Probabilistic Models of Ultimate Strength Reduction of Damaged Ship

The aim of this paper is to develop a probabilistic model of the reduction in the bending moment capacity of an oil tanker following grounding and collision accidents. The approach is based on the Monte Carlo (MC) simulation using the probability distributions of damage parameters proposed by the International Maritime Organization (IMO). The reduction in ultimate strength in the case of grounding is calculated by applying existing design equations using the concept of the grounding damage index (GDI) and assuming grounding on a conically shaped rock. Design equations for collision damage are originally developed in the present paper by assuming rectangular box damage. The modified Paik-Mansour method is employed for residual strength assessment when developing the design equations. A case study is presented for an Aframax tanker resulting in the Weibull probability distributions fitted to the histograms of residual strength obtained with MC simulations. The obtained probability distributions are intended for structural reliability assessment of damaged ships

OMAE2008-57730 DRAFT: ON THE ASSESSMENT OF REDUNDANCY OF SHIP STRUCTURAL COMPONENTS

ABSTRACT This paper firstly sums up some of the views on structural redundancy with particular emphasis on ship and marine structures. Next, it places the engineering decision process in the event space and, consequently, applies the representation of operational modes by systems of events. Furthermore, the paper takes some of the relations from the entropy concept in information theory. The entropy concept in probability theory is employed in the paper to redefine the structural redundancy in terms of conditional entropy of operational modes. The redundancy modeling is presented by systems of operational modes in which some of the transitive events may lead to new operational states. Finally, a ship substructure example of a stiffened panel with a girder is elaborated. The conclusion supports the thesis that the efficient structural redundancy can be comprehended as the most uniform distribution of the operational modes probabilities. Moreover, the efficient structural redundancy can be maximized

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

Uncertainty of ship hull girder ultimate strength in global bending predicted by Smith-type collapse analysis

The engineering modelling of ship hull girder strength consists of global and local levels. The Smith-type progressive collapse analysis is a typical example of this, in which the global model requires input from the local model to describe the underlying 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 light of this, a novel probabilistic method is applied in this research to quantify the uncertainty related to the local models, i.e., the combined computational uncertainty of ultimate compressive strength and post-collapse strength of structural elements. 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 are performed for the first time on four merchant ships under both uni-axial and bi-axial bending load cases. It is shown 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 ship hull girder strength estimation so that improving the ultimate limit state-based reliability analysis

Vjerojatnost sloma trupa oštećenoga tankera za prijevoz nafte

Uzdužna čvrstoća brodskog trupa može se nakon sudara ili nasukavanja značajno smanjiti zbog oštećenja i gubitka nosivosti uzdužnih elemenata strukture. Gubitkom svojstva vodonepropusnosti, a uslijed mogućeg prodora vode, moment savijanja na mirnoj vodi može značajno porasti. Smanjenje granične čvrstoće i promjena ukupnog opterećenja (mirna voda i valovi) uslijed oštećenja mogu dovesti do sloma konstrukcije. Nemogućnost predviđanja takvih događaja ukazuje na potrebu modeliranja parametara oštećenja kao slučajnih veličina te uvođenja novih probabilističkih modela smanjenja granične čvrstoće i promjene momenta savijanja na mirnoj vodi u jednadžbu graničnog stanja oštećenog broda. Cilj istraživanja je definirati probabilističke modele za nove varijable u svrhu određivanja vjerojatnosti sloma oštećenog trupa tankera za prijevoz nafte. Primjena istraživanja je u razvoju novih pravila za gradnju trupa, donošenju odluka o unesrećenom brodu u hitnim situacijama te u procjeni rizika pomorskog transporta u osjetljivim geografskim područjima