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Liquid sloshing in pool due to three-directional earthquake ground motion is analyzed. The liquid pool is represented by a rigid annular circular cylindrical tank. Analytical and numerical solutions are presented and their limitations are discussed. For a given seismic ground excitation time-history, the free surface and the pressure and velocity fields in the pool are calculated by superposition of modal responses. The results show that container vertical acceleration is of secondary importance in determining the free surface displacement, but has a major effect on the pressure load on the container boundary.

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In this paper, a three-dimensional analysis is presented for calculating the level ice resistance for ships that have conventional hull forms. Comparisons with published ship resistance data and other analytical predictions are also provided. The present approach combines two analytical techniques: 1) plastic limit analysis is used to describe the ice failure mechanism and the associated ice velocity field; and 2) linear and angular momentum balances determine the average ice resistance for a ship. In the momentum balance, potential flow theory is used to describe the water motion induced by the icebreaking process. Existing methods for determining ship resistance in ice include numerical methods which depend on solutions of equations of motion that describe the dynamic interaction between the ice and the ship, and empirical methods which depend on model and full-scale icebreaker data to generate empirical correlations for ship resistance. The present results compare reasonably well with published model-scale and full-scale icebreaker data. Comparisons with predictions based on other numerical methods are also discussed.

This paper presents a one-dimensional flexural and longitudinal elastic wave propagation theory for analysis of ice floe impact with a rigid structure having a constant slope. In this paper, governing differential equations were derived following the Timoshenko beam theory which includes the rotary inertia and shear deformation of the ice beam, as well as the buoyancy effect of the water. The ice material was treated as a homogeneous, isotropic, and linearly elastic solid. Interactions between the longitudinal and flexural waves in the ice sheet, and the boundary conditions imposed by the rigid slope, have been considered. Solution procedures were developed based on the method of characteristics using a fixed grid finite difference approximation in both space and time. Computer solutions were obtained and plots were provided to show ice impact force-time histories and the wave propagation phenomenon for a range of floe impact problems of current interest. Comparisons were also made with other existing methods for calculating ice bending loads on sloping structures.