A higher order FEM for time-domain hydroelastic analysis of large floating bodies in an inhomogeneous shallow water environment

Abstract

The study of wave action on large, elastic floating bodies has received considerable attention, finding applications in both geophysics and marine engineering problems. In this context, a higher order finite-element method (FEM) for the numerical simulation of the transient response of thin, floating bodies in shallow water wave conditions is presented. The hydroelastic initial-boundary value problem, in an inhomogeneous environment, characterized by bathymetry and plate thickness variation, is analysed for two configurations: (i) a freely floating strip modelling an ice floe or a very large floating structure and (ii) a semi-fixed floating beam representing an ice shelf or shore fast ice, both under long-wave forcing. The variational formulation of these problems is derived, along with the energy conservation principle and the weak solution stability estimates. A special higher order FEM is developed and applied to the calculation of the numerical solution. Results are presented and compared against established methodologies, thus validating the present method and illustrating its numerical efficiency. Furthermore, theoretical results concerning the energy conservation principle are verified, providing a valuable insight into the physical phenomenon investigated.

Time-domain, shallow-water hydroelastic analysis of VLFS elastically connected to the seabed

“…The plate is modelled as an Euler-Bernoulli strip, while the linearized shallow water equations are used for the hydrodynamic modelling. The main novelty of the present contribution, compared to the previous work carried out by the authors [17], lays on the inclusion of multiple elastic connectors in the developed shallow-water, time-domain model. The elastic connectors are represented by simple spring-dashpot systems distributed along the structure.…”

“…Shallow-water conditions are assumed in the following analysis. The general formulation of the above problem, for a freely- floating elastic strip, has already been presented in Sturova [16] and Papathanasiou et al [17]. In the present contribution, the strip is assumed to be elastically connected to the bottom boundary, at both edges, while additional N-1 elastic connectors are distributed along the strip length (see Fig.…”

“…For the derivation of the variational formulation of the problem the same standard process is followed as in Papathanasiou et al [17]. The reader is directed to the given work for a more detailed account.…”

“…15), domain  is discretized and the unknown fields are approximated by means of the higher order finite element scheme developed in [17]. The discrete approximate solutions of the variational problem are given as,…”

“…Subsequently, a Newmark time integration scheme (see [17]) is employed in order to calculate the solution.…”