This master’s thesis investigates the fatigue resistance similarity between small-scale test specimens and large-scale structures, specifically focusing on steel welded joints. The primary goal is to improve the understanding of how fatigue data from small-scale tests can be reliably applied to predict the performance of full-scale maritime structures, thereby reducing conservatism in design and optimizing material usage without compromising safety. Fatigue resistance is a critical factor in the design and maintenance of maritime structures. Traditional design methods often use S-N curves derived from small-scale specimen tests, which can be overly conservative when applied to full-scale structures. This conservatism, while ensuring safety, leads to increased material use and associated costs. The aim is to identify and quantify the scaling phenomena that influence the transfer of fatigue data from small-scale specimens to full-scale structures. By proving fatigue resistance similarity and understanding these scaling effects, the research seeks to refine the fatigue design process, thereby enhancing efficiency and reducing environmental impact. The research utilizes various fatigue assessment concepts, including the Nominal Stress Concept (NSC), Hot Spot Structural Stress Concept (HSSSC), and the Effective Notch Stress Concept (ENSC). Finite Element (FE) models of large-scale specimens, created using Abaqus, are used to test these concepts. The study also explores the application of mean stress correction models to improve the fit of large-scale data within small-scale data scatter bands. The methods are evaluated based on their ability to incorporate local geometry information and their effectiveness in reducing scatter in fatigue data. The study demonstrates that incorporating local geometry information is crucial for achieving fatigue resistance similarity between small-scale and large-scale specimens. The HSSSC and ENSC, which account for local geometrical variations, provide better fits for large-scale data within the small-scale data scatter bands compared to the NSC. This confirms the hypothesis that local weld geometry plays a significant role in fatigue resistance similarity. Furthermore, applying a mean stress correction improves the alignment of large-scale data with small-scale data, highlighting the importance of considering residual stresses and load ratios in fatigue assessments.
The findings can have practical implications for the design and maintenance of maritime structures. By improving the accuracy of fatigue life predictions, the research supports the development of more efficient and cost-effective designs. The insights gained from this research help address uncertainties and improve design assumptions for vessel fatigue performance. By incorporating local geometry information and applying mean stress corrections, the research provides a more accurate and less conservative approach to fatigue life prediction. These advancements have the potential to reduce material usage and costs in maritime structure design, while maintaining high safety standards.

In an era where global energy consumption has been rising steadily, the demand and supply of renewable energy sources have become increasingly important. Offshore wind is a promising renewable energy source, which has been actively developed in the last decades in the form of bottom-founded offshore wind, bound to shallow water. Floating Offshore Wind Turbines (FOWT) offer a solution for countries without shallow coastal waters with an abundance of wind potential. In a competitive market with different solutions, Bluewater Energy Services (Bluewater) has developed a tension leg platform (TLP) type substructure to support a 15MW turbine.

These FOWT installations are subject to the random nature of environmental loading which is highly stochastic in terms of amplitude, frequency and phase angle and is hence considered multiaxial non-proportional (random) variable amplitude loading. Multiaxial loading does not, however, guarantee a multiaxial stress response. One of the considerations for offshore structures subject to repetitive loading is fatigue lifetime estimation, which is predominantly done using uniaxial assessment methods. This is not an issue if the stress response is dominantly uniaxial, however, literature has demonstrated that evaluating a specimen subject mode-{I,III} multiaxial stress response using uniaxial (mode-{I}) assessment methods can lead to a significant overestimation of the fatigue lifetime.

To investigate the (multiaxial) stress response of fatigue-critical weld seams in TLP-type FOWT substructures, a new simulation methodology needed to be developed, which allowed for the structure's rigid body motions and elastic deformations to be captured. This methodology was built on an existing hybrid rigid-flexible modelling approach. It was improved upon by considering local (panel-based) hydrodynamic pressure and kinematic structural boundary conditions in order to conduct coupled (aerodynamic-hydrodynamic-mooring) analysis with integrated structural analysis. This approach allowed for the system motion and structural response to a dynamic metocean environment to be simulated using a range of commonly occurring seastates. The integrated coupled analysis was completely conducted within the Ansys environment.

Next, time-varying mode-{I,III} stress signals were reconstructed from the structural analysis model using a traction-based structural stress assessment method. In order to assess the extent to which fatigue-critical weld seams are subject to multiaxial stress response, a damage accumulation calculation should be conducted. However, given the added computational expense of such a calculation, a screening method was first considered in order to better understand the characteristics of stress response behaviour. The screening method considered was based on a Minimum-Circumscribed Ellipse method.

From this screening method, it was found that stress response behaviour is predictable and can be related to specific loading & response frequencies. Furthermore, it was found that parts of the considered structure were subject to significant levels of multiaxial non-proportional stress response and that applying uniaxial fatigue assessment criteria risks overestimating lifetime estimation and misplacing the governing fatigue hotspot. Finally, it was concluded that fatigue-critical weld seams in a FOWT TLP-type substructure are subject to multiaxial stress to the extent that multiaxial damage accumulation models should be considered. If this is not possible, a multiaxial stress response screening should be conducted to identify fatigue governing locations in the welds, as well as locations subject to multiaxial stress.

In marine structures, fatigue is typically the dominant limit state. The fatigue resistance of welded joints in steel marine structures is a critical aspect of ensuring the structural integrity and safety of the components. To determine the structural response, finite element method is necessary to evaluate structural stress. For thin-wall structures, shell element model is usually preferred to solid element model, because the former can save time in calculations. In order to study the effect of weld modeling in shell model, the structural stress levels of the shell model in both the as-welded and unwelded cases are investigated respectively, using the solid element model results for reference purposes. The first chapter is the introduction and the second chapter is literature survey of state-of-the-art research. Chapter 3 and chapter 4 focus on the structural stress estimation with respect to frame-stiffener structure and stiffener-plate structure. The traction forces based procedure is clarified and applied to evaluate HS structural stress. In consequence, the preliminary conclusion on the influence of weld modeling on the structural stress of the shell model is obtained.

Apart from that, fatigue resistance data for arc-welded joints are typically derived from small-scale specimens. However, structural aspects can affect fatigue resistance characteristics. Therefore, to validate whether the fatigue resistance observed in small-scale specimens accurately represents that of full-scale structure, similarity research is necessary. In Chapter 5, the effective notch stress of large-scale specimens is evaluated. Fatigue failure criteria are discussed to derive the appropriate lifetime. Finally, the LSS fatigue resistance data evaluated by the effective notch concept are substituted into SSS fatigue resistance scatter band, to validate the similarity between SSS and LSS.

Maritime structures, such as offshore support vessels and floating wind turbines, face time-varying loads from environmental elements like wind and waves, as well as operational loads from machinery. This exposure leads to fatigue, a progressive cracking process triggered by cyclic loading, which is a significant concern for structural integrity. Fatigue cracks often originate at stress concentration points, which can occur at different scales due to material defects and structural features. In steel structures, welded joints are particularly vulnerable due to their stress-concentrated geometry, making fatigue analysis crucial for their longevity.

Fatigue in maritime structures is inherently multiaxial due to various external loads and complex structural responses, involving mode-I, mode-II and mode-III loading. In typical maritime applications, mode-I induced damage is inherently governing, but multiaxial loads from torsional moments and out-of-plane forces can also impact fatigue life. Modelling these multiaxial loads accurately is necessary to predict fatigue life in welded joints, which experience both fatigue initiation and crack growth phases.

Fatigue life modelling involves assessing both intact and cracked geometries. For welded joints, fatigue life is typically crack-growth dominated due to inherent defects from welding. Linear elastic models, such as Basquin’s equation, often relate stress to fatigue life, showing a log-log linear relationship. Mode-I and mode-III loading modes differ in their strength and mechanism contributions, which can vary based on whether the load cycles are proportional or non-proportional.

The research focuses on a systematic approach for multiaxial fatigue analysis of arc-welded joints in steel maritime structures. The goal is to develop an accurate, reliable, and simple methodology for assessing fatigue life. This includes selecting appropriate fatigue criteria and developing robust cycle-counting techniques for handling non-proportional multiaxial loads. A von Mises stress-based failure criterion is used, supported by a mode-dependent shear strength coefficient to improve the accuracy of fatigue predictions. Literature-derived coefficients help capture the distinct behaviour of mode-I and mode-III contributions.

To evaluate mode-III response characteristics, new formulations for weld toe notch stress distributions were developed. A linear damage accumulation model offers simplicity in life estimation, while semi-analytical methods improve prediction accuracy. Both intact and cracked geometry parameters show reliable life estimates, though each brings specific strengths – the former for averaging capability and the latter for detailed physics of fatigue.

Fatigue resistance data available in the literature were used to create a general S-N design curve for typical weld quality. For high-quality welds, new fatigue tests conducted using a specially designed hexapod platform revealed higher resistance than standard predictions. This high-capacity, six-degree-of-freedom testing apparatus allows rigorous multiaxial fatigue assessments, filling gaps in non-proportional load data and providing a foundation for improved life predictions.

Ultimately, by combining theoretical modelling, experimental data, and novel testing methods, this research advances multiaxial fatigue assessment in maritime steel structures, with findings that emphasize the critical need for mode-specific contributions and the potential benefits of enhanced testing for accurate fatigue life predictions.@en

Ships at sea encounter wave-induced cyclic loading, meaning fatigue is a governing limit state. The structural response introduces stress concentrations, hotspots, at notch geometry like welded joints locations. At the same time, the welding process typically introduces defects, meaning welded joints are typically the governing fatigue-sensitive details. Accurate predictions of the fatigue lifetime are paramount for ensuring safety and economic viability in the maritime sector.

Because of the welding-induced defects, the fatigue lifetime of welded joints is growth rather than initiation-dominated; adopting a cracked geometry-based fatigue damage criterion like the stress intensity factor seems straightforward. Weld notch characteristic crack growth behaviour, however, becomes crucial. Since both short and long crack growth are considered important, a typical one-stage Paris relation-based long crack model must be extended, particularly since most of the welded joint fatigue lifetime is spent in the notch-affected short crack growth region. The short crack growth behaviour can be both non-monotonic as well as monotonically increasing, depending on the elastoplastic response conditions. A two-stage crack growth model, incorporating both short crack growth behaviour and the long crack growth characteristic, has already been proposed in a different project based on compact tension (CT) specimen crack growth testing results obtained using potential drop measurements. However, the corresponding strain/stress field possibly explaining the crack growth behaviour in terms of elastoplasticity is not part of the output. Images have been captured, which can be analyzed with Digital Image Correlation (DIC) to provide the field measurements.
\noindent The first aim of the research has been to explore dedicated displacement field formulations to capture the crack tip location and corresponding stress intensity factor simultaneously by developing a one-step DIC approach. The expected benefits of this approach over other DIC methods consist of an expected increase in accuracy and the elimination of a post-processing step. Current DIC methods generally exist out of a two-step approach. First, a DIC procedure is employed with a generalized kinematic basis. Secondly, a post-processing step is employed to determine the crack tip location and stress intensity factor (SIF). Specifically for the crack tip, the post-processing step generally assumes a dedicated kinematic basis function describing the field around the crack. Directly incorporating the dedicated function into the DIC procedure allows for the intermediate generalized kinematic assumptions to be eliminated.
The resulting crack size and SIF from this approach can be used to determine the crack growth relationship. This relationship can be used for the second aim of this thesis, which has been to determine the material parameters of the proposed two-stage crack growth model and validate its ability to capture the short crack growth behaviour.
However, the SIF values obtained with the developed one-step DIC do not align with the analytically obtained values. Regarding the crack growth relationship, this difference in loading introduces a mean shift. Nevertheless, the observed crack growth behaviour aligns with the trends established in prior investigations, which combined potential drop crack size results with analytically determined SIF values.
A three-step approach has been adopted to investigate the accuracy of the SIF determination:
Step 1: A direct approach using a finite element formulation based on global rather than local DIC, enforcing displacement field continuity as required for a crack path-independent SIF calculation. \par
Step 2: An indirect approach using the global DIC-based displacement field (step 1) and Williams' crack tip displacement field formulation to obtain the crack tip location and SIF at the same time.
Step 3: A direct approach using Williams' crack tip displacement field formulation to obtain the crack tip location and the SIF simultaneously.
Analyses showed that involving Williams' asymptotic solution (steps 2 and 3) for long cracks in a simple far-field stress condition is beneficial. Accurate crack tip location and SIF estimates have been obtained. However, for complex stress fields at notched geometries additionally containing geometry boundaries in the same region, higher order terms are required to obtain a converged displacement field. An accuracy improvement has been observed when adopting a direct approach (step 3) rather than an indirect one (step 2) approach. A global FEM-based direct approach (step 1) allows for describing complex displacement fields and obtaining SIF estimates independent of the Williams' formulation. The resulting estimates from this approach agree with the Williams-based estimations (steps 2 and 3). From this, it can be concluded that the obtained difference in the SIF follows from a fundamental difference in the load obtained by analytical determination and the DIC approaches. This conclusion is supported by the difference in the structural stress obtained from the DIC approaches compared to the analytical estimate.
The second aim of this thesis requires further investigation into the loading discrepancy before the total life model can undoubtedly be validated. Nevertheless, preliminary usage remains possible with the usage of consistent SIF determination. Resulting in the establishment of model parameters using likelihood regression for the CT and as-welded joint specimens. \par
For the final aim of this thesis, the total life fatigue strength criterion is obtained by integrating the two-stage crack growth model. This criterion is applied in a case study to estimate the total fatigue lifetime of a critical welded joint in a general cargo carrier. In order to determine the estimated lifetime of the critical joint, the fatigue loading is required. While knowledge of the cargo load is available, the impact of wave-induced loading requires investigation. Two distinct approaches have been used to determine the wave loading. Initially, Four representative wave loading scenarios established by Bureau Veritas regulations are considered. The cumulative fatigue damage resulting from these scenarios is then extrapolated to encompass the entirety of loading conditions experienced by the ship.
Secondly, a wave spectrum approach is undertaken to address uncertainties in loading analysis. A hydro-structural solver is utilized to calculate loading across various sea states. The total fatigue damage is based on a weighted average of a representative sea spectrum. The fatigue lifetimes derived from these methodologies are compared to the hot spot structural stress concept as typically adopted in industry for reference purposes. A comparison of the results shows that the hot spot structural stress concept underestimates the fatigue lifetime due to the increased conservatism required in this model.

Fatigue might be the governing limit state in marine structures mainly induced by the waves and wind. Therefore, using a lap joint for the shell plating to replicate the appearance of a riveted joint for a retro yacht is critical due to the limited fatigue resistance. For this joint type cracks initiated at the root, which should always be avoided due to hard detectability, might appear. Arc- and laser-welded lap joints are researched to estimate fatigue resistance and reduce the risk of root failure.
The hot spot peak stress of weld toe and weld root notches is insufficient to reflect the fatigue strength, explaining why an effective notch stress parameter is used, able to deal with both weld toe and weld root notch induced fatigue. Semi-analytical weld notch stress formulations are established in order to avoid solid finite element modelling to capture the effective notch stress. Particular attention is paid to the lap joint characteristic extreme weld notch load carrying level. A second-order weld load carrying stress formulation is introduced. Since the (laser) weld is typically small in comparison to the plate thickness, a dedicated way of weld modelling is proposed, assuming a shell finite element type of formulation, allowing to capture the far field stress for both the weld toe and weld root notch accurately.
Fatigue tests are performed to obtain the laser-welded lap joint mid-cycle fatigue resistance information, including the material characteristic length as effective notch stress coefficient. Particular attention is paid to mean (residual) stress effects in comparison to the arc-welded joint equivalent to explain the fatigue performance.
Comparing the lap joint fatigue resistance in arc-welded and laser-welded configurations to the resistance of other joint types, the results turned out to be aligned. Investigating different material characteristic parameters, either an effective point or an effective line is used. A line based parameter shows a better performance. The main reason is that the actual notch stress gradient is explicitly considered. The mean (residual) stress seems to be larger for arc-welded joints. Furthermore, the mean (residual) stress correction seems at the same time to be one reason for toe induced- rather than expected root induced failure. For arc-welded joints, the change in failure location induced by stress level dependent secondary bending moments is another reason. The fatigue resistance parameter confidence for laser-weld weld joints is relatively low in comparison to the confidence for arc-welded ones, as a result of data size: respectively ≈190 and ≈3000.
When not considering the change in secondary bending moments in the fit of a Se-N curve, the overall fit parameters and quality do not change significantly for arc-welded lap joints. However, the influence on the effective stress range is substantial and changed the value on average by 4.7 % and up to 14.7 %.
Considering only the mid-cycle fatigue resistance, laser welding is superior to arc welding when exposed to low load and response ratios resulting from the lower residual stress level. The FAT class design curve of arc-welded joints for the hot spot structural stress concept with a load and response ratio of 0.5 can be used with a mean stress correction to estimate the fatigue resistance of laser welds.

Fatigue lifetime has proven to be a leading design parameter for naval vessels. In the field of fatigue analysis and design of welded joints, two overall methods are distinguished: the temporal and spectral approach. Using empirical models, the spectral approach is typically preferred due to its efficiency, even though damage estimates are conservative. With the temporal approach, nonlinear effects can be captured, providing higher accuracy at the cost of additional computation time.

Within this framework, an improvement of the spectral approach was pursued, focusing on incorporating the mean stress effect. Past efforts to include mean stress corrections were continued by focusing on applying the Walker correction.
Nonlinear effects on the mean stress response were investigated and were found to be quite small for the case of a pontoon vessel. This enabled the use of the still water bending moment as a single input to the spectral mean stress model. By using Walker in the spectral mean stress correction, an overall reduction of conservatism of 21% was achieved.

Future research should focus on testing new wave cases, applying additional fatigue models and investigating the effects for hull shapes of naval vessels.

Due to the growing quest for renewable energy, wind turbines grow in size. This means that higher demands are posed on the transporting structures, also called tower grillages, which brings its challenges for their design. The fact that the structures considered in this thesis are placed on a ship makes the design even more complicated. Therefore, a procedure is developed in this thesis that is able to optimize a tower grillage, while keeping the underlying ship intact. This tool is based on a combination of size and shape optimization.

The optimization is performed with the dual annealing algorithm. The objective is mass reduction, with the stress in the grillage, and stress and buckling in the ship as constraints. These constraints are taken into account by a penalty function. The design variables are the angles at which the radial supports attach and the thicknesses of the radial supports and the other elements of the grillage. The main question that is answered in this thesis is how this optimization procedure can help in the design of a tower grillage, where the underlying ship structure is implemented as a boundary condition.

First, a single layout is optimized with the ship modelled as a rigid boundary condition. Next, a model of a section of the ship is made and used as the boundary condition on the tower grillage. A comparison between these models showed that the main differences in stress between the two optimization results
are seen in the largest parts of the grillage: the sides, the flanges and the can. The maximum stress in the latter two elements is larger, which also results in larger thicknesses in the optimization with the ship. This affects the average mass in the ship, which is increased with 5.7% when compared to the grillage on the rigid constraint.
After that, a full grillage is optimized. A first attempt demonstrated that the stress in the ship could only be decreased a little with the initial settings of the optimization. That required a slightly different model, to make sure that the stress in the ship remains acceptable. With that model, a mass decrease
of 32 tons could be obtained, which is a decrease of 9.1 % compared to the original design by Vuyk Engineering.

From the different optimization steps became clear that the main factors influencing the optimal distribution of radial supports are the lengths of the supports, and the location of the outer brackets. The compliance of the ship changes the stresses in the grillage, and therefore the optimization result. The
stress in the ship can be reduced only to some extent, so the effect of a stress violation in the initial design is that a new bracket design needs to be made. The results show that the stress is governing for the current optimization, and buckling is not.
The conclusion is that the current procedure can help in the design by providing a global image of lighter layouts which avoid stress and buckling constraint violations in the ship. However, the limitation of the research is that the result is only a global image. It is therefore considered not worth the effort and
time to apply the current method in an engineering environment. It does however show the potential of this method, so future enhancements can make the procedure suitable for engineering.

Fatigue is typically a governing limit state for maritime structures, and weld joints are the most critical locations. Various fatigue damage criteria have been developed involving either an intact or cracked geometry parameter, incorporating local or global information. In this thesis, the effective notch stress based total life fatigue damage criterion has been used in order to improve the accuracy of fatigue lifetime prediction and reduce the workload of engineers in the early design stage. First, the Battelle structural stress calculation procedure is clarified and examined with three models. A hot spot type A, B and C mesh convergence study are conducted. In order to quantify the influence of mesh quality, several ugly mesh models are tested with their good mesh counterparts. For validation purposes of the total life model, a large scale specimen fatigue test result has been used and the mesh quality investigations are included. The DNVGL based life time estimate is provided for the sake of comparison. Finally, several conclusions and recommendations are provided for future applications.

Solar energy is considered to be one of the most promising energy alternatives among many renewable energy sources. On the pathway towards achieving climate goals, dramatic scale up of clean technologies is required, however the installation of solar energy has the burden of intense land requirement. Therefore, the onset of floating solar technology can be the turning point to give incentive for more substantial deployment of solar energy, avoiding land occupancy concerns. Besides the potential of installing bodies on water, floating solar brings the benefit of an efficiency increase superior to 10 percent in relation to land based solar, depending on the solar panel technology and environmental conditions. This efficiency increase can be attributed to the natural cooling effect of the seawater, located below the solar platform.

The current fatigue assessment methods for naval ships are intentionally conservative. This is in part due to uncertainties in the fatigue capacity (i.e. fatigue resistance) of the ship: the nominal and hot spot structural stress incorporate implicit conservatism due to the inherent data-scatter and the Linear Damage Accumulation Model (LDAM) by Palmgren and Miner is not sufficiently accurate to assess random variable amplitude loading histories. The safe-life engineering solution to this is to employ a safety factor. This typically reduces the critical damage from 1.0 to 0.5, or even 0.2, based on engineering judgement. The main flaw of the Linear Damage Accumulation Model is that it does not properly account for the effects of the loading history. To address this flaw the non-linear probabilistic fatigue damage accumulation model by Leonetti is researched and thoroughly validated with variable amplitude fatigue data from the literature. The combination between the effective notch stress and the model from Leonetti poses significant improvements in the quality of the fatigue life predictions. The effective notch stress is used to formulate a generalised fatigue resistance curve (reducing scatter due to different geometries, hot spot types and mean stress ratios), after which the non-linear probabilistic fatigue damage accumulation model is used to work towards a generalised damage accumulation model. For the considered variable amplitude fatigue databases from literature, the Effective Notch Stress Concept (ENSC) - Non-Linear Damage Accumulation Model (NLDAM) combination proves to reduce the lifetime ratio scatter index (1:1.13, instead of 1:1.28) the most in relation to the DNV method (Hot Spot Structural Stress concept with the LDAM), allowing to reduce the implicit conservatism in the fatigue-life model.

Fatigue strength is typically a governing limit state for marine structures. Predicting an accurate fatigue lifetime is important for structures (e.g. wind turbines) that are supposed to be out at sea for decades. It is valuable for all type of structures that encounter stochastic sea loadings to optimise the design so that fatigue failure is predicted for, or material is saved in preventing over conservative estimates. This research contributes to the investigation of multiaxial fatigue concepts by getting insight in the mode-III loading & response conditions for the effective notch stress concept. The mode-III loading & response will in this research be represented by a tubular welded joint loaded under torsion. A semi-analytical formulation is developed to describe the weld notch shear stress distribution analytically. This formulation can be used as input for the effective notch stress concept. The formulation is based on three components, the notch stress, weld load carrying stress and far field stress component. Furthermore, the static force and moment equilibrium is satisfied. The weld load carrying stress component is based on a weld load carrying stress estimate. This coefficient is used because the weld geometry causes a local change in stiffness, a shift in neutral axis, meaning the weld becomes load carrying up to some extent. The distribution must be corrected for this phenomenon which is done by this estimated term. The geometry is a tubular welded joint. This specimen can be loaded with torsion which in the case of the tubular joint cause mode-III shear in the through thickness direction at the weld notch level. The weld load carrying stress estimate is based on the geometry ratios of the assessed specimens. It is individually fitted for all 6,300 geometries by comparing the results to stress distribution obtained with 2D finite element analysis. The results of the individual fitted load carrying stress estimates are used as input of a multi variable polynomial regression analysis. The regression analysis led to a polynomial function that describe the load carrying stress estimate which uses geometry ratios as input. The far field information and geometry dimensions are the input for the semi-analytical formulation to obtain the weld notch shear stress distributions analytically. Accurate results are obtained and therefore the formulation can be used as input for the effective notch stress concept. The effective notch stress concept is also based on a material characteristic length, ρ*, over which the stress distribution can be integrated to obtain the effective notch stress. This parameter is obtained using a log likelihood regression analysis and led to a value of ~1 [mm]. Although this is a good result, the confidence regarding the value is low due to low variety in the experimental data set and little data in general. The findings of this study will be used in further research regarding the 4D fatigue project and the effective notch stress concept in general at the Delft University of Technology.

Fatigue is one of the driving limit states in the design of wind turbines, as they are subject to varying loadsfrom winds, waves and gusts. One such governing area is the butt-welded connection from the shell to thering flange. To optimize the tower design and to help focus future research, more insight on the influence ofmaterial properties and geometrical features on the fatigue life of these butt welds is needed. Due to thecosts associated with testing, SGRE stated the need for a model that could assess the total fatigue life of buttwelds subject to Mode I cracking in a rather quick way. After literature study, it was proposed to use theUniGrow model.The UniGrow method is a total fatigue life model in which the material is considered to consist of elementaryblocks. Fatigue is modelled as a process of continuous crack initiation of the elementary block ahead of thecrack tip. In this model, the plastic compressive residual stress ahead of the crack tip plays an importantrole in the determination of the crack growth speed. These plastic compressive residual stresses ahead ofthe crack tip can either be determined analytically (analytical UniGrow) or by using numerical methodssuch as FEA (numerical UniGrow). The plastic compressive residual stresses ahead of the crack tip areconverted into a plastic residual SIF that is used to reduce the applied residual stress intensity factor (i.e.plasticity decreases crack growth speed). Due to the application of a number of methods such as theCreager-Paris equations, the current UniGrow implementation is solely valid for pure Mode I crack growth.Validation of the UniGrow method in the crack propagation range has been performed with results fromexperiments on CT specimens made of S355 steel. Good correspondence between the experimental resultsand predicted crack growth rates were found for all stress ratios except R = 0.25. Both Analytical andNumerical Unigrow methods have been analysed. Based upon the results of the validation it wasrecommended to use a numerical method (elastoplastic FEA) to determine the plastic residual stressesahead of the crack tip as this provides more physically accurate results. The analytical method can be usedto obtain an initial guess of the elementary block size, as it is a much faster method. Furthermore, using theMorrow method for the determination of the fatigue life of the elementary block ahead of the crack tip wasfound to provide more accurate results than the SWT damage parameter. This is due to the fact that in theelementary block ahead of the crack tip, cyclic stress relaxation occurs and, therefore, mean stress effectsneed not be accounted for. For short cracks, the fatigue life of the elementary block is usually outside theLCF range (Nf > 5*104 cycles). Here, the use of the Morrow method without considering residual stresses isnot recommended since cyclic stress relaxation does not occur due to limited plasticity.The performance of the UniGrow method as total fatigue life was studied using literature research and acomparison to another total fatigue life model: Two-Stage-Model. In the studied literature, researchers tendto use the weight function method to determine the SIF in welded geometries. Analysis comparing theweight function method to FEA results showed that the WF method generally overpredicts the SIFscompared to FEA. For a flat plate, the difference was found to be a maximum of 3.5%, whereas for the weldedgeometry, the difference was up to 12%.From the literature and the comparison of the UniGrow model to the Two-Stage-Model, it was concludedthat the UniGrow model is incapable of predicting proper fatigue crack initiation lives as it is unable tocapture the complexity of short crack growth. The model provides satisfactory results for cracks wherecrack propagation is a dominant part of the fatigue life (such as welded geometries and notched specimensin the LCF regime). It was proposed to use the UniGrow model to determine fatigue lives of notchedspecimens up to 105 cycles. It was found that this limit also depends on the SCF present in the specimen.For welded geometries, available results in literature showed good correspondence. However, the weldsused by SGRE are of better quality (lower SCF) than the ones used in UniGrow research. This means thatrelatively more of the fatigue life will be spent in fatigue crack initiation. More research is therefore neededto examine whether this affects the functioning of the UniGrow method for welds.The UniGrow method was lastly used to determine which of the parameters controlling the geometry of theweld excess (the weld flank angle, weld toe radius and weld excess height) is of greatest influence on thefatigue performance of a butt weld. From this analysis it was concluded that changing the weld excessheight, followed by the weld flank angle has the most beneficial effect on the fatigue life. The results fromthis parametric study should be used with great care: the usage of the UniGrow method combined withneglecting the residual stresses could lead to incorrect predictions of fatigue crack initiation life.Simplifications of the material and crack type could also have had an influence on the results.

Offshore wind turbines are designed to persist harsh environmental conditions, including corrosion. Pitting corrosion is one of the most dangerous forms of corrosion. In combination with a fatigue loading, a corrosion pit could result into the failure of a structure, due to a minimal weight reduction. Of the corrosion fatigue process, the transition of a corrosion pit to a fatigue crack is one of the less understood topics. In this thesis, a combined analytical/numerical model is presented that implements mechanisms of both the fatigue, and the corrosion process to determine the moment in time and location in the corrosion pit of the pit-to-crack transition. The hypothesis used to build the model, is that the pit-to-crack transition occurs at the moment that a fatigue crack initiates. Assumptions are made to be able to predict the level of stress and strain at the surface and below the surface of a corrosion pit using a FEM model. Using the stress and strain levels, damage is accumulated until the failure criterion is reached, i.e. when a fatigue crack will initiate. In this research study, elliptical pit shapes are considered, with and without a certain roughness at the surface of the corrosion pit. From the results it is found that a more sharp shaped corrosion pit is a more favourable location for fatigue crack initiation, than a more blunt shaped corrosion pit. The number of cycles to fatigue crack initiation resulting from the developed model are higher, than the number of cycles to failure found by the DNV GL B1 SN-curve for free corrosion conditions. Also, the DNV GL SN-curve is more steep, than a fitted curve through the data points resulting from the developed model. Through a sensitivity study and by considering the number of assumptions and simplifications made in this research study, it is concluded that the spread and uncertainty of the outcome of the developed model is too large to be able to draw conclusions based on the comparison between the results and the DNV GL SN-curves. More research on the input parameters of the developed model will give more certainty and a better validity to the model. It is found that the effect of surface roughness to the fatigue crack initiation life is not substantial, because it affects the stress and strain levels only up to a relatively small depth. The location of fatigue crack initiation is in the pit bottom for blunt shaped corrosion pits, and in the pit wall for sharp shaped corrosion pits. For circular shaped corrosion pits, the difference between the fatigue crack initiation life at the pit wall and the pit bottom is negligible. It is concluded that the model gives a comprehensive basis for the prediction of the pit-to-crack transition, but more (experimental) research on the input parameters will be necessary to be able to give a substantiated estimate of structural life of offshore wind turbine foundations.

The common practice of designing a ship is to look for ships with similar specifications and alter it to the client's needs. This often leads to structurally redundant and therefore overdimensioned ship designs. Hence, much improvement could be expected from ship structures where optimization algorithms help advise in the design process. In this research, the midsection of a Trailing Suction Hopper Dredger (TSHD) is optimized. A TSHD midsection generally consists of longitudinal stiffened panels and transverse web frames. The typical web frame and longitudinal stiffener layout is optimized, as a weight improvement of this section can have a large effect on the total weight of the ship since it is repeatedly reoccurring.

This research has optimized the midsection of a reference TSHD in two ways; the first step was to perform a shape optimization for the longitudinal stiffener arrangement, which was followed by a topology optimization for the transverse web frame. Both optimization objectives were to minimize mass. The order of optimization follows the hierarchy in which stresses are introduced into the structure; from the plates that make up the hull toward the stiffeners and eventually the web frames. The complete optimization was performed a total of seven times, for seven different web frame spacings ranging from 25% to 175% of the web frame spacing of the reference TSHD.

For the shape optimization, a Simulated Annealing algorithm was used. The reference ship was simplified to be able to parameterize the geometry into eleven panels with T-stiffeners. Each panel has a set of variables that describe its geometry; the plate thickness, number of stiffeners, stiffener web height, flange width and web and flange thicknesses. Although feasible results came out of the optimization, no clear parallel was found when comparing the plates of different web frame spacings. This is due to the fact that it is a high dimensional problem. Although no clear parallels were found, the results were able to cope with all the loads.

The topology optimization was performed with a modified Bi-directional Evolutionary Structural Optimization (MBESO) method. The applied modifications ensure a fast convergence for large topology optimization problems. The new method was first verified by comparing results to two benchmark cases from the original BESO method, which was followed by three examples of common topology optimization benchmarks. Once established that the modified method was capable of reproducing test cases, an aspect ratio analysis was performed to better understand the transmission of stress. After that, the full geometry of the midsection was divided into smaller basic models and the same optimization was carried out in order to help interpret underlying physics of the final results. Finally, the topology optimizations for the seven web frame spacings were performed, resulting in a new orientation of beams. The topology optimization results showed that constructing beams not in an orthogonal way and along the ship hull but rather under various angles could reduce the total mass of the web frame.

To see how the shape optimization result influenced the topology optimization, three studies were carried out where all the surrounding plates had the same thickness, except for one that would have a significant smaller thickness. This showed how the web frame supports the hull plating, but also how the web frame is dependent on the stiffness of certain panels to be able to transfer shear into them.

Finally a comparison was made between the reference ship and the optimized structure. The result was a decrease of 23\% in weight for the midsection. Due to practical production considerations this weight is likely to be higher in practice, however it is a promising start toward a more efficient ship design. The innovative combination of shape optimization combined with the MBESO procedure could help in early design stages where the main components of the construction are defined.

Offshore solar power installations can be increased in size and efficiency compared to land based installations due to the availability of space and the cooling effect of water. To increase survivability in large waves, very large floating solar platforms can be made flexible. However, a flexible structure is susceptible to wrinkling due to combinations of mooring loads, wave dynamics and the flexibility of the platform. Wrinkling is a limit state which is not commonly researched in maritime engineering, since generally structures are designed to be as stiff as possible. Wrinkling can lead to the global collapse of a very large flexible solar platform and should therefore be minimised. Very large floating platforms have an impact on the environment due to the shadow underneath. This problem can be diminished by adding holes to the platform. Furthermore, holes can be functional as manholes for maintenance of the bottom of the platform. Scientific research on the wrinkling behaviour of membranes has pointed out that wrinkling behaviour depends on the geometry of the membrane, which can for example be changed by adding holes to the membrane. The aim of this thesis is to set up a design and analysis framework for wrinkled membranes with permeability. In order to define this framework, (i) reliable computational indicators are developed; (ii) the influence of permeability on membrane wrinkling is investigated and; (iii) the framework is verified on a fictive case of an integrated stiff solar panel on a membrane. The first objective in this thesis is to find reliable computational indicators to assess the wrinkling behaviour of a membrane. Current concepts of offshore solar platforms are flexible membranes including mooring systems based on concentrated tension loads. To study the wrinkling behaviour of a (subregion) of such a flexible floating solar platform, in this study, it is modelled as a rectangular membrane subjected to uniaxial tension; following the available literature on the wrinkling problem. Numerical analysis of the wrinkling behaviour is first done by non-linear post-buckling calculations. However, it appeared that the results of this calculation are highly dependent on the initial deformation which is used. An alternative method which does not depend on user defined input was found in studying the second principal stress field: when negative second principal stress is present in the membrane, wrinkling can occur. When no negative second principal stress is present in the membrane, wrinkling will not occur. Furthermore, the distribution and the area of the negative second principal stresses region are indicators for the wrinkle distribution and amplitude. For a robust assessment of the susceptibility of a membrane to wrinkling, a study of the negative second principal stress field should thus be preferred over a post-buckling analysis. The second goal of this thesis is to research the influence of permeability on membrane wrinkling. The effect of holes on the wrinkling behaviour is researched by studying their influence on the second principal stress field. The aim is to find wrinkle free configurations and study the mechanisms which minimise wrinkling behaviour. Therefore, the size, location and shape of holes are varied systematically in membranes of different sizes. It was found that holes should be chosen so that when the membrane is strained, they deform in a way so that they bring tension in the regions of the membrane which are subjected to negative second principal stress in the non-permeable configuration. Furthermore, holes should be chosen such that the loadpaths in the membrane are not interrupted. The framework to research and design wrinkle free very large flexible solar platforms by adding permeability is verified and has proven to be effective by applying it on the configuration consisting of a stiff solarpanel mounted on a flexible membrane. In this configuration, the framework has led to holes by which the wrinkling region is localised. From the three parts of this thesis, it is concluded that a research framework for wrinkling of membranes with permeability was found in the analysis of the second principal stresses and the driving mechanisms were investigated and verified. To further develop this framework, research on the effect of stiffening the membrane and minimising wrinkling under load conditions other than tension are recommended.

The aim of this study is to conclude which parameters are influencing the most the hydrodynamic interaction between the two moored vessels in side-by-side configuration using frequency and time domain simulations. Furthermore to show what is the added value of the hydrodynamic input used in time domain investigations using 2 different integration schemes. Ultimately identify what is the impact on the mooring arrangements and what it needs to be done to ensure safe offloading operations.
During the offloading process (18 to 24 hours), the transfer equipment needs to accommodate the relative motions between the two vessels. There are several parameters which might influence the operations, which are dependent on the location (i.e. environmental conditions) and on the mooring system (i.e. vessels size, draft, mooring arrangements, etc.).
The side-by-side mooring system analyzed consists of a turret moored FLNG and various size of off-take carriers. A sensitivity analysis is done with respect to the physical parameters (i.e ship dimensions, loading conditions and separation distance) and modelling parameters (i.e parameters dependent on damping factor) in order to determine the effects on the first and second order quantities using frequency domain analysis. This represents the input for time domain numerical investigations in order to assess the relative motions and line tensions under certain environmental conditions.
It is known that the diffraction-radiation tools overestimate the results in the gap region. This is an effect of using potential flow which do not count for viscous effects. To overcome this problem and to describe in a realistic mode, multiple methods or numerical techniques has been proposed. With this regard a detailed numerical investigation has been carried out to conclude what is the impact of varying the dissipation factor (i.e between 0 and 0.4) on first and second order quantities.
Traditionally, the relative motions are determined using experimental tests which might be time-consuming. In particular for sensitivity analysis, numerical investigations are preferred in order to shape a main conclusion. Ultimately some of the results can be validated thorough experiments.
The hydrodynamic interaction revealed important aspects, especially with respect to the off-take carrier. If the carrier is smaller the impact is higher due to the presence of the FLNG. Such that the carrier rolls significantly when there are head or following seas. Furthermore decrease in heave motion of the FLNG at the resonance frequency due to the roll of the carrier has been noticed. The same phenomena occur for heave of the carrier. Thus, this represents a strong coupling between heave-roll motion of the two vessels. Another important aspect revealed is with the respect to the shielding effects under beam conditions. In general FLNG is slightly influenced by the presence of the carrier. In particular, it can be noticed only when it is in ballast condition due to the fact that the draft and thus the displacement of the carrier is considerably higher.
The sensitivity analysis points out that the modelling parameters (i.e dissipation factor) does hardly influence the response of the vessels even if it is considered or not. On the other hand drift forces are highly dependent on these parameters as a consequence of sharp changes of the wave elevations between the vessels. Such that if there is no dissipation factor to damp the wave elevation the resulted forces are extremely high compare to the cases where the dissipation factor is different than 0. This occurs only at the wave gap resonance and towards higher frequency region when diffraction effects are important. This is emphasized by the time domain analysis which prove that under the sea-states close to the gap resonance the lines and fenders tension reaches extreme magnitudes. Outside the gap resonance the relative motions and tensions are not influenced by the variation of the dissipation factor.
The moored system (i.e FLNG-LNGC or FLNG-LPGC) is governed relatively by long crested waves. Thus it is expected to have higher line loads under these sea-states. The actual mooring design shows that under squall conditions (i.e Tp of 14s) the mooring lines exceeds the safe working limit for the FLNG-LNGC, while for FLNG-LPGC exceeds the minimum breaking load. In terms of relative motions for the same environmental conditions, the criteria is not satisfied.
The proposed optimization of the mooring lines does bring reduction in the mooring line tensions, but not enough to drop below safe working limit for FLNG-LPGC configuration. On the other hand for FLNG-LNGC, the line tension is within the limits, but the relative motions still exceeds the criteria. Therefore choosing the optimum mooring configuration is a trade-off between line stiffness and location of the connection points of the mooring lines which sometimes may lead to unpractical solutions.

At Damen’s Research and Development department, continuous improvements are made to existing design practices using recent technological developments and fatigue design is currently on the anvil. High speed craft operating around the globe are subject to millions of load cycles (resulting from ocean waves) and therefore suffer from metal fatigue. As per current practice, such vessels are designed for fatigue using inhouse software with a nominal stress approach supported by static sea-state scatter data and judgement based operational profiles.
Recently, new data sources with real time sea-state data over the whole globe have come available, including GPS locations of ships. Together, this enables it to generate real time operational profiles for its ships. A total stress concept has been developed based on results from a JIP called VOMAS. This approach has shown to provide accurate fatigue lifetime estimates for arc-welded aluminium joints. Similar results are expected for steel joints as well.
The main goal of this thesis was to explore possible improvements for the fatigue design methodology. A tool called Tanaav was developed for this purpose which makes use of both remote monitoring data and the total stress concept and provides an estimate of the yearly fatigue damage and fatigue lifetime. The tool has been used to predict the fatigue lifetime for three fatigue sensitive details in 46 FCS5009 vessels. Results have been compared to corresponding predictions using current and past fatigue analysis practices. It was observed that using both remote monitoring data as well as the total stress concept provides significant improvements in the predicted fatigue life time.
Uncertainties in fatigue influence parameters affecting the predicted fatigue damage can be incorporated using probabilistic. This thesis proposes a method for this and presents two cases as a proof of concept. Work done in this thesis will be validated by Damen in future with the help of full-scale testing on an actual FCS5009 vessel during an offshore measurement campaign. After validation, this method will help in improving fatigue design practice, increasing design flexibility and in optimizing vessel weights in a responsible way.

With increasing attention to climate change,renewable energy generation has become a major topic for research anddevelopment. Wind and solar energy are generated on land, whereas wave, windand tidal energy generators are getting attention in the offshore domain. Anovel extension of onshore solar energy is the concept of offshore solar energyusing floating platforms. As little research has been performed on the conceptof offshore solar energy generations, main challenges in the field are relatedto consequences to the marine ecology, economics and production and structuraldesign of the platforms. In this thesis, a numerical model to assess wrinklingbehaviour of thin, floating sheets with application to the structural design ofoffshore solar platforms is developed.
Since wrinkling of thin sheets, in general, isinitiated by a structural instability (i.e. buckling), the developed modelconsists of an arc-length method that is capable to deal with bifurcationpoints and to switch to bifurcation branches. In this way, buckling andpost-buckling behaviour of thin sheets are modelled and wrinkled shapes can beassessed without imposing a priori definition of unbalancingimperfections or loads. The computational model is developed using a shelldiscretization with Isogeometric rotation-free Kirchhoff-Love elements, whichare higher-order elements with a B-spline or NURBS basis with global supportand global higher-order continuity of the solution. For the illustrativepurpose and future use, a similar Euler-Bernoulli beam model was developed andnumerical solvers for static, dynamic, modal and linear buckling analysis wereimplemented.
The model was verified using various benchmarkstudies for static, modal, (post-)buckling and dynamic analysis. In particular,the post-buckling solver was assessed by modelling the collapse of a sphericalroof and using buckling (post-)bucking of a cantilever strip. Both benchmarkshave shown excellent agreement with previous publications. Additionalverification was done on the approaching accuracy and prediction of bifurcationpoints. It was found that this accuracy showed the accurate prediction of thebifurcation point, although slightly underpredicted for finer meshes and higherorders. Additionally, the model wasapplied to three cases where wrinkling is involved. In these cases, sheets withlow bending stiffness were modelled such that their post-buckling shapes showmultiple half-waves and thus wrinkles. Based on the model of a floating sheetsubject to surface traction (e.g. wind or current), design parameters werevaried. From this case, it follows a decrease in foundation stiffness or anincrease in flexural rigidity (either by varying Young's modulus or thickness)implies the number of wrinkles to decrease and the wrinkling instability tooccur for lower loads. Thirdly, based on the wrinkling geometries of a quarterdisk, design consideration for VLFTSs for offshore solar energy generation weregiven. These are: (i) adding reinforcement to arrest wrinkles and to introducestructural hierarchy for structural reliability; (ii) consider the effect ofdifferent mooring system connections to the (reinforced) platform; and (iii)investigate the effect of holes and point loads on local wrinkling behaviour. Basedon the results of the study, it is concluded that the isogeometric thin shellformulation is suitable for different structural analyses and that in particularthat robustness and accuracy on a per-degree of freedom basis is observed inthe isogeometric post-buckling analysis. This adds post-buckling analysis tothe seamless integration of Computer Aided Design (CAD) and Analysis ofIsogeometric Analysis. Suggestions for further studies include severalimprovements of the current implementation (patch coupling, boundary conditionimplementation), utilization of nonlinear material models for modelling ofrubber-like materials, adaptive re-meshing using THB-splines to capture localwrinkling phenomena and Fluid-Structure Interaction computations with anonlinear structural and fluid description of VLTFSs in large waves.