Hydroelastic analysis of Very Large Floating Structures in variable bathymetry regions by multi-modal expansions and FEM

A novel frequency domain numerical method for Very Large Floating Structure (VLFS) hydroelasticity is developed. The problem is formulated in the 2D ocean waveguide, featuring a realistic seabed bathymetry and the presence of inhomogeneous, elastic plates of varying thickness and negligible draft. An in vacuo modal expansion for the elastic body deflection, modelled as a structural plate, is employed to decouple the hydrodynamics from structural mechanics. The inhomogeneous plate is considered to undergo cylindrical bending, while depending on the structure slenderness and excitation wavelength the classical thin plate theory and Mindlin's model, accounting for first order shear deformation effects are implemented. A weighted residual approach is employed to cast the formulated problems into a mixed weak form for which dimensionality reduction is sought. This is achieved by an enhanced vertical representation for the wave potential, able to accurately account for abrupt bathymetric changes, following Athanassoulis and Belibassakis (1999). The reduced two-field, weak problem is solved by means of the Finite Element Method (FEM). Finally, a series of comparisons are carried out against published results for a range of configurations.