Viscoelastic floating membranes can be used as flexible wave breakers to protect coastal and offshore structures or as flexible wave energy converters. Despite their potential, the role of viscoelastic floating membranes in optimally harvesting or dissipating wave energy remains largely unexplored, particularly regarding how spatially varying material properties influence their performance. To address this gap, we develop an adjoint-based PDE-constrained optimization framework, built on a monolithic finite element formulation of the coupled fluid–structure interaction problem, to investigate and optimize the viscoelastic properties of floating membranes. This methodology enables a systematic optimization of design parameters such as the mass, tension, and damping, which govern the response of the membrane at different wave conditions. In this study we demonstrate that the proposed methodology allows for the optimization of homogeneous and inhomogeneous properties of membranes for different wave excitation frequencies, leading to significant improvements in energy absorption. The framework is implemented in Julia using the Gridap package ecosystem, which enables automatic differentiation of adjoints and avoids the need to derive complex adjoint formulations.

Many engineering and scientific problems require the solution of partial differential equations in complex geometries. Often, these problems involve parametrized geometries, e.g. design optimization, or moving domains, e.g. fluid-structure interaction problems. For such cases, traditional methods based on body-fitted grids require time-consuming mesh generation or re-meshing techniques. Unfitted finite element methods, e.g. CutFEM of AgFEM, are appealing techniques that address these challenges. However, they require ad-hoc integration methods and stabilization techniques to prevent instabilities for small cut cells. Recently, the Shifted Boundary Method (SBM), was introduced to prevent integration over cut cells and small cut-cell instabilities. An extension of the SBM was recently introduced, the Weighted Shifted Boundary Method (WSBM), where the variational form is weighted by the elemental active volume fraction, improving discrete mass/momentum conservation properties in simulations with moving domains. In this work we introduce the Generalized Shifted Boundary Method (GSBM), a geometry-agnostic generalization of the SBM and WSBM formulations that avoids the need of redefinition of integration domains and finite element spaces. The GSBM enables a unified formulation for problems with evolving geometries, supports gradient-based optimization of problems with varying geometries including topological changes, and unifies SBM, WSBM, and optimal-surrogate variants within a single framework. In this work we describe the formulation, and corresponding tests, for three model problems, namely: the Poisson problem, linear elasticity and transient Stokes flow.

The Weighted Shifted Boundary Method (WSBM) was recently introduced as an enhanced Shifted Boundary Method (SBM) for the simulation of flows with moving boundaries. Earlier work of the authors on no-slip boundary conditions for the two-dimensional Stokes flow is extended here to the more challenging case of the three-dimensional incompressible Navier-Stokes equations at low and moderate Reynolds numbers. The SBM is an immersed finite element method that reformulates an infinite-dimensional boundary value problem over a surrogate (approximate) computational domain – to avoid integrating over cut cells – and modifies the original boundary conditions using Taylor expansions – to maintain accuracy. The WSBM weights the SBM’s variational form with the elemental volume fraction of active fluid, drastically reducing spurious pressure oscillations in time that occur when the total volume of active fluid changes abruptly over a time step. The WSBM induces small mass (i.e., volume) conservation errors, which converge quadratically in the case of piecewise-linear finite element interpolations, as the grid is refined. An extensive set of two- and three-dimensional tests demonstrates the robustness and accuracy of the proposed approach.

As climate change becomes more critical and renewable energy sources expand, land-based photovoltaic (PV) systems face limitations due to competition with agriculture and housing. The sea offers a promising location for offshore floating PV (OFPV) systems. Understanding fluid–structure interactions is crucial for these systems. This work explores how different parameters affect the structural load on the floating platform and related electrical power losses. We develop a multi-physics framework integrating the mechanical model of a large floating structure with the optoelectrical modeling of PV modules. This framework analyzes a hypothetical OFPV platform design with various floater configurations, from a single large floater to multiple small floaters connected with free hinges. The results reveal a trade-off in the number of floaters. Power mismatch loss is lower for platforms with fewer, longer floaters. However, structural loads vary, with high stresses in longer floaters due to the elastic response. Young’s modulus impacts longer floaters where the elastic response dominates, while cross-section fill ratio affects shorter floaters, where the rigid-body response prevails. The floater-beam thickness has the most significant impact across various floater lengths.

The development of accurate and efficient methods for hydrodynamic analysis of floating structures is essential for advancing offshore renew-able energy technologies. In this work, we evaluate three unfitted Finite Element methods: the Shifted Boundary Method, the Cut Finite Element Method, and the Aggregated Unfitted Finite Element Method. These three methods are assessed for the estimation of added mass and damping coefficients of floating structures in two dimensions. These methods eliminate the need for traditional meshing, simplifying the analysis of complex geometries, particularly those with sharp edges, in the frequency domain using linear potential flow theory. We present a novel implementation of these techniques, highlight-ing their ability to handle multiple geometries with a single background mesh while maintaining high accuracy. Results are validated against experimental, numerical, and analytical benchmarks, demonstrating good agreement. This work not only highlights the potential of unfitted Finite Element methods for efficient and accurate hydrodynamic analysis but also identifies key challenges and knowledge gaps to guide future advancements in wave-structure interaction modeling.

The expansion of floating offshore renewable energy demands reliable mooring solutions. Synthetic mooring ropes offer cost savings and performance benefits but exhibit complex, nonlinear, and frequency-dependent behavior. This study investigates their mechanical response through experimental testing, characterizing quasi-static and dynamic properties. The results inform a viscoelastic material model that captures nonlinear stiffness and dynamic response under marine loading. Based on Schapery’s formulation, this model can be integrated into a Finite Element framework to simulate real-world conditions, improving predictive capabilities for synthetic mooring lines in offshore applications.

Synthetic mooring lines are increasingly considered for lightweight offshore renewables, but their elasticity poses modelling challenges due to large deformations and frequency-dependent dynamic and non-linear stiffness. To address this, we developed a finite element model based on finite-strain theory and dynamic stiffness. We utilise Tangential Differential Calculus for large deformation analysis and Schapery viscoelastic model for the non-linear constitutive relationship. Our results show that in taut systems, viscoelastic effects dominate at higher frequencies, leading to creep and relaxation under cyclic loads. In catenary systems without a chain segment, viscoelastic impacts are minimal due to low tension in the synthetic line.

Offshore floating structures are experiencing harsh environmental conditions risking their safety. Therefore, mooring lines are crucial for ensuring structures’ stability. Sudden increases in tensions after temporarily slack of the mooring line are called snap loads and are the most critical load states. These snap loads and their dependence to various factors are investigated in the present study. 12 study locations in the south-eastern North Sea are selected. For each location, wave and current variables are extracted from a three-dimensional large-scale numerical model covering the European Shelf. Mooring tensions at different rope positions are calculated via a Finite Element model for flexible mooring lines for different hydrodynamic conditions and used subsequently to obtain tension rates as indicator for snap loads. The dependence among 13 variables per study location is modelled via Gaussian copula-based Bayesian Networks (GCBN). This allows for spatial analysis of the relationships between hydrodynamic variables and tension rates, but also to determine the influence of hydrodynamic variables on expected tension rates. Furthermore, distributions of tension rates are obtained under specific constant hydrodynamic conditions. The results indicate that conditionalising on certain hydrodynamic variables can reduce the expected tension rates, as their marginal distributions are characterised by heavy tails. Still, mooring systems should be designed conservatively. However, once specific hydrodynamic information is available, uncertainties can be minimised, enhancing safety and reliability. Thus, accounting for the dependence among hydrodynamic variables and tension rates is crucial for improving the safety of structures under varying environmental conditions.

Mooring failures significantly threaten the stability of Floating Offshore Wind Turbines (FOWT) under extreme environmental conditions. This study presents an innovative integrated damping mooring system incorporating Seaflex dampers to improve structural stability and operational reliability. Dynamic simulations under 1-year and 50-year return period sea states demonstrate the system's effectiveness. Under Ultimate Limit State (ULS) conditions, the system reduces surge displacement by 59%, pitch angle by 47%, and mooring line tension by 72%. Under Accidental Limit State (ALS) conditions, it mitigates load spikes, reduces drift displacement by 60%, and improves safety factors by 50%. The comparison shows chain and wire rope configurations have better load reduction performance in the integrated damping scheme. Lightweight and adaptable, the Seaflex dampers enhance broad-spectrum damping without affecting platform buoyancy. This study offers a robust solution for enhancing FOWT safety and durability in harsh marine environments, thereby enabling large-scale offshore wind energy development.

This work presents a novel application of an Aggregated unfitted Finite Element Method (AgFEM) to solve the linear radiation potential flow problem in the frequency domain to estimate added mass and added damping for floating structures of arbitrary geometry. The flexibility of AgFEM in handling complex geometries makes it a compelling alternative to conventional techniques. The governing equations of the flow problem and the dynamics of the structure are fully coupled. Two case studies are conducted, estimating the loads on a spar and semisubmersible. The results demonstrate that AgFEM captures the general trends of the added mass and damping.

Backward erosion piping is a failure mechanism of dikes. Numerical modelling is crucial for design and assessment against BEP. Over 30 models have been developed, each with a different purpose and approach. This paper provides a comprehensive overview of the available numerical BEP models, highlighting their limitations, capabilities, and associated challenges. It discusses the different assumptions and their implications on the representation of BEP. Key challenges in the numerical modelling of BEP are (1) the flow (regime) inside the pipe, which is often simplified, even though the impact of this is relatively unknown. (2) The type of erosion (primary or secondary) differs per model, and even within a given type of erosion, approaches vary. (3) Overcoming the difference in scale is a trade-off between the computational effort and simplification. (4) Furthermore, validation of the physics in BEP modelling is difficult due to a of lack micro-scale experimental data.

The paper presents a monolithic finite element model for the hydro-visco-elastic analysis of floating membranes interacting with ocean waves. The formulation couples linearised potential flow and viscoelastic membrane equations, offering a versatile tool for modelling arbitrarily shaped floating membranes in varying sea-bed topography. The paper also presents a wet modal analysis for the coupled problem, accounting for the added mass and stiffness of the surrounding fluid. This model is used to study the dependence of the wet natural frequencies of floating membranes on the material properties. It is also used to analyse the reflection, transmission, scattering and absorption of ocean wave energy by 1D and 2D floating membranes. Notably, the paper underscores the impact of proportional material damping on these observed phenomena. The results highlight local peaks in the viscoelastic behaviour at the calculated wet natural frequencies, and demonstrate the outward dispersion of incoming wave around finite 2D membranes. Furthermore, the model is employed to examine the interaction of viscoelastic membranes with other structures, such as a monopile, under the influence of ocean waves. This comprehensive investigation contributes to a deeper understanding of the fluid–structure interaction inherent to certain floating solar, wave-energy converter and floating breakwater technologies.

The Shifted Boundary Method (SBM) belongs to the class of unfitted (or immersed, or embedded) finite element methods, and relies on reformulating the original boundary value problem over a surrogate (approximate) computational domain. The surrogate domain is constructed so as to avoid cut cells and the associated problematic implementation and numerical integration issues. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions: hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we extend the SBM to the simulation of incompressible Stokes flow, by appropriately weighting its variational form with the elemental volume fraction of active fluid. This approach allows to drastically reduce spurious pressure oscillations in time, which are produced if the total volume of active fluid were to change abruptly over a time step. The proposed Weighted SBM (W-SBM) exactly preserves states of hydrostatic equilibrium, and induces small mass and momentum conservation errors, which converge as the grid is refined. This is in analogy to cutFEMs and related unfitted approaches, which rely on an affine representation of cut boundaries. We demonstrate the robustness and accuracy of the proposed method with an extensive suite of two-dimensional tests.

Offshore wind farms, critical for sustainable energy production, face the challenge of optimization among many parameters influencing key performance indicators in competitive ways. This research introduces the novel Integrative Maximized Aggregated Preference Wind Farm Optimization (IMAP-WFO) framework – a comprehensive tool designed to enhance flexibility, accuracy, and uncertainty quantification in offshore wind farm design and operation. Existing methods often fall short due to limitations in adaptability and precision, especially when modeling complex multi-physical behaviors under uncertain conditions. IMAP-WFO overcomes these limitations by combining advanced statistical techniques and simulation methods. At its core are parametric design performance functions, capturing critical aspects of wind farm behavior, including energy production, material usage, and structural fatigue. These functions rely on Kriging meta-models. To address inherent uncertainty, Monte Carlo simulations provide a probabilistic assessment of outcomes. IMAP-WFO's true innovation lies in translating technical functions into socio-economic objectives, including sustainability metrics, annual energy production, capital expenditure, operational expenditure, model uncertainty, and lifetime fatigue. Stakeholders can dynamically weigh these objectives based on their preferences. A validation process ensures the accuracy of design performance functions, comparing simulated results with real-world data. IMAP-WFO's application is demonstrated through case studies: optimizing the levelized cost of energy and exploring wind farm control strategies.

The reliability of mooring systems has long been a challenge for expanding floating wind turbines into deeper waters. The performance of the mooring system directly determines the service life and survival capability of floating wind turbines. To address this issue, our team has developed a shared damping mooring system. This system reduces the fatigue impact from operating sea conditions and effectively minimizes dragging damage at the fairlead. In this study, two widely used dampers were selected to construct the shared damping mooring system, and their effectiveness in enhancing the reliability of semi-submersible wind turbines was explored. Compared to traditional mooring methods, it was found that this shared damping approach can effectively increase the service life of mooring lines, reduce the local stress and tension levels at the fairlead, and improve the stability of semi-submersible wind turbines. Simulation results indicate that the shared damping mooring system can effectively alleviate fatigue damage, and the shaped memory alloy damper provides significant damping force under low-frequency environmental loads. This characteristic significantly enhances the floating foundation's stability and extends the mooring system's lifetime.

The hydrofoil harnesses wave energy and converts it into thrust. In this paper, we present the results of the first experimental study investigating the dynamic behavior of a fully passive foil with spring-loaded pitch and heave in regular waves. Our study shows that the real-time load signal is multi-harmonic with strong superposition, directly proving the robust energy harvesting performance due to the restoring springs. By interpreting the hydrofoil's pose and path from an image sequence captured underwater, we conclude the dynamic evolution of the fully passive hydrofoil interacting with regular waves. The hydrofoil's dynamics exhibit asymmetric surge, pitch, and heave in a motion cycle. Furthermore, we employ a pixel capturing algorithm with self-correction utility to quantify the hydrofoil's forward displacement from the image sequence of the moving carriage. These findings provide valuable insight into the performance and potential of hydrofoils for marine propulsion.

This work aims to develop a low-fidelity model for a lattice support structure for offshore wind applications. The proposed low-fidelity model consists of a sequence of regular Timoshenko beams, each of them characterized by homogenized mechanical and mass properties representative of the single bays of the reference space-frame structure. The homogenized elastic coefficients of the sequence of beams are then computed by means of two alternative procedures: case (a), via analytical expressions available in the literature and accounting for a partially isotropic behaviour; case (b) by means of an optimization procedure, with ad hoc calibration factors. The suggested methods to derive the homogenized elastic coefficients are then tested for both straight and tapered lattice structures. The prediction performance is evaluated in terms of estimation of the first five natural frequencies and mode shapes, response to dynamic loads, and ability to predict rotor-structure interaction phenomena. A parametric study is then performed to evaluate the potential and limitations of the proposed models. To bypass the optimization procedure (b), a data-driven approach is also proposed for the case of straight lattice structures. Overall, the developed low-fidelity model leads to a computational speed-up factor of at least 60. The prediction reliability of the low-fidelity model is discussed for a tapered and regular straight lattice structure. However, for the latter one, a more detailed comparative study between the various modelling assumptions is performed and discussed. With reference to the straight lattice tower, whenever an optimization procedure is used (case (b)), and with reference to a typical subset of the investigated geometrical parameter space, the mean prediction error of the first five natural frequencies is lower than 1%. On the other hand, for case (a) and for the same investigated subset, the mean prediction errors for the first two bending modes and the torsional mode are, 5.2%, 13.3% and 18.8%, respectively. These results are improved in case a data-driven regression model is used to predict the calibration factors, leading to mean prediction errors below 5% for the entire investigated parameter space.

Floating wind farms are a promising solution for offshore wind energy production in deep waters. However, the design optimisation process of these farms is difficult due to their complex and multidisciplinary nature. Furthermore, current optimisation methods: 1) ignore and/or provide no insight into the dynamic interplay between the preference-dominated management domain and the object-performance-dominated engineering domain; 2) are limited to evaluating potentially sub-optimal design alternatives; 3) contain fundamental aggregation modelling errors; 4) do not return a single optimal design point. This paper presents an optimisation framework that overcomes these shortcomings and enables truly integrative multi-objective design optimisation. It includes a surrogate model that interacts with the wind turbine simulation tool OpenFAST to enable preliminary design of the structure’s mooring system. Applied to a demonstration project and validated against real projects in a maritime contractor environment, the workflow shows improvements in tender performance and added value over single-sided cost optimisations.

In this work we present a novel monolithic Finite Element method 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 (Formula presented.) continuity by employing a continuous/discontinuous Galerkin 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.

Flow simulations on porous media, reconstructed from Micro-Computerised Tomography (μCT) scans, is becoming a common tool to compute the permeability of rocks. Still, some conditions need to be met to obtain accurate results. Only if the sample size is equal or larger than the Representative Elementary Volume will the computed effective permeability be representative of the rock at a continuum scale. Moreover, the numerical discretisation of the digital rock needs to be fine enough to reach numerical convergence. In the particular case of using Finite Elements (FE) and cartesian meshes, studies have shown that the meshes should be at least two times finer than the original image resolution in order to reach the simulation's mesh convergence. These two conditions and the increased resolution of μCT-scans to observe finer details of the microstructure, can lead to extremely computationally expensive numerical simulations. In order to reduce this cost, we couple a FE numerical model for Stokes flow in porous media with an unfitted boundary method for cartesian meshes, which allows to improve results precision for coarse meshes. Indeed, this method enables to obtain a definition of the pore–grain interface as precise as for a conformal mesh, without a computationally expensive and complex mesh generation for μCT-scans of rocks. From the benchmark of three different rock samples, we observe a clear improvement of the mesh convergence for the permeability value using the unfitted boundary method on cartesian meshes. An accurate permeability value is obtained for a mesh coarser than the initial image resolution. The method is then applied to a large sample of a high-resolution μCT-scan to showcase its advantage.