  In this work we present a novel monolithic Finite Element Method (FEM) for
the hydroelastic analysis of Very Large Floating Structures (VLFS) with
arbitrary shapes that is stable, energy conserving and overcomes the need of an
iterative algorithm. The new formulation enables a fully monolithic solution of
the linear free-surface flow, described by linear potential flow, coupled with
floating thin structures, described by the Euler-Bernoulli beam or
Poisson-Kirchhoff plate equations. The formulation presented in this work is
general in the sense that solutions can be found in the frequency and time
domains, it overcomes the need of using elements with C1 continuity by
employing a continuous/discontinuous Galerkin (C/DG) approach, and it is
suitable for Finite Elements of arbitrary order. We show that the proposed
approach can accurately describe the hydroelastic phenomena of VLFS with a
variety of tests, including structures with elastic joints, variable bathymetry
and arbitrary structural shapes.
