A higher-order-coupled boundary element and finite element method for the wave forcing of a floating elastic plate

Abstract

We present a higher-order method to calculate the motion of a floating, shallow draft, elastic plate of arbitrary geometry subject to linear wave forcing at a single frequency. The solution is found by coupling the boundary element and finite element methods. We use the same nodes, basis functions, and maintain the same order in both methods. Two equations are derived that relate the displacement of the plate and the velocity potential under the plate. The first equation is derived from the elastic plate equation. The discrete version of this equation is very similar to the standard finite element method elastic plate equation except that the potential of the water is included in a consistent manner. The second equation is based on the boundary integral equation which relates the displacement of the plate and the potential using the free-surface Green function. The discrete version of this equation, which is consistent with the order of the basis functions, includes a Green matrix that is analogous to the mass and stiffness matrices of the classical finite element method for an elastic plate. The two equations are solved simultaneously to give the potential and displacement. Results are presented showing that the method agrees with previous results and its performance is analysed.