3D.

The thickness of the elements is divided into 3 layers for nonlinear calculation [R3.07.04]. Each
layer comprises 3 points of integration in higher skin of layer, in the middle of each layer and
in lower skin of layer. The model here studied thus includes/understands 7 points of integration in
the thickness of the plate.

Boundary conditions:



AB (GROUP_NO: AB): DX = DY = DZ = DRX = DRY = DRZ = 0


TOUT: “OUI”: DZ = DRX = DRY = 0

Loading: two types of loading are applied:
·
nodal forces out of C and D and E (node medium on the side CD) FX (C) = FX (D) =pxLh/6 =0.08333N.

FX (E) =2pxLh/3=0.33N.
·
force distributed on the side CD FX = 5N/Misters.


12.2 Characteristics of the grid

A number of nodes:
75 external + 24 interns
A number of meshs and types:
24 TRIA7 + 1 SEG3

12.3 Functionalities
tested

Commands


AFFE_MODELE
MODELISATION
COQUE_3D
AFFE_CARA_ELEM HULL
EPAIS

A_CIS
AFFE_CHAR_MECA
FORCE_NODALE


FORCE_ARETE
STAT_NON_LINE COMP_INCR
RELATION
“VMIS_ISOT_LINE”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
12/14

13 Results of modeling E

13.1 Values
tested

With the sequence number 10 = 1 is T. The results are identical with FORCE_NODALE or
FORCE_ARETE.

Identification Référence Aster (mm)
% difference
DX (X)
0.02743 0.0275
0.244
DY (X)
­ 0.2804 ­ 0.2820
0.556

13.2 Parameters
of execution

Version:
5.02.20


Machine:
Origin 2000
System:
UNICOS 8.0
Obstruction memory: 100 Mo
Time CPU To use: 78.8 seconds
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
13/14

14 Modeling
F

14.1 Characteristics of modeling

y
0
X
C
Fx
Z


Cutting: 20 segments => 20 segments SEG3. Modeling COQUE_D_PLAN.

The thickness of the elements is divided into 7 layers for nonlinear calculation [R3.07.02]. Each
layer comprises 3 points of integration in higher skin of layer, in the middle of each layer and
in lower skin of layer. The model here studied thus includes/understands 15 points of integration in
the thickness of the plate.

Boundary conditions:



(NOEUD: 0): DX = DY = DZ = DRX = DRY = DRZ = 0

Loading:
· nodal force out of C: FX (C) = p H = 5N/Misters.
X

14.2 Characteristics of the grid

A number of nodes:
41
A number of meshs and type:
20 SEG3

14.3 Functionalities
tested

Commands


AFFE_MODELE
MODELISATION
COQUE_D_PLAN
AFFE_CARA_ELEM HULL
EPAIS

A_CIS
AFFE_CHAR_MECA
FORCE_NODALE


STAT_NON_LINE COMP_INCR
RELATION
“VMIS_ISOT_LINE”
NEWTON
MATRICE
“ELASTIQUE”
“TANGENTE”
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

Code_Aster ®
Version
5.0
Titrate:
SSNV115 - Tôle undulated in nonlinear behavior

Date:
16/11/01
Author (S):
P. MASSIN, D. BUI, A. LAULUSA Key
:
V6.04.115-B Page:
14/14

15 Results of modeling F

15.1 Values
tested

With the sequence number 10 = 1 is T. Values given by using as tangent matrix that
calculated numerically are:

Identification Référence Aster (mm)
% difference
DX (X)
0.02743 0.02753
0.381
DY (X)
­ 0.2804 ­ 0.2848
1.556

With the sequence number 10 = 1 is T. Values given by using as tangent matrix the matrix
rubber band are:

Identification Référence Aster (mm)
% difference
DX (X)
0.02743 0.02753
0.383
DY (X)
­ 0.2804 ­ 0.2848
1.558

Note:

To put 3 layers for integration in the thickness leads to an error of 2.4% on the estimate
DX (X).

15.2 Parameters
of execution

Version:
5.02.20


Machine:
Origin 2000
System:
UNICOS 8.0
Obstruction memory: 100 Mo
Time CPU To use: 72.5 seconds

16 Summary of the results

One notices the good adequacy of the reference solution Aster 2D deformation planes with
results obtained by modelings in voluminal hulls. The variation on displacements at the point
of maximum arrow on the initial geometry is indeed lower than 1%. The variation with modeling in
linear hull is of about a 1.5% on the estimate of the maximum arrow of sheet. This variation
becomes more important for modelings in elements of plates which do not take into account
curvature of corrugated sheet. The relative error on the estimate of the maximum arrow does not seem
to want to go down in lower part from 3%, and this same by increasing the number of layers for
to improve integration of plasticity in the thickness of the element. It is noticed for this reason that one
increase in the number of layers in the thickness makes it possible to improve the estimate of displacement
DX at the point where the arrow is maximum without to improve the estimate of the latter, and it,
for the whole of the studied models. The difference in quality of results between the various models
undoubtedly comes from the taking into account of the curvature of corrugated sheet.
Handbook of Validation
V6.04 booklet: Nonlinear statics of the voluminal structures
HI-75/01/010/A

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