Hydroelastic Analysis of of Very Large Floating Structure (VLFS) using Boundary Element Approach

Abstract

Hydroelasticty is a subject of interest in marine science and technology involving the mutual interaction of water waves and elastic bodies. It is a branch which deals with the elastic deformation of bodies which is in contact with liquids. Interdisciplinary subjects like this require the knowledge of structural mechanics, fluid mechanics, concepts of water wave propagation and boundary conditions. In this thesis, a numerical procedure has been proposed to analyze the equation of motion of the elastic plate which is having a shallow draft, L/d ≤ 1/20 (small thickness) with arbitrary geometry subjected to monochromatic gravity waves.The numerical model is capable of investigating the Very Large Floating Structure (VFLS) at finite (0.05 ≤h/λ≤ 0.5) and infinite (h/λ≤ 0.5) water depths. Herein, VLFS is considered to behave as thin elastic plate due to its dimensions. VLFS of rectangular, triangular and trapezoidal geometries are considered and elastic motion or vertical deflections of these shapes have been studied. A hybrid numerical model which combines Boundary Element Method (BEM) and Finite Element Method (FEM) is developed and used to solve fluid structure interaction between the elastic thin plate and water wave. A Higher Order Boundary Element Method (HOBEM) has been adopted in order to maintain the same order basis function and contains the same nodes between BEM and FEM. Two equations have been derived to develop the relationship between the displacement of the plate and the velocity potential under the plate. The first equation is derived from the equation of motion for the plate and is solved by Finite Element Method (FEM) to extract the displacement of the floating structure. The second equation is from water wave theorywhich is based on Boundary Integral Equation (BIE) that relates the displacement of the floating plate and velocity potential using free-surface Green’s function. A modified Green’s function which differs from the bygone Green’s function has been developed by using Bessel’s, Hankel and Struve functions of order zero. Both the equations are solved simultaneously to get the displacement of floating elastic plate and velocity potential. The results obtained are validated with Wang and Meylan (2004). The performance of the developed model is examined by checking the convergence rate and simulation time.It is learnt that the model gives its better performance in finite depth, whereas, its performance in infiniteii depth lags by an average of 20% in simulation time than the results obtained by Wang and Meylan (2004).It is concluded that the model works better in finite water depth for rectangular and trapezoidal plates