This paper presents a set of analytical expressions which can be used to calculate the reaction force on a ship bottom deformed by a conical rock with a rounded tip. Closed form solutions are given for the resistance of inner and outer bottom plating, longitudinal stiffeners, girders and bulkheads and transverse frames, floors and bulkheads. The expressions are derived by use of an energy method or a type of 'upper bound' method which rigorously takes into account the effects of large plastic deformations, friction and fracture. A high level of generality for the methodology has been obtained by postulating a global mode of deformation for the structure around the rock with one free parameter, the plate split angle, related to the shape of thedeformation mode. It is assumed that intersections between structural components stay intact during the entire deformation process so the resistance of the individual structural members are derived according to the global deformation mode. The resistance of the entire structure is found by minimizing the energy disspiation from all the deformed members with respect to the plate split angle. In a subsequent paper it is shown that the theoreticl model predicts the damage of four large scale tests and an accidental grounding with errors less than 10%. Moreover, it is illustrated by an example that the model evaluation of a grounding scenario is sufficientlty fast to be used in a probabilistic framework in a Formal safety Assessment.
|Publication status||Published - 1997|