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.

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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.

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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.

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This article presents an approach to identify naturally developed damage in low-speed bearings using waveform-similarity-based clustering of acoustic emissions (AEs) under fatigue loading. The approach is motivated by the notation that each recorded AE signal from a particular damage is defined by the convolution of the source signal, transfer function of the propagation path and transfer function of the utilised sensor, and may thusly be used to identify consistent AE sources, for example due to crack growth. A sequential clustering procedure is proposed, that is based on waveform cross-correlation. The supporting theoretical background of waveform similarity, rooted in an analytical formulation of waveform propagation and transmission in complex structures, is discussed. The presented methodology is evaluated through application to AE data obtained in a low-speed run-to-failure experiment utilising a densely instrumented purpose-built linear bearing segment. The implemented sensor system comprises arrays of three types of AE transducers, that is relatively low - (40–100 kHz), mid - (95–180 kHz) and high-frequency (180–580 kHz), that are situated on both the raceways and supporting substructures of either side of the bearing. Over the course of 225,000 cycles of extension and retraction, wear has been developed. A total of about ∼2,300,000 AE signals have been recorded. Analysis of the recorded data suggests the rate of degradation increases from around 70,000 cycles onwards. Highly consistent structures of clusters indicative of a localised defect in the raceway have been identified from around 170,000 cycles onwards. These clusters are characterised by hit-rates in the range of 1–2 hits per cycle and an average similarity of 93%, they comprise about half the AE activity for the periods they have been identified for. These results highlight that the proposed cross-correlation-based clustering of AE waveforms and identification of multi-channel formations in said clusters compose a suitable methodology for assessment of damage in low-speed roller bearings.@en

In the condition monitoring of bearings using acoustic emission (AE), the restriction to solely instrument one of the two rings is generally considered a limitation for detecting signals originating from defects on the opposing non-instrumented ring or its interface with the rollers due to the signal energy loss. This paper presents an approach to evaluate transmission in low-speed roller bearings for application in passive ultrasound monitoring. An analytical framework to describe the propagation and transmission of ultrasonic waves through the geometry and interfaces of a bearing is presented. This framework has been used to evaluate the transmission of simulated damage signals in an experiment with a static bearing. The results suggest that low- to mid-frequency signals (<200 kHz), when passing through the rollers and their interfaces from one raceway to the other, can retain enough energy to be potentially detected. An average transmission loss in the range of 10–15 dB per interface was experimentally observed. @en

In order to obtain valuable information from an Hull Structure Monitoring system, a large data set and consistent analysis of that data is required. The monitoring requires significant efforts over multiple years and as a result, uncertainties obtained from in-service measurements are rarely published. Instead, researchers have to rely on numerical simulations and conjecture to quantify certain parameters. In this article, two years of continuous monitoring data is used to quantify several sources of uncertainties of the hull structure of an FPSO. These sources include uncertainty related to the future extrapolation of loads and statistical uncertainty of the long-term sea states which is quantified using a Bayesian re-sampling scheme. Next, the uncertainty introduced through the use of analytical load distribution models is addressed. Finally, the uncertainty in the calculation method is quantified. These data are then used in a case study for the particular FPSO which has been monitored to demonstrate their practical application using a simple reliability model. Multiple stochastic models for the long-term description of loads are examined. Besides the traditional Weibull model, the less frequently used Pareto, Lognormal and Gumbel model were tested and compared against an uncertainty modal based on a spectral fatigue assessment. The Pareto and Weibull models are considered appropriate models and were compared against design stage analyses. Good design procedures adopt conservative parameters to describe the uncertainties. In the presented example, this was found to be true and therefore the inclusion of measurement data in Risk Based Inspection analysis for the presented case results in prolongation of the inspection interval.

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Risk-based design of marine pressure hulls require computationally efficient and precise models predicting collapse pressures of ring stiffened cylindrical shells as a function of realistic geometrical imperfections. However, the empirical interframe collapse models commonly implemented in design codes do not explicitly depend on imperfections, and the existing analytical models are only valid for axisymmetrically imperfect shells. The goal is to derive an analytical model that explicitly depends on axisymmetric and asymmetric imperfections. In order to derive such a model, first the stress development is investigated using the nonlinear Finite Element Analysis (FEA) of twelve marine pressure hulls having axisymmetric imperfections only. The knowledge gained from these investigations is used to qualify three collapse models. One of them, the integral model introduced by the authors, is accurate and sufficiently precise. It uses a new definition of interframe collapse, which also allows for asymmetric imperfections.

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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.

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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.

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Modelling nonlinear phenomena in thin rubber shells calls for stretch-based material models, such as the Ogden model which conveniently utilizes eigenvalues of the deformation tensor. Derivation and implementation of such models have been already made in Finite Element Methods. This is, however, still lacking in shell formulations based on Isogeometric Analysis, where higher-order continuity of the spline basis is employed for improved accuracy. This paper fills this gap by presenting formulations of stretch-based material models for isogeometric Kirchhoff–Love shells. We derive general formulations based on explicit treatment in terms of derivatives of the strain energy density functions with respect to principal stretches for (in)compressible material models where determination of eigenvalues as well as the spectral basis transformations is required. Using several numerical benchmarks, we verify our formulations on invariant-based Neo-Hookean and Mooney–Rivlin models and with a stretch-based Ogden model. In addition, the model is applied to simulate collapsing behaviour of a truncated cone and it is used to simulate tension wrinkling of a thin sheet. @en

Wrinkling or pattern formation of thin (floating) membranes is a phenomenon governed by buckling instabilities of the membrane. For (post-) buckling analysis, arc-length or continuation methods are often used with a priori applied perturbations in order to avoid passing bifurcation points when traversing the equilibrium paths. The shape and magnitude of the perturbations, however, should not affect the post-buckling response and hence should be chosen with care. In this paper, our primary focus is to develop a robust arc-length method that is able to traverse equilibrium paths and post-bifurcation branches without the need for a priori applied perturbations. We do this by combining existing methods for continuation, solution methods for complex roots in the constraint equation, as well as methods for bifurcation point indication and branch switching. The method has been benchmarked on the post-buckling behaviour of a column, using geometrically non-linear isogeometric Kirchhoff-Love shell element formulations. Excellent results have been obtained in comparison to the reference results, from both bifurcation point and equilibrium path perspective.@en

Fatigue damage of offshore floating structures is a long-term cumulative process, which is mainly attributed to ocean waves. The natural variability and human-induced climate change may affect the wave climate and consequently result in the change of fatigue damage. This paper aims to investigate the effect of climate change on the fatigue damage of offshore floating structures operating in three offshore oil fields of the North Sea (Alma/Galia, Pierce, and Rosebank oil fields, located in 56.2° N/2.8° E, 58° N/1.45° E, and 61° N/4° W latitude/longitude). Then it can detect whether human-induced climate change has a considerable impact on fatigue damage. Therefore, firstly the natural variability of wave height and fatigue damage was investigated through 30-year control simulations by coupling wave models to climate models, ignoring the effect of human activities. After that the sea states and annual fatigue damages were projected in three decadal periods (2011–2020, 2051–2060, and 2091–2100) based on widely recognized climate scenarios including the greenhouse gas emission trajectories. The effect of human-induced climate change has been detected, and it has been found that the higher the emission, the less the fatigue damage in considered floating structures in the North Sea. In addition, although wave height is the dominant wave characteristic in fatigue calculations, the change of other wave characteristics should also be considered to improve the quality of fatigue designs.

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The metal magnetic memory method is a novel technique for monitoring fatigue cracks in steel structures, which can reduce operational expenses and increase safety by minimizing inspections. The crack geometry can be identified by measuring the self magnetic flux leakage, which is induced by the Earth’s magnetic field and the permanent magnetization. The finite element method can be used to simulate the induced magnetic field around cracks to help interpret the self magnetic flux leakage measurements, but it is unclear what material properties to use. This study aims to determine the magnetic permeability of structural steel for accurate simulation of the induced magnetic field around cracks by the finite element method. The induced magnetic field was extracted from measurements above two square steel plates, one without defect and one with a straight slit, and compared with finite element results in function of the relative permeability. For both plates, a uniform relative permeability could be found for which experimental and numerical results were in good agreement. For the plate without defect and a relative permeability of 350, errors were within 20% and were concentrated around the plate’s edges. For the plate with the slit and a relative permeability of 225, errors were within 5%.@en

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.

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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.

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Wireless crack monitoring on ships and offshore structures based on Self Magnetic Flux Leakage (SMFL) measurements is a promising method to guarantee the structural integrity in a more effective way, leading to reduced operational costs and increased safety. For accurate crack sizing, the SMFL measurements must be interpreted correctly, also during cyclic loading. Not much research has been done that focus on the effect of high cyclic stresses on the magnetization of ferromagnetic steels in weak magnetic fields. The aim of the research presented in this paper is to investigate the effect of stress-induced magnetization on the SMFL in the stress concentration zone of a structural steel plate, and its implications for crack monitoring by the SMFL method. By means of an experiment, measured stress magnetization curves were obtained in a grid of points around an elliptical hole in a steel plate that was cyclically loaded up to the yield stress. The results show that the stress-induced magnetization causes a maximum variation of the measured signal of 25 μT, which is fully reversible. It is concluded that, depending on the application, this stress-induced variation may need to be taken into account for the interpretation of the measured signals by a crack monitoring system using the SMFL method.@en

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.

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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.

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Marine structures, continuously subjected to action of waves, suffer from fatigue cracks developing predominantly in welded connections. For this reason, marine structures have to be regularly inspected in order to confirm sufficient level of their structural integrity. A crack monitoring system can help keeping this level with less frequent inspections, because detected fatigue cracks need time to reach unacceptable sizes. This study is part of a research and development program aiming at developing a wireless crack monitoring system which is based on the Self Magnetic Flux Leakage (SMFL) phenomenon. Although this phenomenon is very attractive, still many knowledge gaps exist that prevent a successful application to marine structures. The goal of this research was to investigate different sources of magnetization and their effects on slit induced SMFL in a square steel plate. A slit in the plate was representing a through thickness fatigue crack in a marine structure. The combined effects were measured experimentally, whereas effects induced by the Earth’s magnetic field were determined numerically using steel magnetic properties defined in a separate experiment. The difference between the experimental and numerical SMFL was caused by permanent magnetization. The numerical simulation shows that the SMFL induced by the Earth’s magnetic field is constant over the slit length. The SMFL induced by the permanent magnetization is one order of magnitude higher and varies linearly over the slit length for the investigated plate. The study concludes that it is feasible to develop a monitoring system for detected cracks in marine structures based on the SMFL.@en

In the present study, feasibility of implementing an acoustic emission (AE) system for condition monitoring of highly-loaded and low-speed roller bearings has been quantitatively investigated. To evaluate the transmission of damage-induced AE signals inside the bearing and their detectability on the accessible surfaces, stress wave propagation through the complex geometry and interfaces of a representative offshore bearing has been studied experimentally. The results suggest that in the investigated frequency ranges, the AE signals that pass through the bearing rollers and their interface with the inner and outer raceways can potentially remain of sufficient strength to be detected for condition assessment of these bearings.@en