Hydroelastic interaction between ocean waves and large floating structures in the inhomogeneous ocean environment

Abstract

Interaction of waves with Very Large Floating Structures (VLFS) and sea ice formations present similarities permitting a common mathematical treatment and numerical modelling. Wave-induced structural response and its underlying effect on the hydrodynamic field are fundamental to the in-depth understanding of physical processes like ice shelf calving as well as the design of marine structures operating nearshore. The common features of the aforementioned systems are: (a) their low bending rigidity, (b) their inherently complex geometries and material inhomogeneity and (c) their extent over large horizontal domains, dictating the need to address the effects of bathymetric variations. The common ground allows for the development of joint computational tools for the treatment of the above coupled wave-structure-seabed interaction problems. Intricacies lay on the very same features, namely the large horizontal domains along with geometric and material inhomogeneity. In this work a novel methodology is proposed based on finite elements, in conjunction with coupled-mode system formulation, which is derived by appropriate local-mode representations of the vertical structure of the wave field. Confined in the linear regime, potential theory is employed. The floating body is assumed to be thin in the vertical direction within the limits of reduced elastic plate models. Depending on the structure slenderness and the excitation wavelength-to-plate thickness ratio, the structure is modelled using either Classical Thin or Reissner-Mindlin Plate theory to account for first order shear deformation effects. The wave field is decomposed in the propagating component over the variable bathymetry (in the absense of the body) and the diffraction and radiation parts both due to the rigid motions and the elastic plate deflection. An in vacuo modal expansion for the plate deflection is employed to partially decouple the hydrodynamics from structural mechanics. The employed decomposition allows for the formulation of a propagating wave field and a series of radiation-type sub-problems, formulated by following a domain decomposition approach using different vertical local-mode expansions enabling the consistent satisfaction of the boundary conditions on the free-surface and elastic body subdomains. The formulation is supplemented by introducing matching conditions on the interfaces separating the above subdomains. A weighted residual approach is employed to derive a permissive form of the latter facilitating a FEM-based scheme. To this end, radiation-type problems are re-cast into a mixed weak form by means of Lagrange multipliers defined on the interface between the plate-covered and the free surface regions, aiming at the weak satisfaction of the essential continuity requirement across the transmission interface. This approach circumvents the complexity of constructing appropriate finite element subspaces that would ab initio satisfy the Dirichlet type constraint. Subsequently, the dimensionality reduction of the problems at hand is achieved by the introduction of suitable local-mode vertical representations for the velocity potential in each sub-region, ultimately yielding the variational form of coupled-mode systems on the horizontal plane. The reduced weak forms allow the development of a FEM scheme that employs conventional Lagrange elements, capable of h-p refinement. Finally, the numerical tool incorporates a Perfectly Matched Layer, featuring an unbounded absorbing function, for the numerical domain truncation. Numerical results for a number of configurations are presented in both the 2D and 3D examples. Extensive comparisons are presented against results and data from the literature illustrating the accuracy of the method and showcasing its capabilities in modelling inhomogeneity.