ABSTRACT:

In this paper, the finite element technique incorporating the infinite element is applied to the wave diffraction and radiation problems. The hydrodynamic forces are assumed to be inertially dominated, and the viscous effects are neglected. Two types of elements are developed to discretize the fluid domain efficiently_ They are the infinite elements developed to model the radiation condition at infinity, and the fictitious bottom boundary elements introduced to avoid extensive fluid domain discretizations for the case of deep water. The shape functions of the infinite elements, in the radial direction, are derived from the asymptotic expressions for the progressive wave and the first evanescent mode components in the analytical boundary series solutions. Numerical analyses are performed for vertical axisymmetric bodies to validate the infinite elements and the fictitious bottom boundary elements developed m this study. Comparisons with the results from other available numerical solution methods show that the present method gives fairly good results. Numerical experiments are also carried out to determine the proper distance to the infinite elements and the fictitious bottom boundary elements from the sohd body, which directly affect accuracy and efficiency of the solution.

INTRODUCTION

The linear wave diffraction theory IS commonly used to evaluate the wave forces on large offshore structures. In general, there are two classes of numerical solution techniques for the wave diffraction and radiation problems. They are the Integral equation method and the finite element method. The integral equation formulations are more frequently adopted. However, the methods fail at so-called critical or irregular frequencies(John, 1950), and are more difficult to be applied to the cases with complex structural geometries such as sharp corners. Application of the finite element method to wave diffraction and radiation problems have been reviewed by Mel(1978) and by Zienkiewicz et al(1978).

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