Brazil 2014ugm Imperfections in Structural Resistance of Submarines

8/20/2019 Brazil 2014ugm Imperfections in Structural Resistance of Submarines

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Imperfections’ influence in the structural

resistance of submarines

Fabíola Tomasin

Thiago Pontin Tancredi

Departamento de Eng. Naval e Oceânica – PNV2512 – 05/12/2013


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PRESENTATION TOPICS

• Introduction and objectives

• Shell buckling

– Analytical model;

– Element finite model;

• Shell with imperfections

– Imperfections: shell not concentric;

– Imperfections: oval conformation;

• Conclusions

Departamento de Eng. Naval e Oceânica


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INTRODUCTION


The objective of this work is to determine the influenceof the design parameters and defects (imperfections) in

the collapse pressure of structure of submarine.

‘Submarine Design and development’

Numerical evaluation of the buckling pressure of a

submarine with imperfections in the structure.


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CYLINDRICAL SHELL

• External pressure

• Buckling pressure is

proportional to square of

length

Allen, H.G; Bulson, P.S. (1980)

Analytical model


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CYLINDRICAL SHELL WITH STIFFENERS

• External pressure with rigidstiffeners

• Buckling pressure is proportionalto square of distance betweenrings

• The buckling is localized betweenthe rings with no deformation ofthem


Analytical model


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CYLINDRICAL SHELL WITH STIFFENERS

• External pressure with

flexible stiffeners

• Global buckling of the structure

with deformation and rotation ofthe rings


Analytical model


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RESULT COMPARISON: Buckling first mode

• t = 0,021m;

• l = 87,6m;

• d = 5,4m;• E = 210 GPa;

• ν =0,3

Buckling pressure


Cylindrical shell with axial pressure. Benchmark case

Ansys Analytical

7,8 * 108 Pa 9,9 * 108 Pa


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RESULT COMPARISON: Buckling third mode

• t = 0,021m;

• l = 87,6m;

• d = 5,4m;• E = 210 GPa;

• ν =0,3

Buckling pressure


Cylindrical shell with external pressure. Benchmark case

Ansys Analytical

2,9 * 104 Pa 3,0 * 104 Pa


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CASE OF STUDY: Sreelatha P. R. (2013)


Stiffeners height 336 mm

Stiffeners section area 12558 mm2

Web thickness 18 mmFlange thickness 28 mm

Material Steel

Coefficient of Poisson 0,3

Benchmark case


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RESULT COMPARISON: Global buckling

Simulation results Original results


(SREELATHA P.R , 2013)

Benchmark case


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RESULT COMPARISON: Between stiffeners


(SREELATHA P.R , 2013)

Benchmark case

Simulation results Original results


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ANALYSIS OF RESULTS

The simulation results were close to the

analytical results

The simulation results were close to the

benchmark case published in the literature


Benchmark case


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What are the motives for the differencesbetween the theoretical buckling pressureand the practical buckling pressure?


• Initial deformation before the buckling;

• Variation in constraints;

• Imperfections in initial geometry;

• Imperfections in material;

• Imperfections resulted of the fabrication process.


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IMPERFECTION: SHELL NOT CONCENTRIC

Imperfections


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Imperfections

Buckling pressure (Mpa) Distance between centers (mm) Distance between centers /

original thickness Reduction %

27,9 0 0% 0

22,50 1,36 4% 19%

20,49

2,72 8% 26%

18,57 4,08 12% 33%

14,99 6,8 20% 46%


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14

16

18

20

22

24

26

28

30

0% 5% 10% 15% 20% 25%

B

u c k l i n g P r e s s u r e ( M p a )

Distance between centers / original thickness

Buckling Pressure

Buckling pressure (Mpa) Distance between centers (mm) Distance between centers /

original thickness Reduction %

27,9 0 0% 0

22,50 1,36 4% 19%

20,49

2,72 8% 26%

18,57 4,08 12% 33%

14,99 6,8 20% 46%

Imperfections



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RESULTS: Oval conformation

a (m) % R b (m) a/b Buckling pressure

(105 Pa)

Reduction %

4 0,0% 4,00 1,00 7,09 0%

4,04 1,0% 3,96 1,02 6,94 2%

4,08

2,0% 3,92 1,04 6,76 5%

4,12 3,0% 3,88 1,06 6,56 7%

4,16

4,0% 3,84 1,08 6,34 11%

4,32

8,0% 3,68 1,17 5,42 24%

5

5,5

6

6,5

7

7,5

0,95 1 1,05 1,1 1,15 1,2

B u c k l i n g p r e s s u r e ( 1 0 5 P a )

a/b

Buckling pressure

Imperfections


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Shell with stiffeners and oval deformation

Stiffener buckling

Buckling between stiffeners Global buckling


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Shell With Stiffeners And Oval Deformation

a (m)

%

b (m)

a/b

Buckling Pressure (107Pa)

Reduction %

4,00 0,0% 4 1,00 2,634 0%

4,02 0,5% 3,98 1,02 2,558 3%

4,12

3,0% 3,88 1,04 2,308 12%

4,32

8,0% 3,68 1,06 1,718 35%

0

0,5

1

1,5

2

2,5

3

0,95 1,00 1,05 1,10 1,15 1,20

B u c k l i n g P r e s s u r e ( 1 0 M p a )

a/b

Shell with stiffeners and oval

deformation


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CONCLUSIONS

There is a great sensitivity in buckling in function of the initialimperfections.

With small reductions in thickness, the buckling pressure can

decrease significantly.

In the oval conformation, the thickness was kept constant so

the influence of the a / b ratio was not so expressive.

In fact, with the oval conformation, the thickness is variable

and the influence is even bigger.



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Thank you!Questions?


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References

• [1] A. GODOY, Thin Walled Structures with Structural Imperfections: Analysis and Behavior,L. Pergamon. Press, Oxford, U.K., 1996.

• [2] BUCHER, Roy; RYDILL, Louis. Concepts in submarine design. Cambridge.New York:Cambridge University Press, 1994. Tese (de livre docência) em Engenharia Naval eOceânica. Escola Politécnica da Universidade de São Paulo. São Paulo.

• [3] BUELTA, Miguel A. M.. Projeto do casco resistente de submersíveis. 1. ed.. São Paulo,1987.

• [4] GABLER, Ulrich. Projeto de submarinos. 1 ed.. Rio de Janeiro: Arsenal de Marinha,1991.

• [5] ALLEN, H.G; BULSON, P.S. Background to Buckling. London New York : McGraw-HillBook Co. ,1980.

• [6] LEWIS, Edward V. Principles of Naval Architecture. 3. ed.. Jersey City: The Society ofNaval Architects and Marine Engineers, 1988.

• [7] O Primeiro Humaita. Site utilizado: Visitado em 20/04/2013.

• [8] SIMITSES, G. J., "Buckling and Post buckling of Imperfect Cylindrical Shells: a Review," Applied Mechanics Reviews, 39, 1517-1524 (1986).

• [9] SREELATHA P.R et al. International Journal of Engineering Science and Technology(IJEST), 2010.

http://www.submarinosdobr.com.br/PrimeiroHUMAITA.htmlhttp://www.submarinosdobr.com.br/PrimeiroHUMAITA.htmlhttp://www.submarinosdobr.com.br/PrimeiroHUMAITA.html

Brazil 2014ugm Imperfections in Structural Resistance of Submarines

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