Coupled boundary element method (BEM) and finite element method (FEM) for hydroelastic analysis of floating plate

Abstract

In the present study, a numerical model is developed to analyse equation of motion of the plate which is elastic in nature and has a shallow draft L/d ≤ 1/20 (small thickness). The platform may be of any shape (geometry) subjected to monochromatic waves. The developed numerical model is capable of investigating the VFLS of any geometry (arbitrary shape) at finite (0.05 ≤ h/λ ≤ 0.5) depth. A hybrid numerical model 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 determined to build the connection between plate displacement and velocity potential. Displacement of the floating platform has been obtained by solving the plate equation of motion. To solve the plate equation of motion, FEM has been adopted. The equation which relates the plate displacement and water is solved by Boundary Integral Equation (BIE). A modified Green’s function which differs from the bygone Green’s function has been developed by using the Bessel, 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 (J. Fluids Struct. 19:557–572, 2004 [22]). © Springer Nature Singapore Pte Ltd. 2019.