Global Structural Model of Bow Indentation into Ship Side
Since the pioneering work of Minorsky in 1958 the collision damage of ships has been extensively studied in literature. In the past few yearsthere has been renewed interest in this type of problem, as exemplified by for example , . For a complete review of the subject, the reader is referred to the work by Jones, , and subsequent reports of the International Ship Structure Committees. Three main approachesemerged in the literature. The empirically based methods (Minorsky, Woisin), the Finite Element Method (DYNA-3D, PAM-CRASH, ABAQUS, ADINA, DYTRAN) and the analytical, approach (McDermott et al. Hysing, Reckling, etc.) The present report belongs to the latter category. The underlying philosophy of the present approach is rooted in the First Principles of Mechanics and is consistently based on the energy methods in plastic structural mechanics with finite displacements and rotations.The objective of this report is to develop a theoretical basis for studying collision damage of the side structure of a stricken ship. It is not our intention to predict the extent of damage to any particular ship. Instead, a number of fundamental problems not previously treated in the literature were formulated and solved. The report consists of four self-contained and independent parts.In the first part a plate strip model is developed for a longitudinally stiffened single hull ship which includes finite strength of transverseframes. It is shown that the dent size is increasing with the indentation depth. The rate of spreading of deformation to the neighbouring baysdepends on the plastic strength of the supporting structure relative to the longitudinal strength of the plate strip. Another interesting result of thepresent solution is the effect of evening-out of strains over several bays in the case of a low longitudinal resistance of the supporting frames.In the second part of this report two kinematically admissible solutions for a square rigid-plastic plate under a point load are compared. One is a 2-dimensinal solution with all components of the strain tensor retained. The other one is a simplified solution in which the plate strength is derived from two perpendicular sets of plate strips where the shear strength isneglected. A full equivalence of both solutions was proved by taking on Mises yield condition in the plate solution and a limited interaction curve in the plate strip solution.The third part of the present report is devoted to the derivation of an exact solution of punch indentation into a curricular plate. A distinguished feature of the solution is a progressive contact (wrapping) of the platearound a hemispherical punch. It is shown that the force-deflection relationship and the critical strain to rupture depend on the radius of theplate as well as the punch radius. An approximate solution was also developed which opened a way for generalizing the circular plate solution to a rectangular plate subjected to an eccentric impact. The solution was further extended to cover orthotropic plates.The resistance of decks/bulkheads to in-plane indentation of a rigid punch is treated in the fourth and last part of this report. The analysis is similar in spirit to the earlier solution for web crushing presented as Reports # 23 and 38 of the Phase I Tanker Safety Project. The importantnew contribution of the present approach is that the length of the folding wave is not assumed, as in the previous analyses, but found as a part ofthe solution. A simpler force-displacement relationship is obtained in the case of both symmetric and unsymmetrical impact.The solution is valid up to the point of first fracture. Beyond that point the plate will fail in the central cut mode or the concertina folding mode, depending on the geometry of the impacting bow, location of the indentation site and direction of deck stiffeners. The central cut failure mode is covered in a very comprehensive way in the Report # 1 of the Collision Project. References to the concertina tearing solutions were given earlier.It is believed that the results of the present study (Reports # 1 and 2, together with the relevant deliverables of Phase I Tanker Safety Project) will give important background information for developing more detailed structural models of collision induced damage of a broad class of ships.