SSNS501 - Great displacements dun simply supported cylindrical panel

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Titrate:

SSNS501 - Great displacements of a cylindrical panel

Date:

03/05/02

Author (S):

P. MASSIN, F. LEBOUVIER

Key

V6.05.501-A

Page:

1/10

Manual of Validation

V6.05 booklet: Non-linear statics of the hulls and the plates

HT-66/02/001/A

Organization (S):

EDF/AMA, DeltaCAD

Manual of Validation
V6.05 booklet: Non-linear statics of the hulls and the plates
Document: V6.05.501

SSNS501 - Great displacements of a panel
cylindrical simply supported

Summary:

This test represents a calculation of stability of a cylindrical panel simply supported subjected to an effort
concentrate in its center. The behavior of the panel changes completely and shows points clearly
of return in load and displacement “snap-through/snap-back”. In this case a piloting in displacement
diverge and a piloting in length of arc must be selected.

It makes it possible to validate modeling finite elements COQUE_3D with meshs TRIA7 and QUAD9 in
geometrical non-linear quasi-static field in the presence of strong instabilities.

Displacements and the critical load are compared with a numerical reference solution.

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SSNS501 - Great displacements of a cylindrical panel

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P. MASSIN, F. LEBOUVIER

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V6.05 booklet: Non-linear statics of the hulls and the plates

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Problem of reference

1.1 Geometry

y, v

Z, W

X, U

L = 0.254 m
R = 2.54 m
H = 0.00635 m
= 0.1 rd

With

1.2

Properties of material

The properties of material constituting the plate are:

= 3. 10275 X 10

Young modulus

= 0.3

Poisson's ratio

1.3

Boundary conditions and loadings

- C.L panel simply supported on sides EC and GF (null displacements, free rotations)

- One seeks the successive states of balance under a load P imposed on point A.

1.4 Conditions

initial

Without object

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SSNS501 - Great displacements of a cylindrical panel

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V6.05 booklet: Non-linear statics of the hulls and the plates

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Reference solution

2.1

Method of calculation used for the reference solution

The reference solution was obtained with a finite element of hull DKT24 (mesh 4x6) with
4 nodes with 6 degrees of freedom per node in Total Lagrangian Formulation. This solution is
described in details in [bib2].

2.2

Results of reference

With

(x10

Charge P

(KN)

Charge

P/Pmax

With

(x10

Charge P

(KN)

Charge

P/Pmax

With

(x10

Charge P

(KN)

Charge

P/Pmax

0.0 0.000

0.0000

 16.4 0.480 0.8000 14.0 0.295 0.4916

 1.7 0.150

0.2500

 16.7 0.415 0.6916 14.3 0.345 0.5750

 3.5 0.265

0.4416

 16.9 0.350 0.5833 15.0 0.370 0.6166

 4.9 0.345

0.5750

 17.0 0.290 0.4833 16.1 0.380 0.6333

 6.8 0.410

0.6833

 17.1 0.225 0.3750 17.3 0.375 0.6250

 8.4 0.475

0.7916

 17.1 0.150 0.2500 18.7 0.350 0.5833

 9.8 0.520

0.8666

 17.0 0.090 0.1500 20.3 0.305 0.5083

 11.1 0.555 0.9250

 16.8 0.020 0.0333 21.8 0.230 0.3833

 12.2 0.580 0.9666

 16.4 0.035 0.0583 23.5 0.120 0.2000

 13.1 0.595 0.9916

 16.0 0.085 0.1416 25.2 0.025 0.0416

 14.0 0.600 1.0000

 15.3 0.130 0.2166 26.8 0.210 0.3500

 14.9 0.585 0.9750

 14.8 0.155 0.2583 28.5 0.445 0.7416

 15.5 0.565 0.9416

 14.2 0.195

 0.3250

 16.1 0.525 0.8750

 14.0 0.240

 0.4000

Displacement |W

With

| (mm)

Charge |P| (KN)

Not limits 1

Not limits 2

Not limits 3

Not limits 4

- 0,5

- 0,4

- 0,3

- 0,2

- 0,1

0,0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

10 12 14 16 18 20 22 24 26 28 30

2.3

Uncertainties on the solution

< 2% numerical solution

2.4 References

bibliographical

[1]

HAMMADI Fodil: Formulation and evaluation of finite elements with C° continuity of the geometry
for the linear and non-linear analysis of the hulls.

[2]

JAAMEI S.: Study of various Lagrangian formulations for the nonlinear analysis of
plates and thin hulls elastoplastic in great displacements and great rotations,
Thesis of doctorate, University of Technology of Compiegne 1986.

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Titrate:

SSNS501 - Great displacements of a cylindrical panel

Date:

03/05/02

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P. MASSIN, F. LEBOUVIER

Key

V6.05.501-A

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Manual of Validation

V6.05 booklet: Non-linear statics of the hulls and the plates

HT-66/02/001/A

3 Modeling

With

3.1

Characteristics of modeling

With

Modeling COQUE_3D (TRIA7)

Boundary conditions:
- Side CD: U = v = W = 0
Conditions of symmetry:
- Side AB:

U =

- Side AD: v =

A quarter of the plate is modelized.

The successive states of balance are
obtained thanks to a method of
piloting by length of arc.

In this case,

ETA_PILOTAGE

max

3.2

Characteristics of the mesh

A number of nodes: 241
A number of meshs and type: 72 TRIA7

3.3 Functionalities

tested

Controls Key word

factor

Key word

AFFE_MODELE AFFE

MODELISATION=' COQUE_3D'

AFFE_CARA_ELEM HULL

THICK

A_CIS=0.833

COEF_RIGI_DRZ = 0.001

AFFE_CHAR_MECA FORCE_NODALE FZ

STAT_NON_LINE PILOTING

TYPE=' LONG_ARC'

Results of modeling A

4.1 Values

tested

Identification Moments

Reference

Aster %

difference

Not limits n°1

1.03

 0.0140

 0.01322

 5.573

Eta_PILOTAGE 1.03

1.0

0.9729

 2.471

Not limits n°2

1.78

 0.0171

 0.01696

 0.847

Eta_PILOTAGE 1.78

0.375
0.250

0.07513 75.96

Not limits n°3

2.3

 0.0140

 0.01458

4.176

Eta_PILOTAGE 2.3

 0.400
 0.492

 0.533 19.67

Not limits n°4

2.48

 0.0161

 0.01617

0.452

Eta_PILOTAGE 2.48

 0.633

 0.6442

1.717

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SSNS501 - Great displacements of a cylindrical panel

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V6.05 booklet: Non-linear statics of the hulls and the plates

HT-66/02/001/A

4.2 Remarks

The strategy of calculation used breaks up into two stages:

calculation in loading imposed to P = 582.N agent on 97% of the critical load,

calculation in “imposed displacement”: then, one imposes a displacement imposed while using
technique length of arc imposed on all the structure (option LONG_ARC in
STAT_NON_LINE).

The use of the technique length of arc makes difficult the definition of the value of reference to
to introduce into control TEST_RESU, since these values cannot be imposed. For

to define the values of reference, we sought the values of the closest possible DZ
those listed in the table of [§2.2] and we deferred the values of the parameter of piloting
that one was to obtain for the values of DZ in question.

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Titrate:

SSNS501 - Great displacements of a cylindrical panel

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P. MASSIN, F. LEBOUVIER

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V6.05.501-A

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V6.05 booklet: Non-linear statics of the hulls and the plates

HT-66/02/001/A

5 Modeling

5.1

Characteristics of modeling

With

Modeling COQUE_3D (QUAD9)

Boundary conditions:
- Side CD: U = v = W = 0
Conditions of symmetry:
- Side AB:

U =

- Side AD: v =

5.2

Characteristics of the mesh

A number of nodes: 169
A number of meshs and type: 36 QUAD9

5.3 Functionalities

tested

Controls Key word

factor

Key word

AFFE_MODELE AFFE

MODELISATION=' COQUE_3D'

AFFE_CARA_ELEM HULL

THICK

A_CIS=0.833

COEF_RIGI_DRZ = 0.001

AFFE_CHAR_MECA FORCE_NODALE FZ

STAT_NON_LINE PILOTING

TYPE=' LONG_ARC'

Results of modeling B

6.1 Values

tested

Identification Moments

Reference

Aster %

difference

Not limits n°1

1.03

 0.0140

 0.01318

 5.886

Eta_PILOTAGE 1.03

1.0

0.9724

 2.760

Not limits n°2

 0.0171

 0.01702

 0.462

Eta_PILOTAGE

0.375
0.250

0.101 67.69

Not limits n°3

 0.0140

 0.01446

3.269

Eta_PILOTAGE

 0.400
 0.492

 0.558 25.177

Not limits n°4

 0.0161

 0.007

Eta_PILOTAGE

 0.633

 0.640

1.120

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Titrate:

SSNS501 - Great displacements of a cylindrical panel

Date:

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P. MASSIN, F. LEBOUVIER

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Manual of Validation

V6.05 booklet: Non-linear statics of the hulls and the plates

HT-66/02/001/A

6.2 Remarks

The strategy of calculation used breaks up into two stages:

calculation in loading imposed to P = 582.N agent on 97% of the critical load,

calculation in imposed displacement: then, one imposes a displacement imposed while using
technique length of arc imposed (option LONG_ARC in STAT_NON_LINE).

The use of the technique length of arc makes difficult the definition of the value of reference to
to introduce into control TEST_RESU, since these values cannot be imposed. For

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Titrate:

SSNS501 - Great displacements of a cylindrical panel

Date:

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P. MASSIN, F. LEBOUVIER

Key

V6.05.501-A

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Manual of Validation

V6.05 booklet: Non-linear statics of the hulls and the plates

HT-66/02/001/A

Summary of the results

Normal displacement at the top of the panel according to the force

- 600

- 400

- 200

200

400

600

800

0,005

0,01

0,015

0,02

Displacement W (m)

Charge (NR)

Appear 7-a: normal Displacement in the node of the panel according to the force applied.

Enlarging around the point limits 1

Appear 7-b: normal Displacement in the node of the panel according to the force applied

standardized by its maximum value

The results for the two loads limit 1 and 4 are correct. The maximum error is 2.5% for
mesh TRIA3 and of 2.8% for mesh QUAD9. On the other hand, the error on vertical displacement is
more important. It is 5.6% for mesh TRIA7 and 5.9% for mesh QUAD9.

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Titrate:

SSNS501 - Great displacements of a cylindrical panel

Date:

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P. MASSIN, F. LEBOUVIER

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Manual of Validation

V6.05 booklet: Non-linear statics of the hulls and the plates

HT-66/02/001/A

The results between the two loads limit 1 and 4 are qualitatively correct. They well are detected
points limit 2 and 3. Quantitatively the values of displacements for these points are good with
less than 1% for the point limits 2 and to less than 5% for the point limits 3. On the level of the loads
corresponding, the load at the point limits 2 is very strongly underestimated (about 70%) and
that at the point limits 3 strongly over-estimated (about 20%).

Whatever the mesh, the behavior pre-buckling is correctly evaluated. Pace in
postbuckling makes it possible to determine displacements at the points correctly limit 2 and 3.
loads obtained are further away from the reference solution. From the point limits 4, one
find a good agreement between the reference and our solution.

The coefficient of correction of transverse shearing A_CIS was put at 0.833, corresponding to
thick hulls. The value (2500=10

xH/L) which should have been taken into account does not allow

to carry out calculations, because of a bad conditioning of the matrices of rigidity.