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.

This manuscript presents a formulation for mooring line dynamics using Tangential Differential Calculus (TDC) framework to handle geometric non-linearities in catenary and taut systems. Based on finite-strain theory, the model accounts for large deformations, self-weight, buoyancy, seabed interaction, and hydrodynamic drag. The study presents two solution procedures, GNL-FEM, a high-fidelity finite element model implemented in Julia, and GNL-ANA, a reduced-order semi-analytical model for efficient preliminary analysis.For GNL-FEM, mesh and element order convergence studies demonstrate optimal performance, followed by validation against MoorDyn for catenary lines. In cases involving swell waves, GNL-FEM is shown to minimise the spurious oscillations typically observed in lumped-mass models during slack-line events. A primary focus of this manuscript is the dynamic behaviour of taut mooring lines under harmonic transverse excitation. GNL-FEM results demonstrate progressive geometric hardening, as the system’s natural frequency increases with higher excitation amplitude. Furthermore, strain spectra exhibit distinct super-harmonics and sub-harmonics. GNL-ANA is shown to be accurate up to the second natural frequency, even under high pre-tension and excitation, providing a valuable tool for identifying energy hotspots and optimising material properties in synthetic lines. Overall, the framework provides a consistent and versatile basis for modelling complexities in mooring systems.

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.

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 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.

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.

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.

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.

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.

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.

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.