A coupled mode – hp FEM for the hydroelastic analysis of shear-deformable floating bodies of general thickness in variable bathymetry

Abstract

An efficient computational procedure is presented for the solution of coupled hydroelastic problems involving bodies of general thickness, floating over variable bathymetry regions. The problem is treated by the coupled mode system of horizontal equations derived by Athanassoulis and Belibassakis (2009), for the analysis of floating, shear deformable plates or beams. The proposed beam (or plate) model is based on the addition of extra vertical elastic deformation modes, at each horizontal position along the floating body, permitting shear strain and stress to vanish on both the upper and lower boundaries and extending third-order plate theories. The final coupled mode system is derived from a variational principle combining the one – field functional of the elastodynamics in the plate region with the pressure functional in the water region. The wave potential in the water column is represented by means of a local – mode series containing an extra mode, accounting for not mildly sloped bottom variations. The addition of the additional modes results to increased convergence rate, enabling high accuracy with the use of a relatively small number of vertical modes. In the present work the hp-version of the Finite Element Method is applied to the solution of a simplified version of the resulting system of coupled horizontal differential equations with respect to the modal amplitudes, providing good convergence rates and adaptivity capabilities, and increasing the overall efficiency of the solution strategy. Numerical results are presented demonstrating the applicability of present method.