Lyuben D. Ivanov

Challenges and possible solutions of the time-variant reliability of ship's hull girder

The main theme of the paper centres on the use of probabilistic methods to assess the hull girder bending capacity to be used in a risk-based inspection planning framework. The effect of corrosion wear on hull girder geometric properties is also discussed, and the annual probabilistic distributions and the probabilistic distributions for given time period are built. A new procedure is then proposed for the probabilistic presentation of the still water and wave-induced hull girder hogging and sagging loads as a single phenomenon. Lastly, the rules of the composition law of the constituent variables are used to build the probabilistic distribution of the total hull girder load and the corresponding total hull girder bending stresses. Thus, it becomes possible to calculate the probability of exceeding any given limit of the total hull girder stresses.

Deterministic and probabilistic assessment of the critical buckling strength of ships’ grillages (gross panels)

An analytical method for control of the strength of a grillage (gross panel) under unidirectional in-plane axial load is proposed. It allows us to solve the following tasks: (i) calculation of the critical stiffness of transverse girders, (ii) calculation of the maximum unidirectional in-plane compression load when the structures scantlings are known (iii) and calculation of the required structures scantlings when the unidirectional in-plane compression load is given. The proposed procedure is helpful in the application of probabilistic methods without employing specialised computer programmes, which is an advantage when fast (although approximate) evaluation is needed for the grillage critical buckling strength (e.g. ships deck structure) before applying the finite-element method (FEM) analysis. Results of analytical approach are compared and confirmed using FEM data. A probabilistic method for control of the strength of ships deck structure under unidirectional in-plane axial load is proposed. It allows us to assess the effect of deterioration due to corrosion on the decks buckling strength while avoiding the use of specialised computer programmes.

Probabilistic Presentation of the Still Water Loads: Which Way Ahead?

This paper analyzes the state-of-the-art concerning this subject. The objectives are: 1) to provide data of still water bending moments and shear forces that were collected from loading manuals of dozens of tankers 2) conduct statistical analysis of the loading cases and 3) discuss possible ways for further improvement of knowledge about the variability of still water loads during real ships’ operation.Copyright

Comparison of Load Combination Methods for Determining Maximum Ship’s Hull Girder Bending Moment

Abstract Several load combination methods have been developed for predicting the maximum loads acting on a ship’s hull girder within a specified time period. However, these methods have not been verified by a comparison with measurements. This paper compares predicted and measured maximum hull girder bending moment of a container ship. Point-crossing method, load coincidence method, Ferry Borges-Castanheta model, Moan and Jiao’s method, peak coincidence method, Turkstra’s rule, method of square root of the sum of squares (SRSS) and Söding formula are used for the comparison. The results show that (1) Ferry Borges-Castanheta model and Söding formula provide best estimates, (2) point-crossing method, load coincidence method and Moan and Jiao method provide sufficiently accurate estimates, (3) Turkstra’s rule provide reasonable estimates, (4) method of SRSS provides fairly low estimates and (5) peak coincidence method provides very conservative estimates.

Reliability estimation of ship's hull girder in probabilistic terms when ultimate strength is used as a failure mode

Using the ultimate strength as a failure mode, the hull girder reliability is calculated as the probability of the total bending moment (BM) acting on the ships hull being greater than the ultimate hull girder moment. Both individual amplitude statistics and extreme value statistics are employed to derive the probability density function of the total hull girder BM as a sum of the still water and wave-induced bending moments probability density functions applying the convolution integral. The annual and lifetime probability density functions of the hull girder elastic and plastic section modulus are also derived and used as a base for determining the probability density functions of the first-yield and pure plastic BM. It is shown that the use of the first yield BM as a representative of the hull girder ultimate strength is reasonable only in the case when it is greater than ≈ 85% of the pure plastic BM. An example is given for a 25K DWT bulk carrier.

Assessment of the Total Ship’s Hull Girder Bending Stresses When Unified Model of Sagging and Hogging Bending Moments is Used

A method is proposed for calculating the hull girder bending stresses following the procedure in the class rules but in probabilistic terms, i.e. the still water and the wave-induced bending moments; the total hull girder bending moment; the hull girder section modulus and the hull girder bending stresses are treated as random variables with corresponding probabilistic distributions. The still water and wave-induced hull girder hogging and sagging loads are presented in probabilistic format as one phenomenon, i.e. using bi-modal probability density functions. The probabilistic distribution of the total hull girder load is calculated using the rules of the composition of the distribution laws of the constituent variables. After that, the hull girder geometric properties are presented in probabilistic format as annual distributions and distributions for any given life-span. Thus, it becomes possible to calculate both the annual probabilistic distributions and the probabilistic distribution for any given ship’s life span of the hull girder stresses. Individual amplitudes statistical analysis and extreme value statistics are used. Then, the probability of exceeding the permissible hull girder bending stresses in the class rules is calculated. An example is given for 25K DWT bulk carrier.Copyright

Buckling of a simply supported beam on an elastic foundation supported within its span with elastic supports. Buckling of grillages

Abstract In this paper, the buckling strength of a beam on an elastic foundation supported within its span by equally distant elastic supports is treated. A formula is derived for the coefficient of rigidity of these elastic supports that ensure a given value of the Euler force. It has been proved that a specific value of the coefficient of rigidity exists (it is called the critical coefficient of rigidity), beyond which its further increase does not increase the Euler force. Also, assuming the stiffness of the elastic foundation equal to zero, a formula is derived for the coefficient of rigidity of the elastic supports for a beam that does not lie on an elastic foundation. Several examples are given for calculation of the required and critical coefficient of rigidity of the elastic supports.

Semi-probabilistic approach for assessment of the requirement for minimum hull girder section modulus

The paper presents a study on an approximate semi-probabilistic approach for assessment of any given requirement for minimum hull girder section modulus (HGSM). It consists of calculating the HGSM using as input data the reduced (due to corrosion) plates’ thicknesses and longitudinals’ cross-sections with exactly the same probability of exceedance. Its accuracy is checked against results obtained by the complete probabilistic approach developed by the author. In this paper, the requirement for minimum HGSM is based on the IMO (International Maritime Organization)-formulated permissible reduction by 10% of the as-built HGSM. A numerical example is given for a bulk carrier of 25,000 deadweight ton (25K DWT). A comparison between the results obtained by the complete probabilistic method and those obtained by the semi-probabilistic method showed that the accuracy of the semi-probabilistic method is around +8% when the 95th percentile of the corrosion wastage of plates and longitudinals is used, and around −2% when the 99th percentile of the corrosion wastage of plates and longitudinals is used. The semi-probabilistic approach is simpler than the complete probabilistic approach but has relatively high accuracy, especially for higher-order percentiles, and thus is recommended for practical use.

Probabilistic presentation of the total bending moments of FPSOs

The widespread practice for presentation of the still water loads acting on the hull structure of a floating production storage and offloading facility (FPSO) is to use the individual amplitude statistics. When the probability density function of the loads is built, its integration provides the probability of exceeding any given level of loads. Also, once it is available, one can apply the principles of extreme value statistics to obtain the highest value in any number of cycles. The individual amplitude statistics are used in fatigue strength calculations, while the extreme value statistics can be used in ultimate strength calculations. An example is given for the probability density functions of a sample FPSO when the two approaches are applied for assessment of the total hull girder load that can be applied for calculation of its ultimate strength.

On the wave-induced loads used in checking the strength of aging ships

In this paper, a method is proposed for determining the wave-induced hull girder loads used in strength assessment of aging ships for any remaining service life and any probability of exceedence. The hull girder geometric properties are presented in a probabilistic format. The probabilistic distribution of the hull girder stresses is then obtained by the rules of the composition of the distribution laws of the constituent variables. The method allows for assessing not only the absolute values of the stresses but also their level of uncertainty/certainty. An example is given for the deck bending stresses due to wave-induced bending moment.