Brazil 2014ugm Imperfections in Structural Resistance of Submarines
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Transcript of 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
Departamento de Eng. Naval e Oceânica
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
Allen, H.G; Bulson, P.S. (1980)
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
Allen, H.G; Bulson, P.S. (1980)
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
Departamento de Eng. Naval e Oceânica
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
Departamento de Eng. Naval e Oceânica
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)
Departamento de Eng. Naval e Oceânica
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
Departamento de Eng. Naval e Oceânica
(SREELATHA P.R , 2013)
Benchmark case
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RESULT COMPARISON: Between stiffeners
Departamento de Eng. Naval e Oceânica
(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
Departamento de Eng. Naval e Oceânica
Benchmark case
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What are the motives for the differencesbetween the theoretical buckling pressureand the practical buckling pressure?
Departamento de Eng. Naval e Oceânica
• 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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IMPERFECTION: SHELL NOT CONCENTRIC
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
IMPERFECTION: SHELL NOT CONCENTRIC
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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.
Departamento de Eng. Naval e Oceânica
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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.
Departamento de Eng. Naval e Oceânica
http://www.submarinosdobr.com.br/PrimeiroHUMAITA.htmlhttp://www.submarinosdobr.com.br/PrimeiroHUMAITA.htmlhttp://www.submarinosdobr.com.br/PrimeiroHUMAITA.html