Motivated by the motion of a ship in a heavy sea, a mathematical model for the vertical impact of a two-dimensional solid body onto a half-space of quiescent, inviscid, incompressible fluid is formulated. No solutions to the full problem are known, but in the case when the impacting body has small deadrise angle (meaning that the angle between the tangent to the profile and the horizontal is everywhere small) a uniformly valid solution is obtained by using the method of matched asymptotic expansions. The pressure on the body is calculated and is in fair agreement with experimental results. The model is generalised for more complicated impacts and the justifications for the model are discussed. The method is extended to three-dimensional bodies with small deadrise angle and solutions are obtained in some special cases. A variations! formulation of the leading order outer problem is derived, which gives information about the solution and leads to an fixed domain scheme for calculating solutions numerically. A partial linear stability analysis of the outer problem is given which indicates that entry problems are stable but exit problems are unstable to small perturbations. A mathematical model for the effect of a cushioning air layer between the body and the fluid is presented and analysed both numerically and in appropriate asymptotic limits. Finally, the limitations of the models are discussed and directions for future work indicated.

The work presented in this thesis concerns the theoretical analysis of the motion of floating rectangular cross-section bodies in single-frequency harmonic waves. When a conventional laterally symmetric ship is modelled by such a body, the computation of strip-theory coefficients (derived from the solution of Laplace's equation for the fluid surrounding the ship) is simplified. This technique is used here to model a typical barge, with actual cross-sections very close to the assumed rectangular shapes. In particular, slamming motions are investigated using two conventional linear slamming criteria. The rectangular section model is also applied to the investigation of slamming motions by use of 'quasi-harmonic' slamming criteria, which are developed from an updating technique used with conventional strip theory coefficients. Results are presented for an example. / Applied Science, Faculty of / Mechanical Engineering, Department of / Graduate

Optimization techniques are used to investigate changes in structural design which increase the energy absorbing capabilities of a marine vessel in a collision. The structural model of the vessel includes the stiffened shell, web frame supports, and rigid bulkheads. The failure criterion used is hull rupture, appropriate for tanker design. The collision scenario is a right angle strike by a rigid vertical bow midway between two rigid bulkheads. The stiffened shell is modelled as a series of longitudinal beams in plastic bending and plastic membrane tension. Optimization parameters included both the number and dimensions of the transverse web frames and longitudinal beams. The technique was applied to the redesign of a large oil tanker. Minimizing the weight with a constraint on the energy was superior to maximizing the energy with a weight constraint in both computation time and performance. Optimization increased the volume of the shell beams while decreasing their moment-of-inertia. In addition the volume and strength of the frame were decreased precipitating early development of membrane tension in the shell and spreading of damage throughout the compartment. An reduced the number of web frames from optimum design six to two and increased the energy absorbed before rupture by 130%. Lesser collisions energies were found for more conservative designs which included a set number of web frames and restrictions of other design parameters. The use of high strength steel was also investigated. / M.S.