Maro Ćorak

Long-term prediction of combined wave and whipping bending moments of container ships

The purpose of this paper is to propose a practical computational procedure for the long-term distribution of combined wave and whipping bending moments (BMs) of container ships. The problem is formulated in the frequency domain using standard engineering tools for load computation: a seakeeping code for the rigid-body response and a beam finite element model for transient vibratory response. The von Karman approach with correction for pile-up effect is employed for bow flare slamming load assessment. Correlation between wave and whipping BMs is considered. The procedure is demonstrated on the example of a 9200 TEU container ship. Long-term distributions of combined BMs are computed using the standard International Association of Classification Societies scatter diagram for the North Atlantic environment and two additional scatter diagrams for common shipping routes of container ships. The speed profile required for the long-term load prediction is calculated by the seakeeping analysis respecting operability limiting criteria. Conclusions about influence of various environmental and operability parameters are drawn.

Ultimate hull-girder-strength-based reliability of a double-hull oil tanker after collision in the Adriatic Sea

ABSTRACT The aim of this paper is to present a methodology for the assessment of the structural reliability of an oil tanker damaged in a hypothetical collision accident in the Adriatic Sea. Monte Carlo simulation is employed to generate random damage scenarios. Assumption of the damage size is based on the numerical simulation of the ship–ship collision. Residual ultimate strength and still-water bending moment distribution are determined based on the size and location of the damage. Structural reliability analysis is employed to determine the safety index with respect to the ultimate hull-girder failure. Histograms of safety indices are thus obtained, representing new measures for the performance assessment of the damaged ship. If extended to more severe design wave environments and collision scenarios, the presented methodology may be used for general reliability-based comparison of different alternative designs of marine structures with respect to the accidental failure modes or for improvement of ship structural design rules.

Probabilistic Load Combination Factors of Wave and Whipping Bending Moments

Extreme values of wave and whipping bending moments are important in structural design of large containerships. Since the extreme values of these two, partially correlated processes do not occur at the same time instant and even at the same environmental conditions, it is necessary to combine them by using probabilistic load combination methods. The correlation analysis between wave and whipping bending moments is performed and a practical method for calculation of the most probable load combination factor between considered bending moments is presented. Short-term load combination factors are calculated by reconstruction of the signal from the frequency domain solution. Results are validated by comparison with model test data of the 9400-TEU containership for various sea states and speeds and heading angles. Practical regression equations for estimation of the most probable short-term load combination factor are formulated. Regression equations are then used in the computation of the long-term distribution of combined bending moment. The procedure is demonstrated on the example of the two large containerships.

Structural reliability assessment of container ship at the time of accident

Hull girder reliability assessment of the MSC Napoli at the time of accident is presented. Loads considered in the study are still water bending moments, vertical wave bending moments and whipping bending moments, while structural capacity is represented by the hull girder ultimate strength. Load combination between wave and whipping bending moments is considered. The probability of failure is calculated using a first-order reliability method. Sensitivity study is performed in order to investigate influence of the pertinent random variables. The uncertainty model of the basic random variables involved is consistent with the recent proposal by the International Maritime Organization, thus enabling direct comparison of the obtained results with reliability levels proposed by International Maritime Organization.

Structural Reliability Assessment of an Oil Tanker Accidentally Grounded in the Adriatic Sea

The aim of the paper is to present a methodology for the assessment of the structural reliability of an oil tanker damaged in a hypothetical grounding accident in the Adriatic Sea. The grounding accident affects the ultimate hull girder capacity in the damaged region, the still water bending moment (SWBM) distribution along the vessel as well as the vertical wave bending moments (VWBM). The extent of the damage on the ship’s hull after a grounding accident depends on several parameters such as ship`s speed, rock size, penetration depth, longitudinal and transversal location of stranding along the hull. These parameters are in the present study assumed as random variables, described by probability density functions. Based on defined statistical properties, random realizations of grounding parameters are simulated by Monte Carlo (MC) simulation. For each such random grounding scenario, the damage size is calculated by the surrogate model based on numerical grounding simulations. Residual ultimate strength and SWBM distribution are determined based on the size and location of the damage. VWBM is calculated for average sea state in the area with increased risk of grounding accident in the Adriatic Sea. Structural reliability analysis is employed to determine the safety index with respect to the ultimate hull girder failure for salvage period of 12 hours. As each grounding scenario results in different hull- girder reliability, histogram of safety indices is obtained representing new measures for the performance assessment of the damaged ship.