Probability of Collision and Damage Size for Early Design

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Probability of Collision and Damage Size for
Early Design

• George Mermiris

Supervisor Prof. D. Vassalos
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Layout

• Background
• Current approach
• Problem definition
• Collision occurrence
• Water ingress due to collision

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Background

• Despite considerable effort spent in predicting
  and preventing particularly unwanted situations,
  accidents do happen
• Prescriptive regulations fall short enough times
  to hurt the credibility of the maritime industry
• New regulations take time to implement and if
  they do they express only past experience and
  most of the times they lack the ability to
  capture the needs of modern marine vehicles and
  the advanced expectations they should respond to

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Current approach

• Statistical analysis of past accidents
• Expert judgement
• Numerical models for the prediction of structural
  response
• Tank experiments for the prediction of
  survivability of ships

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Problem definition

• Objective minimise loss of life / damage to the
  environment / property loss
• Focus points probability of collision occurrence
  and the probability of water ingress as result.

Focus points
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Probability of Collision (PC)

• Existing numerical models (e.g. Fujii, MacDuff,
  etc.) tend to provide answers in a rather
  idealised way
• Fault Trees and Event Trees cannot capture
  reality adequately in such complex situations
• Bayesian Networks (BN) appeared recently with
  more potentials but with drawbacks as well due to
  their inability to handle continuous
  distributions of data they still remain a very
  promising option for further development

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PC Ship Domain
Ship Domain is the collision-free area around the
ship. This area is a circle with diameter (D)
some multiple of the ships length (L). In the
case where D L ? PC 1
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PC Ship Domain
D ship domain diameter L length of the ship R
response time to a given rudder angle V ships
speed C channel width d traffic density
(number of ships per nm2)
The response time R is accounting for human error
and adverse weather conditions.
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Probability of Water Ingress (PW/C)

• Existing methods of dealing with the probability
  of water ingress are
• Statistical analysis of past accidents and the
  caused damage
• Bayesian Networks (BN) which are based on
  statistical / historical data
• Numerical analysis (FE)
• Analytic formulation is necessary to overcome the
  drawbacks of these approaches

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Probability of Water Ingress (PW/C)

• Low Energy and High Energy collisions
• High Energy collisions
• Breach size
• Location (relative to water line)
• The size of the breach is the most challenging
  part given a stiffened panel and an external
  load to calculate the indentation / penetration

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Probability of Water Ingress (PW/C)

• Available theories for plate (panel) deflection
• Small deflection theory ? d ltlt t
• Large deflection theory ? d O(t)

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PW/C Some facts

1. The load is neither concentrated nor uniformly
   distributed
2. The impacting body is non-deformable (for the
   present analysis)

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PW/C Some facts

1. The process, once started, will not stop until
   the impact energy is totally consumed in terms of
   plastic energy and heat
2. The panel will behave like a solid body, at least
   in the beginning of the process (i.e. plate and
   stiffeners will have a compatible deformation)
3. Due to large strains, tearing of the plate will
   initiate in the area of contact and only there
4. The direction towards which the tearing will
   develop is strongly dependent on the stiffening
   of the plate but it appears to have a chaotic
   behaviour

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PW/C Some facts

1. The same is applicable to the stiffeners they
   are subjected to high strains which impose large
   deflections, torsion and tearing with chaotic
   behaviour
2. Mathematical models predicting the tearing
   process of materials are due to von Mises and
   Tresca very theoretical, yet the only ones
   available (they are based on the yielding of the
   material)
3. No analytical methods available for very large
   deformation of plates and stiffened plates
   subjected to tearing and breaching

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PW/C Approach

• The approach will be as follows
• The formulation will be based on the available
  energy before the impact and the rate of energy
  absorption of a given structural configuration
• The final (total) deformation of the stiffened
  panel will be based on suitable transformation of
  the initial configuration with the addition of a
  certain discontinuity where the crack is
  initiated and developed (Continuum Damage
  Mechanics)
• The Thermodynamics of Irreversible Processes
  (TIP) will be deployed to provide an extra set of
  equations wherever is deemed necessary

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Further work

• Cross check and calibrate the PC model with other
  studies available
• Approximate the first model for large deformation
  and tearing of a stiffened panel based on energy
  considerations
• Cross-check and implementation to FEA

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• Thank you!