Wave-induced Vertical Bending Moment Research Articles

Combination of HOSM and FORM for extreme wave-induced response prediction of a ship in nonlinear waves

This paper proposes a method for predicting the extreme values of linear and nonlinear wave-induced responses of a ship in nonlinear waves. The method is based on a combination of the Higher Order Spectrum Method (HOSM) and First Order Reliability Method (FORM), allowing the most-probable wave episodes for extreme values of interest to be efficiently calculated. The proposed HOSM + FORM approach is first applied to extreme wave crest prediction, and the results are validated through comparisons against Monte Carlo simulations. The HOSM + FORM approach is then used to predict the extreme wave-induced vertical bending moment (VBM) distribution in a container ship. The wave-induced VBM is assumed to be linear with respect to the incident wave profile by leveraging pre-computed VBM transfer functions. Finally, the extreme value distribution of nonlinear roll motion in beam seas is investigated. The proposed HOSM + FORM approach is shown to predict the extreme linear and nonlinear wave-induced responses efficiently and accurately. The effect of wave nonlinearity is found to be significant under circumstances where the VBM is sensitive to high-frequency waves or large roll angles are excited by the wave crests.

Study on simplified estimation formula for long-term predictions of ship response in waves – Application to vertical bending moment

This paper proposed a simplified formula for the long-term maximum wave-induced vertical bending moment (VBM) of ships. First, as a general theory independent of the type of ship response, the relationship between the long-term response and the peak value of the response amplitude operation (RAO) was discussed and its governing factors were clarified, and the methodology of the simplified formula development approach was presented. In particular, if the RAO has two properties, “band parameter-invariance” and “peak value-wavelength correspondence,” the long-term response can be expressed by only the peak value of RAO. Based on this approach, a simplified formula for the long-term maximum VBM was presented. First, focusing on the characteristics of the VBM-RAO in the case of zero speed, a formula with zero speed was derived, and based on this, a formula with a speed of 5 knots was derived. These formulae were validated by comparison with the results of a numerical analysis using 154 actual merchant ship models. The proposed method for developing the simplified formula is physically clear and is valid for all types of ships and responses.

A New Method for Predicting Site-Specific Wave-Induced Hull Girder Loads Acting on Ship-Shaped Offshore Installations in Benign Conditions

The aim of this study is to establish an innovative method for predicting wave-induced hull girder loads acting on ship-shaped offshore installations. Unlike in trading ships, the determination of hull girder loads of ship-shaped offshore installations must consider site-specific environmental conditions. However, the accurate determination of wave-induced loads is not straightforward owing to uncertainties in the ocean environmental conditions and location-dependent complexities, among other factors. This study proposes a probabilistic approach to determine the site-specific design values of wave-induced loads acting on ship-shaped offshore installations that also accounts for the effects of mooring system type. Six target regions – the North Sea, Gulf of Mexico, western coast of Africa, the eastern coast of South America, southeastern coast of Asia and northwestern coast of Australia – were studied to compare the results corresponding to various sea states. A set of wave scenarios representing all possible wave events for each target region were selected using the Latin hypercube sampling technique. To demonstrate this method, the design values of the wave-induced vertical bending moments were determined for a very large crude oil carrier (VLCC)-class structure with a hypothetical floating, production, storage and offloading (FPSO) unit. The effects of the mooring system type (e.g., single-point mooring versus spread mooring) on the wave-induced hull girder loads of the ship-shaped offshore installations were also evaluated. The validation of the developed method was made by comparison with existing results in the literature, its novelty is associated with a new methodology that can accurately determine wave-induced hull girder loads of ship-shaped offshore installations taking into account the effects of site-specific ocean environmental conditions and mooring system type, and its main contribution to the industry is to provide core technology for the safe and economical design of ship-shaped offshore hull structures.

Experimental analysis of wave-induced vertical bending moment in steep regular waves

Recent studies have benchmarked the prediction of the wave vertical bending moment (VBM) of ships in waves and found significant scatter among the numerical codes. A long series of tests with segmented hulls have been reported in the literature over the past 70 years to assess the vertical bending moment. However, alongside the improvement in numerical tools and the modeling of ships’ internal loads, the scientific community still requires accurate experimental data measured in steep waves (ratio of wave height H to wavelength λ, H/λ= 0.1) where the ship behavior and loads are modified by non-linearities. Thus, in order to validate simulation codes, and to establish criteria and requirements that make ships safer to sail in severe sea conditions, some experiments were carried out in the 50 m × 30 m × 5 m hydrodynamic and ocean engineering tank of the Ecole Centrale Nantes. A 1/65th scaled model of a 6750-TEU containership was used. The ship was moored and several combinations of wavelength and wave height were tested. The present experiments were performed on a segmented hull with a 6DOF load sensor located close to amidship, where some measurements were available from previous studies. The design, which did not use strain gauges, was done specifically to increase the first structural mode frequency and the stiffness of the model in order to reduce and make it possible to filter out hydro-elastic effects. The model motion was measured through a Qualisys IR tracking system and accelerometers were located on the fore and aft of the beam. Also, each of the 9 segments is equipped with a 3DOF dynamometer to measure the hydrodynamic loads on the hull. A mathematical description of the relations between the hydrodynamic forces, the load measurements and the internal forces is given in the paper. This makes it possible to retrieve the hydrodynamic loads on the segments and then to compute the shear force and bending moment discretized at each intersegment all over the ship length. Particular care was paid to the reproducibility and repeatability of the tests. The experimental setup and the measured data are presented in the paper. Hydrodynamic loads are reconstructed and the obtained VBM is compared with the 6DOF sensor measurement. The non-linear effects of increasing the wave steepness on motions and bending moment are discussed.

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.

Neural network model for estimation of hull bending moment and shear force of ships in waves

A time-domain technique based on Artificial Neural Networks (ANN's) for estimating wave-induced ship hull bending moment and shear force from ship motions, which are calculated by a theoretical method under regular waves, is presented. The objective of the use of this methodology is to obtain an expedite hull monitoring tool to be used on board the ships. The ANNs are used to model the time-domain relationship between the wave-induced vertical bending moment and shear force and the ship motions: sway acceleration, pitch angle, roll angle, vertical acceleration, heading angle and yaw rate. A mathematical model using a strip theory provides the ship motions data in the frequency domain allowing the validation of the method through simulations.

A new method for determining the design values of wave-induced hull girder loads acting on ships

ABSTRACTThis paper presents a new methodology to determine the design values of wave-induced hull girder loads acting on ships. The method is based on probabilistic approaches associated with selected scenarios that represent possible events in terms of the ship’s functionality, operation and environment. As illustrative examples, the method is used to determine the design values of wave-induced vertical bending moments for as-built ships (a VLCC class tanker, a 9,300 TEU containership and a 22,000 TEU containership) and a hypothetical 25,000 TEU containership. The probabilities of exceedance for wave loads acting on ships are discussed in association with the design load values determined from classification society rules. It is found that both the class rule method and the present method are in good agreement for the considered example ships. The present methodology can of course be applied to determine other components of design wave loads such as horizontal bending moments and torsional moments.

Panel reliability assessment for FPSOs

An assessment method is developed for the panel reliability of ship-shaped Floating, Production, Storage and Offloading units (FPSO). Not only axial compressive loads but also internal and external lateral pressures are taken into account in the reliability assessment. Beam-column buckling and flexural-torsional buckling are regarded as two primary failure modes of stiffened panels. Variability of corrosion wastage and material properties are accounted for in modelling the panel’s time-dependent ultimate strength. Uncertainty of axial compressive loads induced by hull girder bending is evaluated based on probabilistic characteristics of still-water bending moment (SWBM) and vertical wave-induced bending moment (VWBM). A case study is performed to demonstrate this method and the effects of the lateral pressure, the return period of the extreme value of VWBM, the environmental severity factor, and the corrosion wastage on the panel reliability are investigated. Sensitivity measures for random variables are also carried out.

Hull girder reliability assessment for FPSOs

A methodology for reliability assessment for hull girder ultimate strength of FPSOs is presented in the paper. The hull girder ultimate strength of a FPSO is calculated by a progressive collapse analysis using the Smith method. Uncertainty of still-water bending moment (SWBM) is evaluated based on the loading conditions from FPSO operational manuals. A stochastic model of the extreme value of vertical wave-induced bending moment (VWBM) is developed in accordance with the extreme value theories based on the long-term distribution of VWBM. A first-order reliability method coupled with finite difference methods is proposed for reliability estimate dealing with the complicated implicit limit state function for hull girder ultimate strength assessment. Reliability assessments for four FPSOs are performed to demonstrate the capability of the methodology developed. The effects of the return period of the extreme value of VWBM, environmental severity factor and corrosion effects on hull girder reliability are investigated. A sensitivity analysis for each random variable is also conducted.

Effect of the nonlinear vertical wave-induced bending moments on the ship hull girder reliability

In the present paper the effect of the nonlinear vertical wave-induced bending moments on the ship hull girder reliability is evaluated. A chemical tanker for which the nonlinearity of the vertical wave-induced bending moments was found to be significant is adopted as case study. The nonlinear effects on the vertical wave-induced bending moments of the chemical tanker are accounted for in the reliability assessment problem through model correction factors, which are estimated using direct calculation methods based on linear and nonlinear strip theory formulations and the most likely response wave method. It is verified that the design formulation presently used to define the hull girder vertical wave-induced bending moments underestimates the magnitude of the nonlinear effects. The more accurate predictions provided by the direct calculations methods show that the actual hull girder reliability in sagging is significantly smaller. Possible modified design solutions for the midship cross-section of the chemical tanker are evaluated in order to demonstrate the impact of the increase of the nonlinear vertical wave-induced bending moment in sagging in terms of structural design criteria.

Measurements in a container ship of wave-induced hull girder stresses in excess of design values

This paper describes full-scale measurements of the wave-induced vertical bending moment amidships a 9400 TEU container carrier and focuses on the effect of the hydro-elastic high-frequency vibration on the extreme hogging wave bending moment. One extreme event, where the vertical wave-induced hogging bending moment amidships slightly exceeds the design value, is analysed and the measurements are verified by the use of the relationship between measurements of accelerations and strains and simple beam theory. The measurements are found to be reliable. In the extreme case, the high-frequency vibrations caused by impulsive loads are observed to be of the same magnitude as the rigid-body wave-induced response and thus acts to double the total vertical bending moment amidships. It was also found that even though the ship is sailing in bow quartering seas, only the 2-node vertical vibration mode is apparently excited. Following the extreme event analysis and verification, three hours of strain measurements are used for establishing a Gumbel distribution for the extreme value prediction, and it is found that the probability of exceeding the rule design wave bending moment by 50% in the given sea state is quite significant. Finally, the hydro-elastic behaviour of the hull girder is assessed by simple approximations using the measured statistical properties and closed-form expressions and the agreement with the actual measurements is found to be good.

Reliability assessment of ship structures using Bayesian updating

This paper presents an approach for reducing the uncertainty in the performance assessment of ship structures by updating the wave-induced load effects with the data acquired from structural heath monitoring (SHM). The initial information on the wave-induced load effects is calculated based on strip theory. Bayesian updating method is used to incorporate the processed SHM data to update the wave-induced vertical bending moment modeled by the Rayleigh distribution and its extreme values modeled by the Type I extreme value (largest) distribution. Three general cases associated with updating (a) only one parameter, (b) two parameters separately, and (c) two correlated parameters simultaneously in the Type I extreme value distribution are investigated. Aging effect due to corrosion is considered in the resistance modeling. Time-variant reliabilities before and after updating are evaluated. The proposed approach is illustrated with the Joint High Speed Sealift.

Spectral fatigue damage assessment of tanker deck structural detail subjected to time-dependent corrosion

The paper presents a spectral fatigue damage analysis of a double hull tanker structural detail accounting for corrosion wastage over time. The cyclic load of the wave-induced vertical bending moment, analysis using a strip theory on the frequency domain, is considered for two loading conditions. The influence of sea environment parameters and operational profiles including the use of different scatter diagrams, and wave variance spectra have been analyzed. The effect on the time-dependent cumulative fatigue damage as a function of corrosion deterioration is calculated.

Ship Springing Response in Finite Water Depth

The influence of water depth on the vertical wave induced bending moment acting on a hull has been studied. The deep-water second-order nonlinear hydroelastic strip theory, which is based on the relative motion concept, has been generalized to account for a finite water depth. Results for an analytical beam and for a tanker ship are presented and discussed. Short-term load predictions that account for a range of different sea states are given for a tanker ship. As seen from the present study, the effect of intermediate water depth may be a significant factor in calculations of ship springing response.

Stress Combination for Fatigue Analysis of Ship Structures

A methodology for calculating the correlation factors to combine the long-term dynamic stress components of ship structure from various loads in seas is presented. The proposed methodology is valid for a stationary ergodic narrow-banded Gaussian process. The total combined stress in short-term sea states is expressed by linear summation of the component stresses with the corresponding combination factors. This expression is proven to be mathematically exact when applied to a single random sea. The long-term total stress is similarly expressed by linear summation of component stresses with appropriate combination factors. The stress components considered here are due to wave-induced vertical bending moment, wave-induced horizontal bending moment, external wave pressure, and internal tank pressure. For application, the stress combination factors are calculated for longitudinal stiffeners in midship cargo and ballast tanks of a crude oil tanker. It is found that the combination factors strongly depend on wave heading and period in the short-term sea states. It is also found that the combination factors are not sensitive to the selected probability of exceedance level of the stress in the long-term sense.

Estimation of wave-induced ship hull bending moment from ship motion measurements

A time-domain technique for estimating wave-induced ship hull bending moment from ship motion measurements is presented. This technique is developed to improve hull response monitoring systems. Artificial neural networks are used to model the time-domain relationship between the wave-induced vertical bending moment and the coupled heave and pitch motions. The application of the proposed technique is validated using experimental data.

Comparative study on the time-domain analysis of non-linear ship motions and loads

A benchmark study has been performed by comparing the predictions of different non-linear time-domain codes applied to study the vertical wave-induced bending moment in a containership in waves of different steepness. Most methods are based on strip theory formulations applied both to rigid-body and to flexible hull formulations, but one adopts a 3-D formulation.

Effect of Heavy Weather Maneuvering on the Wave-Induced Vertical Bending Moments in Ship Structures

Statistical data are collected so as to quantify the probability of occurrence of voluntary course changes in heavy weather as well as their dependence on significant wave height and on ship heading. Decision rules are established about when and how to change course, on the basis of the analysis of operational data and of interviews with experienced shipmasters. A Monte Carlo simulation is performed so as to determine how an omnidirectional distribution of initial headings is changed by voluntary course changes depending on the significant wave height. Finally, the effect of the nonuniform distribution of headings on the mean wave-induced vertical bending moment is calculated. It is shown that although heavy weather maneuvering eases the ship motions, it can increase the wave-induced bending moments and thus increase the probability of structural failure.