An explicit formulation for restoring stiffness and its performance in ship hydroelasticity

The ship hydroelasticity is an issue nowadays due to the fact that very large container ships, which are quite flexible, are being built. Hydroelastic analysis includes definition of geometrical, structural, hydrostatic, hydrodynamic and, finally, hydroelastic model. Within the hydrostatic model, the modal restoring stiffness, well known in literature as hydrostatic stiffness, is formulated. This problem is approached either from hydromechanical or structural point of view, and, perhaps just for this reason, there are still some open questions. This paper offers a unique formulation of the restoring stiffness. It deals with state-of-the-art, definition of the modal restoring stiffness, flexural and torsional stiffness of pseudo-cylinder, beam finite element formulation, asymmetry analysis of restoring stiffness matrix and incorporation of the restoring stiffness into ship hydroelastic analysis. The application of the developed procedure for determining modal restoring stiffness is illustrated in case of a flexible barge. At the end, some interesting aspects of this challenging task, such as the influence of structure deformation on restoring stiffness and asymmetry of its matrix, are further discussed.