Solving for hydroelastic ship response using a high-order finite difference method on overlapping grids at zero speed

This work extends an existing seakeeping tool (OceanWave3D-seakeeping) to allow for the efficient and accurate evaluation of the hydroelastic response of large flexible ships sailing in waves. OceanWave3D-seakeeping solves the linearized potential flow problem using high-order finite differences on overlapping curvilinear body-fitted grids. Generalized modes are introduced to capture the flexural responses at both zero and non-zero forward speed, but we focus on the zero speed case here. The implementation of the hydroelastic solution is validated against experimental measurements and reference numerical solutions for three test cases. The ship girder is approximated by an Euler–Bernoulli beam, so only elastic bending deformation is considered and sheer effects are neglected. Some controversy has long existed in the literature about the correct form of the linearized hydrostatic stiffness terms for flexible modes, with Newman (1994) and Malenica and Bigot (2020) arriving at different forms. We provide here a complete derivation of both forms (including the gravitational terms) and demonstrate the equivalence of the buoyancy terms for pure elastic motions.