Structural Design and Response in Collision and Grounding

force and extent using closed-form solutions, but theydiffer in the detail in which the structure is defined and itsbehavior is analyzed. The methods also differ in theirtreatment of ship motions. The program DAMAGE wasselected for further testing and analysis, because it isapplicable for a wider range of grounding scenarios.4.2.1 DAMAGE [10]The computer program DAMAGE was developed at MITunder the Joint MIT-Industry Program on Tanker Safety.This project, lead by Professor Tomasz Wierzbicki, wasinitiated in 1991, and in addition to the programDAMAGE the project has produced more than 70technical reports about prediction of grounding andcollision damage. The program DAMAGE Version 5.0can be used to predict structural damage in the followingaccident scenarios:• Ship grounding on a conical rock with arounded tip (rigid rock, deformable bottom)• Ship-ship collision (deformable side,deformable bow)Compared to previous models for prediction of groundingand collision damage, a major advantage of DAMAGE isthat the theoretical models are hidden behind a moderngraphical user interface (GUI) [10]. The program hasbeen developed with the objective of making crashanalysis of ship structures feasible for engineers that donot have any particular experience in the field ofcrashworthiness. Figure 4 shows the input screen fordefining the “ship-ground interaction”, the relativeposition and velocity of ship and ground, coefficient offriction, etc.event, the contact force between ship and ground inducesheave, roll and pitch motion on the ship, and eventuallycauses the ship to stop.The primary mechanisms of energy dissipation are:1. A change in potential energy of the ship and thesurrounding water as the ship is lifted by theground reaction.2. Friction between the ground and hull.3. Deformation and fracture of the hull.Since the lifting of the ship off the rock generally causes areduction in crushing and tearing forces it is important toinclude the coupling between the global ship motions(external dynamics) and the local damage process(internal mechanics). Detailed descriptions of the modelfor the external dynamics can be found in References [11]and [12].For the model to be applicable to optimization forstructural crashworthiness it is important that it capturesthe effect of :• Material strength and ductility• Dimensions and arrangement of major structuralcomponents such as bulkheads, decks, girdersand large stiffeners.The theoretical model is based on a set of super-elementsolutions, i.e. closed form, analytical solutions for theenergy absorption of rather large structural componentsundergoing large deformations. All structural componentsare assumed to follow the same overall mode ofdeformation around the rock. This way it is possible totake into account the structural resistance of all typicalmembers in a ship bottom. The fracture criterion is basedon analytical solutions for plastic response of amembrane. Figure 5 shows a window from an animationof the ship motion over the rock.A description of the procedure including detailedderivations of the super-element solutions can be found inReferences [13] and [14].Figure 4 - Input screen for defining the “Ship-groundInteraction” in the program DAMAGE [10]Initially, the ship is assumed to be on a straight-linecourse with a known velocity and trim. The rock is atsome distance to port or starboard of the ship’s centerline,and at some height above the ship’s baseline. During theFigure 5. DAMAGE simulation of ship motion over arock (only selected structural elements are shown).4