الفهرس 
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Abstract
The main objective of this thesis is to derive anew numerical method to solve various types and dimensions of floating plate problem.
Very Large Floating Structures VLFS are already being used for many engineering structures as storage facilities, industrial space, bridges, ferry piers, docks, rescue bases, breakwaters, airports, entertainment facilities, militarypurposes, even habitation, and other purposes. A selected model of a very large floating structure is used to analyze the hydrodynamic motion of a floating structure and its response to surface water waves
Themain idea in the selected model is to build a very large mat-like structure as a plate whichthickness is very small compared to its horizontal length parameters. Various problems of the interaction between these floating plates and water waves are treated in this thesis. The geometrical sketches of the plate are considered rectangles with arbitrary horizontal plan forms. The plate defection (vertical displacement) and free-surface elevation in the open-water regions with the refraction and transmission of water waves are studied using different theories of applied mathematics, mechanics and hydrodynamics. Water wave propagations, diffraction theories, Kirchhoffs theory of thin plates, and Green’s theorem are the most often used in similar topics.
The elastic domain of floating plate is analyzed numerically by means of an improved Initial Value numerical technique while fluid interaction is considered as added body force computed numerically from the fluid Laplace equation under special types of boundary conditions.Under the plate theory, the equation of motion of the floating plate is a fourth order partial differential equation subjected to special types of boundary conditions and external forces in the fluid domain. On the other hand, under a linear potential theory, the motion of the fluid is governed by the Laplace equation and the related boundary conditions. The hydrodynamic analysis of the VLFS is proposed in the present work. The water is assumed to be inviscid and incompressible and the fluid motion is irrotationa1. A linearized composite free surface boundary condition and an undisturbed far field (infinity) radiation condition are considered. The Green function, or Kernel, of boundary element method (BEM) formulation is a fundamental solution of the Laplace equation assuming an infmite fluid domain.
The dynanlic motions of the floating structure and the surrounding fluid are solvedusing an improved initial value tec1miquecombined with the boundary element method.At first, a combination of the Initial Value method (IV) and the Finite Differences (FD) tools is utilized to develop the present (IVFD) technique. Consequently, the coupled equations of motion governing the interaction between water waves and the floating plateis analyzed duringcoupling the obtained technique (IVFD)withthe boundary element method (BEM).
The validity of the achieved technique is examined for the cases of static and vibrating rectangular plates under various types of boundary conditions. Special concern is given for achieving the solution for floating plate with all edges free. Also three common types of laminated symmetrically cross-ply, orthotropic and isotropic plates are analyzed here. The presented technique is extended to solve the case of stepped thickness plate
which is considered as one of the architecture demands and material saving of structures.Moreover continuous floating plates with internal supported line and internal point supported plates are investigated which are used for floating bridges.
The convergence and accuracy of the presented Initial Value-Finite Differences (IVFD) technique have been examined. Also, the merits and validity of improved technique are satisfied via comparing the obtained results with those available in literature indicating good agreements.
The approach carried out in the thesis can be applied to predict the behavior of floatingstructures and their hydrodynamic response to water waves.