Probability of Collision and Damage Size for Early Design George Mermiris Supervisor: Prof. D. Vassalos

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

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

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

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

Probability of Collision (P C ) 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

P C – Ship Domain Ship Domain is the collision-free area around the ship. This area is a circle with diameter (D) some multiple of the ship’s length (L). In the case where D = L  P C = 1 D L

P C – Ship Domain D: ship domain diameter L: length of the ship R: response time to a given rudder angle V: ship’s speed C: channel width d: traffic density (number of ships per nm 2 ) The response time R is accounting for human error and adverse weather conditions.

Probability of Water Ingress (P W/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

Probability of Water Ingress (P W/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

Probability of Water Ingress (P W/C ) Available theories for plate (panel) deflection: Small deflection theory  d << t Large deflection theory  d = O(t)

P W/C – Some facts 1.The load is neither concentrated nor uniformly distributed 2.The impacting body is non-deformable (for the present analysis)

P W/C – Some facts 3.The process, once started, will not stop until the impact energy is totally consumed in terms of plastic energy and heat 4.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) 5.Due to large strains, tearing of the plate will initiate in the area of contact and only there 6.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

P W/C – Some facts 7.The same is applicable to the stiffeners: they are subjected to high strains which impose large deflections, torsion and tearing with chaotic behaviour 8.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) 9.No analytical methods available for very large deformation of plates and stiffened plates subjected to tearing and breaching

P W/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

Further work Cross check and calibrate the P C 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

Thank you!