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A B-Spline Galerkin scheme for calculating the hydroelastic response of a very large floating structure in waves

 

MASASHI KASHIWAGI

 

Research Institute for Applied Mechanics, Kyushu University, 6-1 Kasuga-koen, Kasuga, Fukuoka 816-8580, Japan

 

Abstract: This paper presents an effective scheme for computing the wave-induced hydroelastic response of a very large floating structure, and a validation of its usefulness. The calculation scheme developed is based on the pressure-distribution method of expressing the disturbance caused by a structure, and on the mode-expansion method for hydroelastic deflection with the superposition of orthogonal mode functions. The scheme uses bi-cubic B-spline functions to represent unknown pressures, and the Galerkin method to satisfy the body boundary conditions. Various numerical checks confirm that the computed results are extremely accurate, require relatively little computational time, and contain few unknowns, even in the region of very short wavelengths. Measurements of the vertical deflections in both head and oblique waves of relatively long wavelength are in good agreement with the computed results. Numerical examples using shorter wavelengths reveal that the hydroelastic deflection does not necessarily become negligible as the wavelength of incident waves decreases. The effects of finite water depth and incident wave angle are also discussed.

 

Key words: very large floating structure, hydroelastic response, B-spline function, Galerkin scheme

 

Received for publication on Aug. 28, 1997; accepted on Dec. 10, 1997

 

Introduction

 

Very large floating structures (VLFS) will become increasingly necessary for airports, storage, and manufacturing facilities. This need comes from the lack of adequate land space and/or environmental concerns about such things as the pollution and noise associated with having such facilities near residential areas.

In Japan, a floating airport is being considered, and its safety and performance in waves are being intensively studied. The preferred configuration is a barge-type structure 5km long, 1 km wide, and a few meters deep. This type of structure has two features: (1) the wave-lengths of practical interest are small compared with the horizontal dimensions of the structure; (2) hydroelastic responses are more important than rigid-body motions owing to the relatively small flexural rigidity of the structure.

Several methods have been proposed to take account of these features (e.g., refs 1-5 and references therein). Among these, the most common is probably the mode-expansion method in the framework of linear potential theory, which represents the structural deflection by a set of“generalized”modes of hydroelastic responses, in addition to the conventional components of the diffraction problem and the six separate radiation problems for rigid-body motions. One of the problems with this method is that accurate computations must be performed for very short wavelengths. Specifically, if realistic waves with wavelengths of 50-100m are considered, the length ratio to a VLFS 5 km long is 1/50-1/100.

The structure under consideration can be approximated by a zero-draft rectangular plate, and thus hydro-ynamically by the pressure distribution on the free surface. This approximation is known as the pressure-distribution method. Several authors 6-8 have presented numerical results for a VLFS on the basis of this method. However, their results are not accurate in the short-wavelength regime, because the integration equation used in this method is discretized with a limited number of panels, and on each panel the unknown pressure is represented by a constant value. If this traditional zero-th order panel method is used for wave-lengths in this investigation, the number of unknowns would have to be O(104), and thus the computational burden would be enormous. Recently, Wang et al.9 proposed two computationally efficient techniques,

 

 

 

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