Underwater Explosion Abaqus Fatih Aruk Presentation

FINITE ELEMENT ANALYSIS OF

RESPONSE OF A FLOATING STRUCTURE

TO AN UNDERWATER EXPLOSION (UNDEX)

M.Sc. Thesis by

Fatih ARUK

Supervisors: Prof. Dr. Tuncer

TOPRAK

Dr. Ergün

BOZDAĞ

What is the importance of UNDEX resistance?

•

Warships should last destructive effects of any near

underwater explosion

.

•

Also shipboard systems must be shock hardened to a

certain level to ensure combat survivability of both

personnel and equipment

.

So,

shock resistance

is a major issue that should be

considered during early design phase of...

warships

, radars, weapons, torpedos or any

other shipboard equipment

Shock Trials (Physical Tests);

•

Extremely Expensive

•

Dangerous

•

Harmful to the surrounding Environment

•

Require years of planning and preparation

•

Due to safety risk, shock trials do

not test up to the ship’s design

limits or even the true wartime

shock environment.

•

These tests are performed after the

first ship is already built.

Shock trials of USS WINSTON S. CHURCHILL

(DDG 81) in 2001

United States Navy spent tens of millions of dollars

•

Years of planning and preparation

Shipboard eqipment testing; MIL-S 901D

(Military Specification for shock testing of ship

board equipment)

Shock Test

Platform

Impact Tests;

expensive experimental tests on simple cylindrical

shells and plate structures.

Computational modeling and response

,

if perfected, can effectively and

accurately replace the experimental

procedures used to obtain the

UNDEX

UNDEX Simulation;

The shock response of an immersed or floating structure is

obtained when subjected to a near UNDEX loading

•

Kwon and Cunningham;

dynamic responses of stiffened cylinder and

beam elements

DYNA3D [Explicit FE Code]+

Underwater Shock Analysis (USA) [BE Code

based on DAA]

•

90s Kwon and Fox;

the nonlinear dynamic response of a cylinder

subjected to side-on underwater explosion

•

Sun and McCoy

UNDEX analysis of a composite cylinder

ABAQUS + a fluid-structure interaction code

Cichocki, Adamczyk, and Ruchwa

implemented fluid-structure interaction

phenomenon, pressure wave distribution, and

the radiation boundary conditions into

Three dimensional ship shock trial simulation of a

UNDEX PHENOMENA;

Similitude Relations (Pressure versus Time)

( )

( , )

a

P R t

P

R

f

τ

 

=  

_{ }

a

v t

R

a

τ

_{=  }

 

 

( )

f

τ

=

e

−

τ

τ

≤

1

1.338

1.805

( ) 0.8251

0.1749

f

τ

=

e

−

τ

+

e

−

τ

τ

≤

7

;

P

;

R

;

c

a

;

t

Pressure

, , , ;

c

c

P v A B

Distance to charge (stand-off distance)

Charge radius

Time

0 1 2 3 4 5 6 x 10-3 0 2 4 6 8 10 12 14 P (M p a ) t(s)

Pressure vs. time history for 25kg of HBX-1 charge, standoff distance of 10m according to Swisdak according to Price

UNDEX PHENOMENA;

Similitude Relations (Pressure versus Time)

Material

Source

TNT (1.52 g/cc)

Coles (1946)

1.42

992

0.13

0.18

TNT (1.60 g/cc)

Farley and Snay (1978)

1.45

1240

0.13

0.23

TNT (1.60 g/cc)

Price (1979)

1.67

1010

0.18

0.18

HBX-1 (1.72 g/cc)

Swisdak (1978)

1.71

1470

0.15

0.29

HBX-1 (1.72 g/cc)

Price (1979)

1.58

1170

0.144

0.24

Explosive Gas Bubble

1 3 5 5 6

(

10)

m

T

K

D

=

+

(

10)

m

a

K

D

=

+

Explosive Gas Bubble

UNDEX PHENOMENA;

Gas Bubble

Period

Max. Gas Bubble

Radius

For our case

( MIL-S-901 D; 27.3 kg HBX-1

at 7.3 m depth)

T=0.64 s

_{amax =4.4 m}

•

Bubble pulses are a strong source of excitation

for ships whose bending vibration mode is near

to the bubble pulse frequency

•

It is especially important for the

late time

response

of the ship

Explosive Gas Bubble,

Geers-Hunter Bubble Model (2002)

UNDEX PHENOMENA;

UNDEX

=

SHOCK WAVE PHASE

+

BUBBLE OSCILLATION PHASE

SHOCK WAVE PHASE

provides initial

conditions for

BUBBLE OSCILLATION

PHASE

ABAQUS includes Geers-Hunter (2002) model for UNDEX loading.

(a fourth-order Runge-Kutta integrator to prescribe the pressure variation)

MIL-S-901 D; 27.3 kg HBX-1 at

7.3 m depth

27.3 kg HBX-1 at

65 m depth

UNDEX PHENOMENA;

Cavitation

Cavitation takes place in water when there is

area of near-zero absolute pressure (about 206.8

Pa)

Two types of cavitation occur in an UNDEX event;

‘bulk’

cavitation;

a large volume of low

pressure due to reflections

from sea surface

‘local’

cavitation;

a small zone of low

pressure at

fluid-structure interaction

surface.

The effect of cavitation on the response of the floating

structures is important and must be properly modeled

to obtain physically meaningful results.

UNDEX PHENOMENA;

Cavitation

‘bulk’

cavitation

0

i

atm

stc

R

P P

+

+

P

+

P

=

Cavitation condition:

(

j

2

j

1

)

c

f

R

R

t

c

−

=

( , ) 0

F x y

=

( , ) 0

G x y

=

Equations of lower and upper

cavitation boundaries:

EXPLOSION VARIATIONS ACCORDING TO

UNDEX PHENOMENA;

Cavitation

‘local’ cavitation

Taylor plate theory

Assumptions;

•

The plate is rigid

•

The shock wave is planar

p

i

r

v

= −

v

v

i

f

f i

r

f

f r

P

c v

P

c v

ρ

ρ

=

=

2

2

dv

m

c v

P

P e

dt

ρ

+

=

=

max

2

( )

(1

)

t

t

p

p

P

v t

e

e

m

β θ

θ

θ

β

−

−





=

_

−

_

−

max

2

( )

1

t

t

p

P

P t

e

θ

β

e

β θ

β



−

−



=

_

−

_

−

As becomes large (a



lightweight plate), cavitation

occurs faster.

UNDEX PHENOMENA;

Cavitation

‘local’ cavitation

max

2

( )

(1

)

t

t

p

p

P

v t

e

e

m

β θ

θ

θ

β

−

−





=

_

−

_

−

max

2

( )

1

t

t

p

P

P t

e

θ

β

e

β θ

β

−

−





=

_

−

_

−

t t

≤

t t

≤

Incident and total pressures behind, and velocity of shock platform

Elements of UNDEX Simulation;

Acoustic Equations

Equilibrum equation for small motions of a compressible, adiabatic fluid

with velocity-dependent momentum loses;

The slow flow assumption is

accurate for

steady fluid velocities up to

Mach 0.1

Acoustic Constitutive Equation;

Acoustic Constitutive Equation

for

cavitating fluid

;

(

)

{

}

max

_v

,

_c

_o

p

=

p

p

−

p

linear

nonlinear

Elements of UNDEX Simulation;

Formulation of Direct Integration, Coupled Acoustic-Structural Analysis

Introducing a variational field δp, integrating over

entire body and applying Green’s theorem

yields;

( )

1

p

T

ρ



∂



=

⋅

_{= − ⋅ }

_

_

_

∂





x

n u

n

x

&&

_{Boundary traction}

term

Elements of UNDEX Simulation;

Formulation of Direct Integration, Coupled Acoustic-Structural Analysis

fp

S

the value of the acoustic

pressure is

prescribed;

ft

S

prescribes motion of the

fluid

particles, modeling

pressure wave

( )

0

f

ft

T

x

=

T

=

n u

−

⋅

&&

fi

S

the radiating acoustic boundary,

waves passing exclusively outward

fs

S

acoustic-structural

interaction

Elements of UNDEX Simulation;

Formulation of Direct Integration, Coupled Acoustic-Structural Analysis

0 1 1

1

1

1

1

0

p

p

p

p

p

dV

pT dS

K

K

p

p

p dS

p

dS

c

a

γ

δ

δ

δ

ρ

ρ

δ

δ







_∂

_∂



+

+

⋅

−

+





_



_

_∂

_∂





_

_











+

_

+

_

−

⋅

=





∫

∫

∫

∫

x

x

n u

&&

&

&

&&

:

0

m

m

m

m

c

V

V

V

m

m

S

S

dV

dV

dV

p

dS

dS

δε

α ρδ

ρδ

δ

δ

+

⋅

+

⋅

+

+

⋅

−

⋅

=

∫

∫

∫

∫

∫

σ

u u

u u

u n

u t

&

&&

the final

variational

statement for

the acoustic

medium

the virtual work

statement for a

structure.

Elements of UNDEX Simulation;

Formulation of Direct Integration, Coupled Acoustic-Structural Analysis

●

The Discretized Finite Element Equations

interpolation functions

up to the number of displacement degrees of freedom.

up to the number of pressure nodes

[ ]

M

_f

{ }

p

&&

+

[ ]

C

_f

{ }

p

&

+

[

K

]

_f

{ }

p

=

[

S

_f

_s

]

{ } { }

u

&&

+

P

_f

[ ]

M

_s

{ }

u

&&

+

[ ]

C

_s

{ }

u

&

+

[ ]

K

_s

{ }

u

=

[

S

_f

_s

]

T

{ } { }

p

−

P

_s

Surface-Based Acoustic-Structural Interaction Procedure

Elements of UNDEX Simulation;

Note that the source point

should be located out of the fluid domain.

Incident Wave Loading

Elements of UNDEX Simulation;

Elements of UNDEX Simulation;

Mesh Refinement

For reasonable accuracy,

at least six representative

internodal intervals of

the acoustic mesh should fit into the shortest acoustic

wavelength

present

in the analysis.

Eight or more will be better.

; maximum linear element length

; the speed of sound

;the number of linear elements per acoustic

wavelength

; max. frequency of excitation which can be simulated accurately

max

max

1500

8 0.05

3750

m s

f

m

f

Hz

≤

⋅

≤

We used an element size of about 50 mm around the

acoustic-structural interface. The element size

increases up to 150 mm at outer fluid regions.

Meshing whole fluid

medium with 50 mm

elements would result in

about 16 million

Explicit Time Integration

Elements of UNDEX Simulation;

2

t

t

u

u

u

∆

+ ∆

=

+

&&

&

&

•

An explicit central-difference time integration rule is used;

•

Each increment is relatively inexpensive because there is

no solution for a set of simultaneous equations.

•

The time increments must be quite small so that the

accelerations are nearly constant during an increment.

Advantages of the explicit time integration method;

Explicit Time Integration

Elements of UNDEX Simulation;

•

Well-suited to solving high-speed dynamic events

•

No global tangent stiffness matrix. Iterations and

tolerances are not required.

●

Stability of Explicit Integration;

●

The Stable Time Increment Estimation;

If damping

included;

Structural Damping

Explicit Time Integration

Elements of UNDEX Simulation;

Mass

Proportion

al Damping

Stiffness

Proportion

al Damping

In names of

natural freq.;

damps

lower

frequenci

es

damps

higher

frequencie

s

Effects of damping on the stable time

increment in Explicit Analysis

R

β

has greater effect on

stable time increment

UNDEX ANALYSIS METHODOLOGY

UNDEX TEST PARAMETERS FROM MIL-S-901D

MIL-S-901D

specification which covers shock testing requirements for

ship board machinery, equipment, system and structures.

heavyweight shock

testing platform

UNDEX TEST PARAMETERS FROM MIL-S-901D UNDEX FE MODEL GENERATION FLUID-STRUCTURE INTERACTION FE ANALYSIS CORRELATION OF UNDEX RESPONSES AND VALIDATION

OF NUMERICAL CODE CONDUCT UNDEX TEST SHORT DURATION DYNAMIC RESPONSE Equivalen t? SHORT DURATION DYNAMIC RESPONSE N O MODIFY UNDEX MODEL/ANALYSES PARAMETERS Y E S

UNDEX ANALYSIS METHODOLOGY

UNDEX CORRELATION METHODOLOGY

UNDEX ANALYSIS METHODOLOGY

SUBMODELING ANALYSIS

MODELING AND ANALYSIS

Weight; about 39

tones

CAD MODELING;

CATIA

V15

MODELING AND ANALYSIS

MESHING;

ABAQUS CAE

Number of nodes:

140316

Number of elements:

142327

Linear

quadrilateral

elements of type S4R

Connections were imposed

by means of kinematic

MODELING AND ANALYSIS

GENERATING A REDUCED (COARSE) MODEL for

tryouts and acoustic mesh convergence studies;

HYPERMESH

Number of nodes: 7858

Number of elements:

8229

Linear quadrilateral

elements of type S4R

538

Linear triangular

UNDEX ANALYSIS WITH REDUCED (COARSE) MODEL

FLUID MESH CONVERGENCE ANALYSIS

Boundary Conditions

1

f

c

=

ρ

K

1

2

f

a

K

β

γ

ρ

ρ ρ









= ⋅

+









Plane type radiating

surfaces;

_f

₌

₁

0

UNDEX ANALYSIS WITH REDUCED (COARSE) MODEL

FLUID MESH CONVERGENCE ANALYSIS

Acoustic-Structural

Interaction

Initial Static Pressure

Incident Wave (UNDEX)

Loading

UNDEX ANALYSIS WITH REDUCED (COARSE) MODEL

FLUID MESH CONVERGENCE ANALYSIS

UNDEX ANALYSIS WITH REDUCED (COARSE) MODEL

FLUID MESH CONVERGENCE ANALYSIS

UNDEX ANALYSIS WITH REDUCED (COARSE) MODEL

ANALYSIS WITH DEFORMABLE PLATFORM

UNDEX ANALYSIS WITH REDUCED (COARSE) MODEL

ANALYSIS WITH DEFORMABLE PLATFORM;

EFFECT OF DAMPING

1.5

R

α

=

0.5

6

R

E

β

=

−

For first two modes; % 0.4

For the first torsional and

bending modes ; 0.25 %

and 0.15 %

UNDEX ANALYSIS WITH REDUCED (COARSE) MODEL

ANALYSIS WITH DEFORMABLE PLATFORM;

UNDEX ANALYSIS WITH MAIN (FINE) MODEL

EFFECT OF MESH REFINEMENT AROUND

ACOUSTIC-STRUCTURAL INTERACTION REGION

Mesh

Convergence

Analysis;

Element size;

150 mm

Number of

DFT Analysis of

Incident Pressure

Waves;

Element size;

50

mm

Number of nodes;

UNDEX ANALYSIS WITH MAIN (FINE) MODEL

EFFECT OF MESH REFINEMENT AROUND

UNDEX ANALYSIS WITH MAIN (FINE) MODEL

EFFECT OF CAVITATION

UNDEX ANALYSIS WITH MAIN (FINE) MODEL

EFFECT OF STRUCTURAL DAMPING

_1.5

R

CONCLUSION AND OUTLOOK

•

Fluid mesh size has important effect

on the structural

response and should be selected carefully for

accurate results;

§

Mesh Convergence Study

§

DFT analysis of loadings

•

Though it requires a nonlinear fluid behavior which

adds to the cost of the analyses,

including cavitation

is a must

to obtain physically meaningful results.

•

The effect of damping was also shown to be

important for peak acceleration estimation in the

late time response of the platform.

•

Submodeling analysis can bu run to obtain

converged stress-strain results at some sub-region

of the structure.

•

Experimental work is a must for the validation of the

numerical code used and of the analysis procedure

followed in this study. The work done in this work will

provide the basis for the future experimental work.

END OF THE PRESENTATION