This paper presents spline-based coupling methods for partitioned multiphysics simulations, specifically designed for isogeometric analysis (IGA) based solvers. Traditional vertex-based coupling approaches face significant challenges when applied to IGA solvers, including geometric accuracy issues, interpolation errors, and substantial communication overhead. The methodology draws on the IGA mathematical framework to deliver coupling solutions that preserve the high-order continuity and exact geometric representation of splines. We develop two complementary strategies: (1) a spline-vertex coupling method that enables efficient interaction between IGA and conventional solvers, and (2) a fully isogeometric coupling approach that maximizes accuracy for IGA-to-IGA communication. Both theoretical analysis and extensive numerical experiments demonstrate that our spline-based methods significantly reduce communication overhead compared to traditional approaches while simultaneously enhancing geometric accuracy through exact boundary representation and maintaining higher-order solution continuity across the coupled interfaces. We quantitatively confirm the communication efficiency benefits through systematic measurements of both transfer times and data volumes across various mesh refinement levels, with experimental results closely aligning with our theoretical predictions. Our benchmark studies further demonstrate the geometric fidelity advantages through exact boundary representation, while also highlighting how the inherent mathematical structure of splines naturally preserves solution derivatives across interfaces without requiring additional computation or specialized transfer algorithms. This work not only provides efficient coupling strategies tailored to IGA-based solvers but also establishes a practical bridge between IGA and traditional discretization methods in partitioned multiphysics simulations. By offering viable options for coupling conventional solvers with IGA-based components, our approach enables broader adoption of IGA in established simulation workflows while ensuring accurate and high-performance interface communications.

Increasing demand for the extended lifetime of structures stresses the need for reliable high-cycle fatigue lifetime predictions for variable amplitude-loaded structures. Design standards (including Eurocode 3, AASHTO and British Standard 7608) provide a fatigue design model based on constant amplitude S-N curves and a linear damage accumulation model. There are minor differences in detail categories between standards, but larger differences between the extensions of the S-N curves for variable amplitude loading. It is known that the load spectrum influences this extension due to load interaction and sequence effects. The validity of the predicted fatigue life by available design standards is checked using a compilation of variable amplitude fatigue test data for steel arc-welded joints from the literature with different loading spectra. The results indicate that the standards are generally conservative in the mid- but not in the high-cycle regime, suggesting that resistance non-linearities should be explicitly addressed.

Facing multiaxial fatigue testing challenges with respect to non-proportional loading conditions, a custom-built hexapod has been used to establish the mode-{I, III} resistance characteristics of high-quality welds in steel maritime structures. Assessment of the hexapod test data using the effective notch stress and total stress, respectively the best performing multiaxial intact and cracked geometry parameters, shows a fit in the reference quality literature data scatter band and provides conservative lifetime estimates. In order to improve the lifetime estimate accuracy, strength, geometry, material and mechanism aspects are investigated. Welding induced residual stress, a strength aspect, predominantly affects the mode-I fatigue resistance including a mean (residual) stress contribution. The weld notch radius, a geometry parameter, primarily influences the mode-III fatigue resistance. Similar material microstructure compositions of the high-quality welds and reference quality ones are observed, implying comparable mode specific mechanism parameters for the effective notch stress and total stress, respectively the material characteristic length and elastoplasticity coefficient. The material microstructure properties and classification criteria for high-quality welds support the residual stress estimates and suggest a smaller welding induced defect size. In general, the high quality is mainly reflected in the larger resistance curve intercept and slope, another strength and mechanism parameter, implying a larger initiation contribution to the total lifetime. For a high-quality resistance curve involving the representative strength, geometry, material and mechanism contributions, more accurate lifetime estimates are obtained, even though the parameter confidence is reduced because of the relatively small data size in comparison to the reference quality one.

Friction stir welding (FSW) is a solid-state joining process that gives welds with excellent mechanical properties. The drive towards electrification has seen FSW adopted by the automotive sector for the fabrication of lightweight aluminium car bodies and battery assemblies. Element Six utilised their expertise in high performance, abrasion and temperature resistant materials to develop a FSW tool for steel and this was trialled at TWI where welding techniques were developed to allow welds to be made both in air and under water. A rigorous, independent assessment of weld quality was undertaken by the Technical University of Delft (TUD) and publications and dissemination resulting from this work has identified a number of potential other applications across the wider transport sector.

Wrinkling is the phenomenon of out-of-plane deformation patterns in thin walled structures, as a result of a local compressive (internal) loads in combination with a large membrane stiffness and a small but non-zero bending stiffness. Numerical modelling typically involves thin shell formulations. As the mesh resolution depends on the wrinkle wave lengths, the analysis can become computationally expensive for shorter ones. Implicitly modelling the wrinkles using a modified kinematic or constitutive relationship based on a taut, slack or wrinkled state derived from a so-called tension field, a simplification is introduced in order to reduce computational efforts. However, this model was restricted to linear elastic material models in previous works. Aiming to develop an implicit isogeometric wrinkling model for large strain and hyperelastic material applications, a modified deformation gradient has been assumed, which can be used for any strain energy density formulation. The model is an extension of a previously published model for linear elastic material behaviour and is generalised to other types of discretisation as well. The extension for hyperelastic materials requires the derivative of the material tensor, which can be computed numerically or derived analytically. The presented model relies on a combination of dynamic relaxation and a Newton–Raphson solver, because of divergence in early Newton–Raphson iterations as a result of a changing tension field, which is not included in the stress tensor variation. Using four benchmarks, the model performance is evaluated. Convergence with the expected order for Newton–Raphson iterations has been observed, provided a fixed tension field. The model accurately approximates the mean surface of a wrinkled membrane with a reduced number of degrees of freedom in comparison to a shell solution.

The response of maritime structures can be multiaxial, involving predominant mode-I and non-negligible mode-III components. Adopting a stress distribution formulation based effective notch stress as fatigue strength parameter for mixed mode-{I, III} multiaxial fatigue assessment purposes, a mode-I equivalent von Mises type of failure criterion has been established at the critical fracture plane. Counting includes a cycle-by-cycle non-proportionality measure and damage accumulation is based on a linear model. Distinguished mode specific and material characteristic strength and mechanism contributions in terms of respectively the resistance curve intercept and mean stress induced response ratio coefficient, resistance curve slope and material characteristic length, have been incorporated. Evaluating the mid-cycle fatigue resistance, the outperformance is impressive. The analysed multiaxial mode-{I, III} data fits the uniaxial mode-I reference data scatter band and a single resistance curve can be used for fatigue assessment.

Arc-welded joints in steel maritime structures are typically identified as weakest links in terms of fatigue limit state performance. Multiaxiality can be involved, consisting of predominant mode-I and non-negligible mode-III components. Aiming to answer the question if a cracked geometry based fatigue strength parameter would outperform an intact geometry based one like the effective notch stress, the total stress is adopted. A von Mises type of criterion is defined at the critical fracture plane and includes mode specific and material characteristic strength and mechanism contributions. A lifetime dependent shear strength coefficient is introduced to cover the resistance curves intercepts and slopes, whereas the total stress parameter contains the mean stress contribution as well as the (mixed) mode dependent notch and crack tip elastoplasticity coefficients, reflecting an interaction mechanism. Cycle counting includes a cycle-by-cycle non-proportionality measure and damage accumulation is based on a linear model. Evaluating mid-cycle fatigue resistance data, the total stress and effective notch stress performance turns out to be similar. However, the total stress related elastoplasticity coefficients are an explicit and sensitive measure to incorporate the actual physics of the fatigue damage process, whereas the material characteristic lengths for the effective notch stress seem to be more implicit and less sensitive ones.

Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines) which add degrees of freedom locally based on finer B-spline bases. Labeling of elements for refinement is typically done using residual-based error estimators. In this paper, an adaptive meshing workflow for isogeometric Kirchhoff–Love shell analysis is developed. This framework includes THB-splines, mesh admissibility for combined refinement and coarsening and the Dual-Weighted Residual (DWR) method for computing element-wise error contributions. The DWR can be used in several structural analysis problems, allowing the user to specify a goal quantity of interest which is used to mark elements and refine the mesh. This goal functional can involve, for example, displacements, stresses, eigenfrequencies etc. The proposed framework is evaluated through a set of different benchmark problems, including modal analysis, buckling analysis and non-linear snap-through and bifurcation problems, showing high accuracy of the DWR estimator and efficient allocation of degrees of freedom for advanced shell computations.

The predominant mode-I response of maritime structures can be multiaxial, involving out-of-plane mode-III shear components. Semi-analytical mode-III notch stress distribution formulations have been established for critical details like welded T-joints and cruciform joints, reflecting (non-)symmetry with respect to half the plate thickness. Using a stress distribution formulation based effective notch stress as fatigue strength criterion, the mode-III welded joint mid-cycle fatigue resistance characteristics have been investigated. In comparison to mode-I, the material characteristic length and resistance curve slope estimate suggest the fatigue damage process to be even more an initiation related near-surface phenomenon. Mean shear stress effects seem insignificant.

The characteristic far field response spectrum of welded joints – the governing fatigue sensitive locations in steel marine structures – is predominantly linear elastic, meaning mid- and high-cycle fatigue (MCF and HCF) is most important for design. Using the effective notch stress- and the total stress concept, involving respectively S_e and S_T as intact- and cracked geometry fatigue strength criterion, one MCF-HCF resistance curve has been obtained for all welded joints. A generalised random fatigue limit model explicitly incorporating the MCF life time and HCF strength limit scatter provides statistically the most accurate fatigue strength and fatigue life time estimates. Similar MCF performance is obtained for S_e and S_T. Although crack growth dominates the MCF damage process, the results for an initiation related criterion like S_e and natural crack growth related criterion like S_T are similar. Adopting S_e rather than S_T as fatigue strength criterion naturally related to the crack initiation dominated HCF region showing the largest data scatter may explain the better effective notch stress concept HCF performance. Since the HCF resistance scatter is relatively large, the MCF-HCF generalised random fatigue limit model design curves show approximately 1-slope behaviour. meaning that for design purposes a linear Basquin model approximation rather than a piecewise continuous bi-linear MCF-HCF formulation according to guidelines, standards and classification notes should be adopted.

The first part of the paper presents a partitioned fluid–structure interaction (FSI) coupling for the non-uniform flow hydro-elastic analysis of highly flexible propellers in cavitating and non-cavitating conditions. The chosen fluid model is a potential flow solved with a boundary element method (BEM). The structural sub-problem has been modelled with a finite element method (FEM). In the present method, the fully partitioned framework allows one to use another flow or structural solver. An important feature of the present method is the time periodic way of solving the FSI problem. In a time periodic coupling, the coupling iterations are not performed per time step but on a periodic level, which is necessary for the present BEM–FEM coupling, but can also offer an improved convergence rate compared to a time step coupled method. Thus, it allows to solve the structural problem in the frequency domain, meaning that any transients, which slow down the convergence process, are not computed. As proposed in the method, the structural equations of motion can be solved in modal space, which allows for a model reduction by involving only a limited number of mode shapes. The second part of the paper includes a validation study on full-scale. For the full-scale validation study a purposely designed composite propeller with a diameter of 1 m has been manufactured. Also an underwater measurement set-up including a stereo camera system, remote control of the optics and illumination system has been developed. The propeller design and the underwater measurement set-up are described in the paper. During sea trials blade deflections have been measured in three different positions. A comparison between measured and calculated torque shows that the measured torque is much larger than computed. This is attributed to the differences between effective and nominal wakefields, where the latter one has been used for the calculations. To correct for the differences between measured and computed torque the calculated pressures have been amplified accordingly. In that way the deformations which have been computed with the BEM–FEM coupling for non-uniform flows became very similar to the measured results.

Highly varying sloshing loads are a superposition of load components resulting from a sequence of different physical phenomena. However, not all features of spatial and temporal variations of sloshing loads and associated phenomena are equally important when failure of structure is considered. Therefore, the prediction of sloshing loads should be focused on those load components which lead to failure. These components can be found by employing a structural model, which should be fast computationally considering the huge number of possible sloshing loads. This paper presents a reduced order model based on the beam-foundation model which is derived for the Mark-III cargo containment system. The model is validated against a detailed finite element model and it conservatively predicts the stresses at failure locations. The calculation time using the model is approximately two orders smaller in comparison to a finite element model computation, which allows the model to be applied for finding governing load components and associated physical phenomena.

A special type of fluid–structure interaction (FSI) problems are problems with periodic boundary conditions like in turbomachinery. The steady state FSI response of these problems is usually calculated with similar techniques as used for transient FSI analyses. This means that, when the fluid and structure problem are not simultaneously solved with a monolithic approach, the problem is partitioned into a fluid and structural part and that each time step coupling iterations are performed to account for strong interactions between the two sub-domains. This paper shows that a time-partitioned FSI computation can be very inefficient to compute the steady state FSI response of periodic problems. A new approach is introduced in which coupling iterations are performed on periodic level instead of per time step. The convergence behaviour can be significantly improved by implementing existing partitioned solution methods as used for time step coupling (TSC) algorithms in the time periodic coupling (TPC) framework. The new algorithm has been evaluated by comparing the convergence behaviour to TSC algorithms. It is shown that the number of fluid–structure evaluations can be considerably reduced when a TPC algorithm is applied instead of a TSC. One of the most appealing advantages of the TPC approach is that the structural problem can be solved in the frequency domain resulting in a very efficient algorithm for computing steady state FSI responses.

Fatigue is a governing design limit state for marine structures. Welded joints are important in that respect. The weld notch stress (intensity) distributions contain essential information and formulations have been established to obtain a total stress fatigue damage criterion and corresponding fatigue resistance curve; a total stress concept. However, the involved weld load carrying stress model does not provide the required estimates and trends for varying geometry dimensions and loading & response combinations. A new one has been developed and performance evaluation for T-joints and cruciform joints in steel marine structures shows that in comparison with the nominal stress, hot spot structural stress and effective notch stress concept based results up to 50% more accurate fatigue design life time estimates can be obtained. Taking advantage of the weld notch stress formulations, the effective notch stress concept performance has improved adopting a stress-averaged criterion rather than a fictitious notch radius-based one.