Ship Hull Girder Research Articles

A framework to analyse the probability of accidental hull girder failure considering advanced corrosion degradation for risk-based ship design

Ship’s hull girder failure could result from maritime accident that can cause human life loss, environmental disaster, and major economic impacts. In risk-based ship design paradigm, accounting for rare phenomena (e.g. ship-ship collision or grounding) is important to provide safe and durable structure. In-service corrosion-induced hull degradation should be considered at the design stage, as it can significantly affect structural strength. The current study presents a novel framework to estimate the probability of ship hull girder failure, accounting for novel corrosion modelling techniques and accidental damage. The associated uncertainties are considered using statistical sampling from evidence-based distributions. A state-of-the-art deterministic model for ultimate strength calculation is applied using Monte Carlo simulation approach, resulting in the probability of hull failure through a reliability assessment. Wave and still-water bending moments are considered random variables. Two case studies of tanker ships with varying sizes are executed to show the applicability of the proposed framework. The results indicate that proper consideration of corrosion is of high importance, as ageing can significantly increase the probability of failure if accidental damage happens. Therefore, whereas future research and model refinement are discussed, the presented framework can serve for risk-based ship design tool and assess existing structures’ safety.

Reliability assessment of ship hull girders considering pitting corrosion and crack

The current study aims to investigate the combined effect of cracking and pitting damage on the ultimate strength of ships. The well-known Smith’s approach is modified considering the random number and distribution of cracked-pitted plates in the ship cross-section. Using the Monte Carlo approach, the structural reliability index of the cracked-pitted ship is determined. A single-bottom oil tanker’s ultimate strength is computed, and it turns out that the reliability indices for various damage scenarios are nearly identical when the ship is at its early age. When the ship ages, its reliability index rises to its maximum if the damage is concentrated at the bottom under sagging conditions and at the sides and longitudinal bulkheads in hogging conditions. The reliability indices in the hogging conditions are often greater than those in the sagging conditions. Furthermore, it is determined that, while the ship is at its early age, the detrimental effect of pitting, cracking, or a combination of both on the reduction of the ship’s hull girder ultimate strength is equal. The lowest reliability index is seen in aged ships when cracking and pitting are combined, followed by cracking and pitting damage separately. It is shown that pitting corrosion has a lower reliability index than the general type of corrosion.

A methodology for ultimate strength assessment of ship hull girder accounting for enhanced corrosion degradation modelling

The presented work shows a methodology for the ultimate strength assessment of a ship hull, considering enhanced corrosion modelling. The approach is based on the classical Smith method. However, the recent findings regarding the impact of corrosion degradation on ultimate strength are incorporated. To this end, the stress–strain relationships for particular elements composing ship hull cross-section are modified using a specially developed correction factor. The proposed approach is validated with experimental results of the corroded box girders available in the literature, showing very good agreement. Further, a case study of a VLCC tanker ship is presented, and a comparison between contemporary and enhanced corrosion degradation modelling in terms of resulting ultimate strength is presented. The results indicate that the currently used method may significantly overestimate the hull’s structure capacity, especially considering the long exploitation period. Thus, current approaches lead to a non-conservative assessment of the ship hull girder’s ultimate strength, potentially increasing the risk of failure. It is therefore recommended to further investigate the proposed method, especially in the context of risk-based ship design approaches and holistic maritime transportation risk management.

Reliability-based assessment of ship hull girder ultimate strength

Abstract A reliability-based approach is presented to investigate the effects of structural and load uncertainties on the reliability estimation of ship hull girders. Structural uncertainties included randomness in material properties, geometric properties, initial geometric imperfections, and corrosion behavior. Load uncertainties included statistical uncertainties, model uncertainties, environmental uncertainties, and uncertainties related to nonlinearity. The hull girder ultimate strength was calculated using Smith’s method, and the probabilistic density function was evaluated by employing Monte Carlo simulations. In the load estimation, the still water bending moment and wave-induced bending moment were calculated using a simplified formula of the International Association of Classification Societies-Common Structural Rules code and then modified with load parameters. The reliability index was estimated using a first-order reliability method considering the operating time, the duration of the ship in the alternate hold loading condition, and the severity of the corrosion rate. As a result, sagging conditions dominated the collapse mode. The reliability indexes were obtained for the observed cases, and the viability of the ship was assessed accordingly.

Uncertainty Of Ship Hull Girder Ultimate Strength in Longitudinal Bending

The engineering modelling of ship hull girder strength usually consists of global and local levels. The Smith-type progressive collapse method is a typical example of this kind, in which the global model requires input from the local model with the underpinning local structural behaviour, i.e., load-shortening curve (LSC). However, the modelling is prone to uncertainty due to the statistical variability of the basic variables (aleatoric uncertainty) and the inadequacy of engineering models in both global and local levels (epistemic uncertainty). The former can be well tackled by a probabilistic sampling, whereas dealing with the latter for ship hull girder strength lacks an established approach. There can be different sources of epistemic uncertainty. In the modelling of ship hull girder strength, this may be partially manifested as that caused by different choices of local engineering models for predicting the LSC. In the light of this, a probabilistic method is applied in this research to investigate and quantify the uncertainty related to the local models. The adopted approach is a hybrid method incorporating the Smith-type progressive collapse method with Monte-Carlo Simulation and an adaptable LSC algorithm. Case studies on four merchant ships show that the ultimate strength in sagging is subjected to the most significant computational uncertainty as compared with those in hogging and horizontal bending. In a bi-axial load case, the computational uncertainty estimated for vertical bending will be counteracted as the horizontal bending increases. Nevertheless, this change is not directly proportional to the bi-axial load component ratio and appreciably varies between different ship types. The insights and data provided by this study may eventually resolve the epistemic uncertainty in the modelling of ship hull girder strength. It would also be useful to improve the ultimate limit state-based reliability analysis with regards to the strength model uncertainty evaluation.

Application of Equivalent Single Layer Approach for Ultimate Strength Analyses of Ship Hull Girder

The objective of this paper is to present the application of equivalent single layer (ESL) approach for the ultimate strength assessment of ship hull girder in the context of numerical finite element (FE) simulations. In the ESL approach, the stiffened panel is replaced with a single plate, which has the equivalent stiffness of the original panel. Removal of tertiary stiffening elements from the numerical model facilitates time-savings in pre-processing and FE analysis stage. The applicability of ESL approach is demonstrated with two case studies, one compartment model and full-sized double hull tanker model in intact and damaged conditions. The damage extents are determined based on the international association of classification societies from common structural rules (IACS-CSR) for oil tanker. Ship hull girder is exposed to distributed pressure with the sinusoidal shape that bends the hull girder. This pressure load is applied separately to bottom and side structures to obtain the vertical and horizontal bending moments of the hull girder, respectively. Ultimate strength predictions obtained from ESL approach are compared to full three-dimensional finite element method (3D FEM) and IACS incremental-iterative method. The comparison between different methods is provided in terms of longitudinal bending moment and cross sectional stress distribution. Overall, ESL approach yields good agreement compared to the 3D FEM results in predicting the ultimate strength of ship hull girder while providing up to 3 times computational efficiency and ease of modeling.

Scaling characteristics of the hull girder's ultimate strength subjected to the combined hogging moment and bottom lateral pressure: An empirically modified scaling criterion

The ultimate strength of the ship hull girder under combined loads is closer to the load-carrying capacity during the actual sailing for considering the negative effect of the secondary load in some cases. Scaled models are designed to represent the prototype in ultimate strength experiments. To study the effect of the bottom lateral pressure on the scaled hull girder under combined loads thoroughly, a series of hull girders of a 10,000TEU container ship under different scale combinations of geometric length and plate thickness are analyzed. The relevant changes in the characteristics of ultimate strength and collapse behaviors caused by bottom lateral pressure are investigated. Results show that the ultimate hogging moment predicted by the traditional or the empirical scaling law proposed in the reference is significantly different from that obtained by numerical analysis when the scale ratio of the plate thickness is much smaller than the geometric scale ratio for ignoring the significant effect of the bottom lateral pressure. Correspondingly, an empirical scaling criterion is proposed to improve the accuracy of the converting process of the ultimate strength between scaled models and the full-scale prototype. Finally, the applicability of the proposed scaling criterion is verified by numerical results of a series of simplified hull girder models.

Experimental and numerical investigations on the collapse behaviour of box type hull girder subjected to cyclic ultimate bending moment

This paper presents experimental and finite element analyses of the ultimate strength and buckling collapse behaviours of a single- and a double-hull girder with a large deck opening subjected to cyclic ultimate bending moments. The cyclic ultimate bending moments here means that the external load in every cycle exceed the ultimate load bearing capacity of the specimens; the aim is to understand how the structures behave under this kind of extreme but not unusual load condition. The results showed that, in general, the plastic deformation would be accumulated under the cyclic loads, and the buckling collapse would expand from the deck plates to the broadside plates in both specimens. However, even if overall buckling occurred on both specimens, the specimens still preserved most of the load bearing capacity for the next ultimate loading cycles, but the double-hull specimen had a higher safety stock. In addition, the different behaviours of these two types of specimens were recorded, and the reasons behind were deeply analysed, which has helped us gain a deeper understanding of how these complex engineering structures perform under this kind of extreme but not well-studied load condition. The conclusions drawn in this works would be beneficial to improve the structural safety of ship hull girders and other similar thin-walled structures.

Experimental and numerical investigation on the ultimate strength of a ship hull girder model with deck openings

This paper presents an investigation on the ultimate strength of a ship hull girder model with openings. A model with relatively large openings in a group of compartments is designed and tested up to the ultimate bearing capacity under a pure sagging bending moment. The failure mode, the load-displacement curve and the ultimate load of the experimental model are analysed by the nonlinear finite element method. The ultimate load of the experimental model is also calculated using a progressive collapse method (Smith based method). The results of the numerical calculations are compared with the results of the model experiment and they are found to be in good agreement. The relative error between the numerical method and the experimental result is −3.9% and 1.6% for ABAQUS and LS-DYNA models respectively, and the relative error between the progressive collapse method and the test result is −1.3%. The experimental results of this paper can provide the basis for the validation of numerical simulations and theoretical methods, and they provide a reference for the design of the ultimate strength of similar ship structures.

A comparison of numerical methods for damage index based residual ultimate limit state assessment of grounded ship hulls

Considerable efforts have been devoted to developing rapid methodologies for predicting the residual strength of ship hull girders for a given damage scenario (e.g., R–D diagram). This task is usually challenged by the difficulty of a proper definition of damaged scenarios, which is a function of the damage location and extent. The concept of damage index (DI) was proposed to resolve this issue, and its application has been demonstrated previously through the incorporation of the Intelligent Supersize Finite Element Method (ISFEM) and Modified Paik–Mansour (P–M) approach. Alternatively, a Smith-type progressive collapse can be adopted. In fact, this may enable a more comprehensive application of the DI concept, as the Smith-type approach is codified in the Common Structural Rule (CSR) for assessing the longitudinal strength of the hull girder. In light of this, the damage index based assessment tools (i.e., R–D diagram) incorporated with a Smith-type progressive collapse method is presented in this paper. This also facilitates a comparison with the R–D diagram previously developed by ISFEM and Modified P–M approach. Discussion is given regarding the discrepancy between different methods, and recommendations for future research are outlined.

수중 폭발에 의한 함체의 비탄성 휘핑 응답에 관한 연구

The primary effect of the far-field underwater explosion (UNDEX) is the whipping of the ship hull girder. This paper aims to verify why inelastic effects should be considered in the whipping response estimations from the UNDEX simulations. A navy ship was modeled using Timoshenko beam elements over the ship length uniformly keeping the constant midship section modulus. The transient UNDEX pressure was produced using two types of the Geers-Hunter doubly-asymptotic models: compressible and incompressible fluids. Because the UNDEX model based on incompressible fluid assumption provided more increased fluid volume acceleration in the bubble phase, the incompressible fluid-based UNDEX model was adopted for the inelastic whipping response analyses. The non-linear hull girder bending moment-curvature curve was used to embed inelastic effects in the UNDEX analyses where the Smith method was applied to derive the non-linear stiffness. We assumed two stand-off distances to see more apparent inelastic effects: 40.5 m and 35.5 m. In the case of the 35.5 m stand-off distance, there was a statistically significant inelastic effect in terms of the average of peak moments and the average exceeding proportional limit moments. For the conservative design of a naval ship under UNDEX, it is recommended to use incompressible fluid. In the viewpoint of cost-effective naval ship design, the inelastic effects should be taken into account.

Progressive collapse analysis of a bulk carrier hull girder under longitudinal vertical bending moment considering cracking damage

Existence of crack causes reduction of the load carrying capacity of ship hull structural elements and eventually reduces the hull girder strength. Previous numerical and semi-analytical studies by the same authors revealed that in addition to the value of ultimate strength, the deflection shape and plastic collapse mechanism of ship hull structural elements will change due to existence of cracking damage. In this paper results from previous studies are used to investigate the way cracks affect ultimate longitudinal strength of ship hull girder. Progressive collapse analysis of an ISSC2000 bulk carrier is carried out to estimate its ultimate strength considering existence of cracking damages at different locations of the hull girder; namely bottom, double bottom, side and deck structures. For this reason, HULLST software which is based on Smith's method was modified to be able to model specific cracks anywhere in the ship hull girder. Results show that the way cracking damage effects the ultimate strength of the ship depends highly on the ship's collapse modes in hogging and sagging conditions as well as behavior of the ship structural elements.

Application of the Sub-Sea Analysis (SSA) capability in numerical simulation of underwater explosion

In order to solve the problem that LS-DYNA fluid-solid coupling algorithm is not suitable for remote underwater explosion simulation and improve calculation efficiency, the numerical simulation of remote underwater explosion is carried out for the subsea analysis function in LS-DYNA. The dynamic response process of ship hull girder under underwater explosive load is analyzed by comparing it with the general software AUTODYN numerical simulation. The method reflects the loading process of underwater explosion load on structure to a certain extent. The calculation speed is fast, but the accuracy is not high and the error of bubble pulsation process is large.

A probabilistic approach to assess the computational uncertainty of ultimate strength of hull girders

The simplified progressive collapse method is codified in the IACS Common Structural Rules (CSR) to calculate the ultimate strength of ship hull girders in longitudinal bending. Several benchmark studies have demonstrated the uncertainty of this method, which is primarily attributed to the variation in the load-shortening curve (LSC) of local structural components adopted by different participants. Quantifying this computational uncertainty will allow the model error factor applied for the ultimate strength of hull girder in a reliability-based ship structural design to be determined. A probabilistic approach is proposed in this paper to evaluate the prediction uncertainty of ultimate strength of the hull girder caused by the critical characteristics within the LSCs. The probability distributions of critical load-shortening characteristics of stiffened panels are developed based on a dataset generated by empirical formulae and the nonlinear finite element method. An adaptable LSC formulation, with the ability to cater for specific response features of local components, is utilised in conjunction with the Monte-Carlo simulation procedure and the simplified progressive collapse method to calculate the ultimate strength of a hull girder at each sampling. The proposed method is applied to four merchant ships and four naval vessels. The computational uncertainties of the ultimate strength of the case study vessels are discussed in association with their mean values and standard deviations. The study shows that the ultimate strength of ship hull girders is subjected to different uncertainties in sagging and hogging. Whist the strength of merchant ships are primarily governed by the ultimate compressive strength of critical stiffened panels, the strength of naval vessels are also sensitive to the post-collapse response of critical members.

A numerical method to compute global resonant vibrations of ships at forward speed in oblique waves

Resonant wave-induced vibrations of a ship hull girder, known as “springing”, is an important issue when addressing fatigue aging of the steel structure. To compute resonant wave-induced vibrations, fluid-structure interactions and associated structural and hydrodynamic properties need to be addressed. This paper introduces a time-domain numerical method that predicts higher-order springing taking into account forward speed. Structural dynamics were computed based on a beam element approach that considers vertical and horizontal bending as well as nonuniform torsion. Furthermore, mass and stiffness matrices accounted for strong coupling effects between hull girder bending and torsion. The hydrodynamic solver coupled the fully nonlinear stationary free surface flow with the oscillatory flow and considered geometrical nonlinearities caused by the changing wetted surface due to the incident waves, nonlinear rigid body motions and linear elastic vibrations. Numerical predictions were validated against model tests of a post-Panamax containerships at forward speed. Dry and wet natural frequencies and midship vertical bending, horizontal bending and torsional moments induced by higher order springing vibrations compared favourably to experimental measurements.

Effect of stress-strain curve changing with equal channel angular pressing on ultimate strength of ship hull stiffened panels

Similar to other structures, ultimate strength values showing the maximum load that the structure can resist without damaging has great importance on ships. Therefore, increasing the ultimate strength values will be an important benefit for the structure. Low carbon steels used in ships due to their low cost and good weldability. Improving the ultimate strength values without interfering with the chemical composition to prevent of the weldability properties of these steels would be very beneficial for ships. Grain refinement via severe plastic deformation (SPD) is an essential strengthening mechanism without changing the chemical composition of metallic materials. Among SPD methods, equal channel angular pressing (ECAP) is one of the most commonly used one due to its capacity for achieving bulk ultrafine-grained (UFG) materials. When the literature is examined, it is seen that there is no study about ultimate strength calculation in ships after ECAP. Therefore, the mean purpose of this study is to apply ECAP to a shipbuilding low carbon steel to be able to achieve mechanical properties and investigate the alteration of ship hull girder grillage system's ultimate strength via finite element analysis approach. A fine-grained (FG) microstructure with a mean grain size of 6 um (initial grain size was 25 um) was after ECAP. This microstructural evolution brought about a considerable increase in strength values. Both yield and tensile strength values increased from 280 MPa and 425 MPa to about 420 MPa and 785 MPa, respectively. This improvement in the strength values reflected a finite element method to determine the ultimate strength of ship hull girder grillage system. As a result of calculations, it was reached significantly higher ultimate strength values (237,876 MPa) compared the non-processed situation (192,986 MPa) on ship hull girder grillage system.

Review of Ultimate Strength Assessment of Ageing and Damaged Ship Structures

The objective of this work is to provide an overview of the ultimate strength assessment of ageing and damaged ship structures in the last decades. Particular attention is paid to the ultimate strength of plates, stiffened panels, box girders, and entire ship hull structures subjected to corrosion degradation, fatigue cracking, and mechanical damage caused by accidental loading or impact. A discussion on the effect of the cyclic load on the plate rigidity, re-yielding, and ultimate load capacity on the ship hull girder is also part of the present study. Finally, some conclusions and discussions about potential future work are provided, identifying that more studies about the impact of corrosion degradation on the structural behaviour of the stiffened panels and the overall hull girders are needed. Studies related to the dynamic collapse behaviour of corroded and damaged ship structures under time-variant load also requires additional attention.

Post-ultimate strength behaviour and collapse severity of ship hull girder under extreme wave load by an analytical method

ABSTRACT When the external load exceeds the ultimate strength of hull girder, the load-carrying capacity is not completely lost due to the supporting and constraint between structure members. It is also determined by the post-ultimate strength behaviour, and the collapse severity needs to be studied to evaluate the consequence of collapse. An analytic approach is presented in this paper to analyse the factors influencing the collapse severity of hull girder under extreme wave load. The equations of motion of hull girder are derived for an external moment unloading in different ranges of the generalised moment-curvature relationship so as to predict the corresponding final severity of collapse. The severity is also analysed from the energy point of view to investigate the influence of the capacity drop on the severity. The complete post-ultimate strength behaviour of hull girder revealed in this study provides a reference for structure safety design of ship hull girders.

Ultimate strength of ship hull girder with grounding damage

ABSTRACT The paper presents a method for the assessment of residual strength of a ship hull damaged in a grounding accident. The strength assessment is based on a coupled beam (CB) method that allows time-efficient analysis. As a case study the method is applied to a double hull tanker. Three grounding damages are defined based on IACS guidelines and with a dedicated grounding assessment tool. The CB method is based on an assumption that global bending response of a ship can be estimated with the help of beams coupled to each other by distributed springs. To include the damage opening in the residual strength assessment, the structural elements in the damaged region are excluded by reducing their elastic modulus. For the validation of the CB method, the residual strength is also evaluated with non-linear finite element method. Good correlation between the methods is reported.

Progressive Collapse Analysis of an FPSO Vessel Hull Girder Under Vertical Bending Considering Different Corrosion Models

Nowadays, with the increasing operational life of ships, the aging effects on their structural behavior need to be investigated precisely. With the corrosive marine environment taken into consideration, one of the important effects of aging that must be studied is thickness degradation. In this paper, with the use of previously proposed equivalent thickness formulations for corroded plates, the progressive collapse analysis software HULLST is enhanced, and then, the effects of different corrosion models of uniform, random, pitting, and tanker pattern types on the ultimate and residual strengths of a floating production, storage, and offloading vessel hull girder are evaluated for the ages of 0 to 25 years. Results reveal that the uniform corrosion and random corrosion models have close outcomes. The value of relative reduction in the ultimate strength of ship hull girder (compared with the intact condition) ranges roughly from 6% for the age of 5 years to 17% for the age of 25 years in the hogging mode. The relative reduction in the ultimate strength ranges from 4% to 16% in the sagging mode. Pitting corrosion and tanker pattern (random) corrosion models lead to higher relative reductions in ultimate strength. The pitting corrosion model leads to a 16%–32% relative reduction in the ultimate strength for the ages of 5–25 years of the ship in either hogging or sagging. The tanker pattern (random) corrosion model leads to a 6%–37% relative reduction in the ultimate strength in the hogging mode and 3%–31% in the sagging mode at ship ages of 5 to 25 years.