Alaa E. Mansour

A simple formulation for predicting the ultimate strength of ships

The aim of this study is to derive a simple analytical formula for predicting the ultimate collapse strength of a single- and double-hull ship under a vertical bending moment, and also to characterize the accuracy and applicability for earlier approximate formulations. It is known that a ship hull will reach the overall collapse state if both collapse of the compression flange and yielding of the tension flange occur. Side shells in the vicinity of the compression and the tension flanges will often fail also, but the material around the final neutral axis will remain in the elastic state. Based on this observation, a credible distribution of longitudinal stresses around the hull section at the overall collapse state is assumed, and an explicit analytical equation for calculating the hull ultimate strength is obtained. A comparison between the derived formula and existing expressions is made for largescale box girder models, a one-third-scale frigate hull model, and full-scale ship hulls.

Estimation of ship motions using closed-form expressions

A semi-analytical approach is used to derive frequency response functions for the wave-induced motions for monohull ships. The results are given as closed-form expressions and the required input information for the procedure is restricted to the main dimensions: length, breadth, draught, block coefficient and water plane area together with speed and heading. The formulas make it simple to obtain quick estimates of the wave-induced motions and accelerations in the conceptual design phase and to perform a sensitivity study of the variation with main dimensions and operational profile.

Modified Paik–Mansour formula for ultimate strength calculations of ship hulls

The objective of this paper is to develop a modified Paik–Mansour formula for the ultimate strength calculations of ship hulls subject to vertical bending moments. The method is based on a credible bending stress distribution over the hull cross-section presumed at the ultimate limit state. The accuracy of this method is demonstrated through comparison with computations obtained using more refined methods, such as non-linear finite-element method, intelligent super-size finite-element method, and idealised structural unit method. Statistical analysis of the hull girder ultimate strength based on comparisons among the various computations is carried out in terms of their mean values and coefficients of variation. The original Paik–Mansour method is found to be inapplicable to the case of a pure vertical bending moment depending on the ships hull type and/or vertical bending direction, but the modified Paik–Mansour method is more general and is able to resolve this issue.

Reliability-based method for optimal structural design of stiffened panels

Abstract A methodology for structural optimization of stiffened panels based on reliability is developed. The stiffened panels are typical of those found in the deck or bottom of longitudinally stiffened ships. They are assumed to be under stillwater and wave induced loads, resulting in predominantly compressive loads. Both serviceability and collapse limit states are considered. The design problem is formulated as a nonlinear programming problem that aims at minimizing weight with behaviour constraints on reliability and physical constraints on the dimensions. The safety index is calculated using a first order reliability method (FORM). The PNET method is then employed to determine the representative failure modes and the system safety index. Finally, a numerical example is carried out to demonstrate the applicability of the design methodology and the results are presented and discussed.

Sensitivity factors and their application to marine structures

Abstract Sensitivity measures suitable for application to marine structures are provided in this paper. Interpretations of these sensitivity and importance factors are made for two modes of failure: ultimate strength under extreme loading conditions and fatigue strength. Four ships of different types have been selected, and the corresponding sensitivity measures have been computed. The results were compared to show the impact of ship type on the relative importance of the design variables. These reliability-based sensitivity factors provide quantitative measures of the importance of the design variables and their impact on structural safety. The paper illustrates the potential for using such sensitivity factors in design decisions and tradeoff studies.

Effects of welding distortions and residual stresses on the ultimate strength of long rectangular plates under uniaxial compression

The ultimate compressive strength of unstiffened plates is very important from the design and safety viewpoint. However, the ultimate compressive strength of these panels will depend quite significantly on the initial welding distortions and residual stresses. Currently, most of the researches concerning the effect of welding distortions concentrate only on the maximum initial distortion amplitude. However, many evidences indicate that the welding distortion shape could also affect the ultimate compressive strength significantly. In this paper, we adopt a combination of the elastic large deflection theory and the rigid-plastic analysis, proposed by Paik and Pedersen and later was generalized by the present authors. Various factors including the initial deflection shape which affect the ultimate compressive strength of unstiffened plates are investigated.

Reliability of jack-up platform against overturning

A probabilistic model for assessing the safety of jack-up platforms against overturning is presented in this paper. Stokes fifth order wave theory was used to determine the wave kinematics and wave forces acting on the platform. Because of the non-linearities associated with the wave forces, the overturning moment and the non-Gaussian character of the wave surface, a probabilistic non-linear response model was used to determine the probability distributions of the overturning moment and the associated extreme value statistics. The probability of overturning (failure) was then developed for short- and long-term sea conditions. In an application to an actual platform, the results indicate that the non-linearities with wave heights play an important role and have a large impact on the probability of overturning. A sensitivity analysis for the platform pointed out the importance of the drag coefficient as a major factor in determining the reliability of the platform.

Stress concentration factor in plates with transverse butt-weld misalignment

Misalignment at butt-welded joints induces bending stresses with the application of in-plane loads only. This stress concentration will have a detrimental effect on both the ultimate strength of the plate and the fatigue strength at the weld. The stress concentration factor is often represented as K 5 1 1 C(e/t), where C is called the stress concentration coefficient in this paper. In the current literature it is found that different values of C have been used, none of which were derived by the plate theory. In this paper, a linear elastic stress analysis of ship plates with a tranverse butt-weld misalignment under uniaxial compression is carried out. It is found that the stress concentration coefficient C is not a constant, but varies with the aspect ratio, the location of the misalignment in the plate and the magnitude of the nominal applied stress.

Return periods and encounter probabilities

A procedure has been developed to determine the probability of a ship encountering a severe storm. The encounter probability has been formulated in terms of the return period of the storm as well as the operation profile of the ship and the wave statistics along its route. The procedure has been applied to four ship routes, two in the Atlantic and two in the Pacific Ocean. The results showed that the ships route has a large impact on the encounter probability. The effect of changes in the degree of correlation between wave conditions in the different zones of a route was found to be relatively unimportant. The procedure is equally applicable to offshore structures. It is believed that the encounter probability offers a much better basis to derive storm design criteria than the usually used return periods of a storm.

Ship hull bottom slamming

A method is presented to evaluate the hull bending moment due to bottom slamming. Theoretical explanations and updates are given to the commonly used empirical results, and some observations are made on slamming. An energy approach combined with a strip theory is used to obtain the hydrodynamic load, and to analyze the effects of the forward velocity. Impacts of simple bodies are simulated numerically to describe these loads. The ship hull is represented as a non-uniform free-free beam, and its response is decomposed into normal modes; only the contribution of the first one is kept. In a numerical example, the bending moment during the impact is determined. It is shown that its value when the impact is over is much harder to predict. The maximum value of the bending moment, however, occurs during the impact, and is an increasing function of the vertical velocity, as expected. A simple expression is given for it.