A regression and beam theory based approach for fatigue assessment of containership structures including bending and torsion contributions

Container shipping has been expanding dramatically during the last decade. Due to their special structural characteristics, such as the wide breadth and large hatch openings, horizontal bending and torsion play an important role to the fatigue safety of containerships. In this study the fatigue contributions from vertical bending, horizontal bending and torsion are investigated using full-scale measurements of strain records on two containerships. Further, these contributions are compared to results from direct calculations where a nonlinear 3D panel method is used to compute wave loads in time domain. It is concluded that both bending and torsion have significant impacts on the fatigue assessment of containerships. The stresses caused by these loads could be correctly computed by full-ship finite element analysis. However, this requires large computational effort, since for fatigue assessment purposes the FE analysis needs to be carried out for all encountered sea states and operational conditions with sufficient time steps for each condition. In this paper, a new procedure is proposed to run the structure finite element analysis under only one sea condition for only a few time steps. Then, these results are used to obtain a relationship between wave loads and structural stresses through a linear regression analysis. This relation can be further used to compute stresses for arbitrary sea states and operational conditions using the computed wave loads (bending and torsion moments) as input. Based on this proposed method for structure stress analysis, an efficient procedure is formulated and found to be in very good agreement with the full-ship finite element analysis. In addition it is several orders of magnitude more time efficient for fatigue assessment of containership structures.     

Sequential sampling method using Gaussian process regression for estimating extreme structural response

A methodology for estimating extreme response statistics for marine structures, that takes both the long-term variability of the metocean environment and the short-term variability of response into account is presented. The proposed methodology uses Gaussian process regression to estimate parameters of the short-term response distribution, based on output from computationally expensive hydrodynamic simulations. We present an adaptive design strategy for sequential updating of the model, focusing on the metocean conditions that contribute the most to the long-term extreme. With this approach, only a limited number of hydrodynamic simulations are needed.The suggested approach is demonstrated on the problem of estimating the 25-year extreme vertical bending moment on a ship. We show that a relatively small number of iterations (full hydrodynamic simulations) are needed to converge toward the “exact” results obtained by running a large number of simulations covering the entire range of sea states.The results suggest that the proposed method can be used as an alternative to contour-based methods or other methods that consider a few sea states using accurate numerical simulations, with little or no added complexity or computational effort.     

Comparing different contour methods with response-based methods for extreme ship response analysis

Environmental contours are often applied in probabilistic structural reliability analysis to identify extreme environmental conditions that may give rise to extreme loads and responses. They facilitate approximate long term analysis of critical structural responses in situations where computationally heavy and time-consuming response calculations makes full long-term analysis infeasible. The environmental contour method identifies extreme environmental conditions that are expected to give rise to extreme structural response of marine structures. The extreme responses can then be estimated by performing response calculations for environmental conditions along the contours.Response-based analysis is an alternative, where extreme value analysis is performed on the actual response rather than on the environmental conditions. For complex structures, this is often not practical due to computationally heavy response calculations. However, by establishing statistical emulators of the response, using machine learning techniques, one may obtain long time-series of the structural response and use this to estimate extreme responses.In this paper, various contour methods will be compared to response-based estimation of extreme vertical bending moment for a tanker. A response emulator based on Gaussian processes regression with adaptive sampling has been established based on response calculations from a hydrodynamic model. Long time-series of sea-state parameters such as significant wave height and wave period are used to construct N-year environmental contours and the extreme N-year response is estimated from numerical calculations for identified sea states. At the same time, the response emulator is applied on the time series to provide long time-series of structural response, in this case vertical bending moment of a tanker. Extreme value analysis is then performed directly on the responses to estimate the N-year extreme response. The results from either method will then be compared, and it is possible to evaluate the accuracy of the environmental contour method in estimating the response. Moreover, different contour methods will be compared.     

Numerical and experimental investigations into the application of response conditioned waves for long-term nonlinear analyses

The coefficient of contribution method, in which the extreme response is determined by considering only the few most important sea states, is an efficient way to do nonlinear long-term load analyses. To furthermore efficiently find the nonlinear short-term probability distributions of the vessel responses in these sea states, response conditioned wave methods can be used. Several researchers have studied the accuracy of response conditioned wave methods for this purpose. However, further investigations are necessary before these can become established tools. In this paper we investigate the accuracy by comparing the short-term probability distributions obtained from random irregular waves with those from response conditioned waves. We furthermore show how response conditioned wave methods can be fitted into a long-term response analysis. The numerical and experimental investigations were performed using a container vessel with a length between perpendiculars of 281 m. Numerical simulations were done with a nonlinear hydroelastic time domain code. Experiments were carried out with a flexible model of the vessel in the towing tank at the Marine Technology Centre in Trondheim. The focus was on the probability distributions of the midship vertical hogging bending moments in the sea states contributing most to the hogging moments with a mean return period of 20 years and 10 000 years. We found that the response conditioned wave methods can very efficiently be used to accurately determine the nonlinear short-term probability distributions for rigid hulls, but either accuracy or efficiency is to a large effect lost for flexible hulls, when slamming induced whipping responses are accounted for.     

Long-term correlation structure of wave loads using simulation

This paper proposes a new method for combining the lifetime wave-induced sectional forces and moments that are acting on the ship structure. The method is based on load simulation and can be used to determine the exceedance probabilities of any linear and nonlinear long-term load combination. It can also be used to determine the long-term correlation structure between these loads in the form of the long-term correlation coefficients. They are essential part of the load combination procedures in design and strength evaluations as well as in the fatigue and reliability analysis of ship structures.The simulation method treats the non-stationary wave elevations during the ship’s entire life (long-term) as a sequence of different stationary Gaussian stochastic processes. It uses the rejection sampling technique for the sea state generation, depending on the ship’s current position and the season. Ship’s operational profile is then determined conditional on the current sea state and the ship’s position along its route. The sampling technique significantly reduces the number of sea state-operational profile combinations required for achieving the convergence of the long-term statistical properties of the loads. This technique can even be used in combination with the existing long-term methods in order to reduce the number of required weightings of the short-term CDFs. The simulation method does, however, rely on the assumption that the ship is a linear system, but no assumptions are needed regarding the short-term CDF of the load peaks.The load time series are simulated from the load spectra in each sea state, taking into account the effects of loading condition, heading, speed, seasonality, voluntary as well as involuntary speed reduction in severe sea states and the short-crested nature of the ocean waves. During the simulation procedure, special care has been given to maintaining the correct phase relation between all the loads. Therefore, time series of various load combinations, including the nonlinear ones, can be obtained and their correlation structure examined. The simulation time can be significantly reduced (to the order of minutes rather than hours and days) by introducing the seasonal variations of the ocean waves into a single voyage simulation. The estimate of the long-term correlation coefficient, obtained by simulating only a single voyage with the correct representation of seasonality, approaches the true correlation coefficient in probability. This method can be applied to any ship and any route, or multiple routes as long as the percentage of the ship’s total lifetime spent in each of them is known.A study has been conducted to investigate the effects of ship type, route and the longitudinal position of the loads on the values of the correlation coefficients between six different sectional loads; vertical, horizontal and twisting moments, as well as shear, horizontal and axial forces. Three ocean-going ship types have been considered; bulk carrier, containership and tanker, all navigating on one of the three busy ship routes; North America-Europe, Asia-North America and Asia-Europe. Finally, the correlation coefficient estimates have been calculated for five different positions along the ship’s length to investigate the longitudinal variation of the correlation coefficient.     

Experimental study of slam-induced stresses in a containership

Experiments for the ship motions and sea loads were carried out on a segmented model of a container ship in ballast condition. Comparisons between the measurements and the theoretical results were carried out for the vertical motions and bending moments. For the evaluation of the primary stresses it is assumed that the total vertical bending moment induced by waves is divided into one component obtained by the linear theory and another one is due to the slamming loads. Several formulations for the determination of the slamming loads are compared with experimental results. The vibratory response of the model is calculated by modelling the hull with rotational springs and rigid links. Linear finite elements with a consistent mass formulation are adopted for the structural model and the response is obtained by modal superimposing and direct integration methods.     

Design safety margin of a 10,000 TEU container ship through ultimate hull girder load combination analysis

Assessment of the ultimate longitudinal strength of hull girders under combined waveloads can be of particular importance especially for ships with large deck openings and low torsional rigidity. In such cases the horizontal and torsional moments may approach or exceed the vertical bending moment when a vessel progresses in oblique seas. This paper presents a direct calculation methodology for the evaluation of the ultimate strength of a 10,000 TEU container ship by considering the combined effects of structural non-linearities and steady state wave induced dynamic loads on a mid ship section cargo hold. The strength is evaluated deterministically using non-linear nite element analysis. The design extreme values of principal global wave-induced load components and their combinations in irregular seaways are predicted using a cross-spectral method together with short-term and long-term statistical formulations. Consequently, the margin of safety between the ultimate capacity and the maximum expected moment is established.     

Estimation of nonlinear long-term extremes of hull girder loads in ships

This paper deals with a estimation of long-term extreme value for a given return period, say D=100 yr. In principle, this response is obtained by combining the response in all the sea states. The long-term response for a linear system can be effectively obtained by determining the response for each sea state, specified by the significant wave height, H_s, and the peak period, T_p, in the frequency domain. However, if the response is nonlinear, time domain simulation and a long time series would be required, to limit statistical uncertainty. Therefore, the long-term analysis becomes rather complicated and time consuming. For the long-term analysis, it is crucial to introduce ways to improve the efficiency in the calculation. In this work, it is shown that, the long-term extremes can be estimated by considering only a few short-term sea states. A long-term analysis based on identifying the most important sea state, defined by the coefficient of contribution, using linear analysis is applied. An iteration procedure is thereafter used to find the nonlinear long-term extreme values. It is concluded that only a limited number of sea states is necessary to get an acceptable estimate of the nonlinear D-year response as long as the most important sea states are included, i.e., the sea state with the maximum coefficient of contribution.     

Practical estimation methods of the design loads for primary structural members of tankers

Various design loads used in the strength evaluation of ship structures have been introduced currently by classification societies. As most of these design loads have been determined as the standard loads for the sake of convenience, the relationships between the design loads and the sea states actually encountered by ships seem to be weak. Accordingly, it may be difficult to refer and utilize them as the fundamental design concepts for ship designers or the operational guidelines for ship operators. To overcome these difficulties, the authors have developed practical estimation methods of the design loads having transparent and consistent backgrounds to the actual loads acting on primary structural members of tankers. In this paper, the design sea states that closely resemble the actual sea states which are considered as the most severe for hull structures are firstly proposed. Secondly, the practical estimation methods of the design sea states are proposed by parametric studies using the results of series calculation of representative tankers. Thirdly, the practical estimation methods of design regular waves resulting in the same level of stresses with that induced in irregular waves under the design sea states are proposed. Finally, the practical estimation methods of the design loads such as ship motions, accelerations, hull girder bending moments and hydrodynamic pressures that are induced under design regular waves are proposed.     

Modified environmental contour method for predicting long-term extreme responses of bottom-fixed offshore wind turbines

Predicting extreme responses is very important in designing a bottom-fixed offshore wind turbines. The commonly used method that account for the variability of the response and the environmental conditions is the full long-term analysis (FLTA), which is accurate but time consuming. It is a direct integration of all the probability distribution of short-term extremes and the environmental conditions. Since the long-term extreme responses are usually governed by very few important environmental conditions, the long-term analysis can be greatly simplified if such conditions are identified. For offshore structures, one simplified method is the environmental contour method (ECM), which uses the short-term extreme probability distribution of important environmental conditions selected on the contour surface with the relevant return periods. However, because of the inherent difference of offshore wind turbines and ordinary offshore structures, especially their non-monotonic behavior of the responses under wind loads, ECM cannot be directly applied because the environmental condition it selects is not close to the actual most important one.The paper presents a modified environmental contour method (MECM) for bottom-fixed offshore wind turbine applications. It can identify the most important environmental condition that governs the long-term extreme. The method is tested on the NREL 5 MW wind turbine supported by a simplified jacket-type support structure. Compared to the results of FLTA, MECM yields accurate results and is shown to be an efficient and reliable method for the prediction of the extreme responses of bottom-fixed offshore wind turbines.     

On board measurement of stresses and deflections of a Post-Panamax containership and its feedback to rational design

One of the most important points in structural design of containerships is the strength of hatch corners. Formerly, hatch corners used to be assessed by combining the component induced by hull girder vertical bending and the component induced by hull girder torsion. In the design of new generation containerships without deck girders, the effect of cross deck fore-aft deflection has also become prominent.Another point is the impact of structural displacement on the deck fittings. About new generation ships, large fore-aft deflection of cross decks raised the new problem of interference of hatch covers, lashing bridges and other deck fittings.To cope with such problems, comprehensive analysis has been carried out during the design stage of a Post-Panamax containership. In parallel with this analysis, on-board measurement had been conducted for 3 years after delivery, in order to confirm wide varieties of structural reaction of a large container ship in seaways. Procedure to derive components of stress and deformations from selected measurement points was developed, and actual values were calculated based on actual measurement.From long-term prediction of each component, it was found that design assumption was in general appropriate. However, regarding the fore-aft deflection of cross deck strip, actual stack load is generally much smaller than the design value, and the resulting predicted extreme value was much smaller than design assumption. This factor should be taken into account in the design stage.Regarding the correlation between hull girder vertical bending and fore-aft deflection of cross deck strip, design assumption of full combination is too conservative. From the measurement, no explicit correlation was observed. Regarding the correlation between hull girder vertical bending and wave induced torsion, design assumption of no correlation was appropriate. From these results, new formulae to combine these three deflection modes were proposed.Whipping was observed in the measured data, indicating that more careful attention should be paid to avoid large stress concentration in deck area to enhance fatigue strength.     

考虑弹性地基的复合材料曲梁径向应力的研究

运用弹性力学理论和经典层合板理论,推导了有弹性地基作用情况下,复合材料曲梁弯曲时径向应力的计算公式,该公式还可以得到曲梁纯弯曲情况下的解析解。利用所推导的公式,讨论了弹性地基对复合材料曲梁径向应力以及径向最大应力位置的影响。     

Experimental and numerical study of containership responses in severe head seas

An accurate determination of the global load effects in a ship is vital for the design of the vessel. This paper addresses an experimental and numerical study of containership responses in severe head seas. Experimental results were obtained using a flexible model of a containership of newer design. The experiments showed that, taking hull flexibility into account, the fourth and sixth harmonic of the vertical bending moments had a maximum value of between 25% and 50% of the first harmonic. We also demonstrated that hull flexibility can increase the vertical bending moment by up to 35% in sea states relevant for design. Comparisons of moments found experimentally with results from a nonlinear hydroelastic strip theory method showed that the effect of nonlinearities on the rigid body moments was slightly over-predicted in the aft body. The method also tends to over-predict the increase of the bending moments due to hull flexibility. In general however, the numerical results compared reasonably well with the experimental ones.     

Ultimate load analysis of a 10 MW offshore monopile wind turbine incorporating fully nonlinear irregular wave kinematics

Loads from storm waves can in some cases be dimensioning for offshore wind turbine substructures. Accurate determination of nonlinear wave loads is therefore important for a safe, yet economic design. In this paper, the fully nonlinear waves, realized by a fully nonlinear potential wave solver OceanWave3D, are incorporated into coupled aero-servo-hydro-elastic simulations for a reduced set of wave-sensitive design load cases, in comparison with the widely used linear and constrained waves. The coupled aero-elastic simulations are performed for the DTU 10 MW reference wind turbine on a large monopile at 33 m water depth using the aero-elastic code HAWC2. Effect of the wave nonlinearity is investigated in terms of the ultimate sectional moments at tower bottom and monopile mudline. Higher ultimate moments, 5% at tower bottom and 13% at monopile mudline as maximum, are predicated when the nonlinear waves are used. It could be explained by the fact that the extreme nonlinear waves, that are close to the breaking limit, can induce resonant ringing-type responses, and hereby dominate the ultimate load responses. However, the constrained wave approach shows marginal difference compared to the standard linear wave approach. It can be concluded at least for the present configuration that the industry standard approaches (linear and constrained wave approach) underestimate the ultimate load responses on offshore wind turbines in severe sea states.     

Vertical and horizontal bending moments on the hydroelastic response of a large-scale segmented model in a seaway

Wave-induced vertical bending moment (VBM) and horizontal bending moment (HBM) on a large-scale segmented model with a box-type backbone beam in short-crested irregular seas are systematically analyzed using sea trial measurement data. New insights into the relationship between nonlinear VBM and HBM of the ship sailing in short-crested sea waves are explored and presented. The results indicate that the HBM significantly contributes to the total sectional loads when the ship is sailing in a seaway and the HBM has a strong correlation with VBM in both magnitude and tendency. Therefore, design loads of HBM and the corresponding lateral structural strength issues should also be concerned in addition to VBM at the ship design phase.     

Evaluating transfer velocity-wind speed relationship using a long-term series of direct eddy correlation CO2 flux measurements

Long-term observations of the marine atmospheric boundary layer were performed by an eddy correlation system, which was set-up on a platform in the Baltic Sea. In this experiment the three-dimensional wind vector and the turbulent fluxes of momentum, sensible and latent heat and CO₂ were measured for one and a half years. Simultaneously the CO₂ partial pressure p_CO2 in surface water was measured by a submersible autonomous moored instrument for CO₂ at the platform in 7-m depth. The high-resolution eddy correlation measurements of the atmospheric CO₂ flux F_CO2, together with the measurements of the CO₂ partial pressure differences between air and sea Δp_CO2 led to a long-term data set which provided the possibility to investigate the parameterization of the CO₂ transfer velocity k as a function of 10-m wind speed u in a statistical manner. From half-hour mean CO₂ fluxes and CO₂ partial pressure differences, k was calculated using k = F_CO2 / (K₀Δp_CO2), with K₀ the CO₂ solubility. The half-hour mean data points, used for the determination of the k–u parameterization, show large scatter. However, assuming a linear, quadratic dependency the analysis yields: k₆₆₀ = 0.365u² + 0.46u (k at 20 °C and salinity 35 psu) with a correlation coefficient of r² = 0.81. The large scatter indicates that the kinetics of the air–sea CO₂ transfer velocity is not only a function of the wind speed alone, but might also be controlled by other environmental parameters and mechanisms, such as sea state and surface coverage with surfactants.     

Field experiments on laterally loaded piles for an offshore wind farm

Pile foundations are widely used to support offshore wind turbines due to their cost effectiveness and rapid constructions. Offshore piles must be designed with enough capacity to withstand overturning moments caused by wind turbines and other environmental factors such as wave excitations and extreme winds. In this study, a full-scale field experimental test is undertaken to determine the pile behaviour under various lateral loading conditions. A distributed fiber optic sensing technology is used to measure strains along two instrumented piles. The bending moments and lateral deflections are calculated from distributed fiber optic sensors, and then analysed with the various p-y methods. Field measurements indicated that for two offshore piles ZK01 and ZK28 with diameter of 2 m and length of 71.5 m and 77.5 m, the maximum lateral movements under a given lateral load of 800 kN were 369.1 mm and 351.7 mm, respectively. The maximum bending moment occurred at 6.5 m and 5.5 m below seabed level with the corresponding depth of 12.15D and 11.95D for pile ZK01 and ZK28, respectively. The position of “zero crossing” of soil resistance for two instrumented piles is almost the same, even though the piles have different lengths. The lateral deflections and bending moments of the two instrumented piles are predicted by the API and hyperbolic method, which indicates that the hyperbolic method yields larger prediction errors than the API method. A modified p-y approach is then proposed for more reliable predictions when compared with field measurements.     

Extensive study on the design loads used for strength assessment of tanker and bulk carrier structures

ClassNK has undertaken wide-ranging basic research covering many aspects related to the safety of ship structures, including design loads, structural analysis, strength assessment of buckling, collapse, and fatigue, and rational corrosion margins to develop new design standards which have transparency and consistency. Among the wide-ranging basic research, this article summarizes the results of extensive work on the design loads used for strength assessments of tanker and bulk carrier structures. The main aim of the research was to develop practical estimation methods of design loads with rational technical backgrounds relating to the actual loads acting on the primary structural members of tankers and bulk carriers. During this study, we proposed the following methodology. Design sea states that closely resemble the actual sea states which are considered to be the most severe for hull structures. Find practical estimation methods for the design sea states by parametric studies using the results of series calculations on representative tankers and bulk carriers. Find practical estimation methods for design regular waves which will result in the same level of stresses as those induced in irregular waves under the design sea states. We also briefly introduced some practical estimation methods for the design loads, such as ship motions, accelerations, hull-girder bending moments, and hydrodynamic pressures that are induced under design regular waves. The findings in this study have been summarized and implemented in the new design standards for tanker and bulk carrier structures.Updated from the Japanese original which won the 2003 SNAJ prize (J Soc Nav Archit Jpn 2002; 191:195–207; 2002; 191:208–220; and 2002; 192:723–733)