Long-Term Properties and Combinations of Stochastic Hull Girder Loads on Ships
- Author(s): Petricic, Martin
- Advisor(s): Mansour, Alaa E
- et al.
This dissertation presents a novel simulation-based method which provides a consistent and rational framework for long-term hull girder load combination analysis. During its lifetime, which is typically a period of 20 to 25 years (long-term), a ship structure will be subjected to many different dynamic loads. Most of them are caused by very harsh and constantly changing ocean environment and they are random. Therefore, methods of classical statistics and time series analysis have to be applied in order to analyze the structural response to these loads. Many of currently available methods rely on the assumption of weak stationarity of the wave elevation process. This assumption usually holds for a period of up to three hours (short-term) and these methods cannot be used to analyze long-term statistical properties of the loads and their combinations. Long-term methods that can handle the non-stationarity of the wave elevation process often involve many assumptions and require the knowledge of short-term probability density functions of loads or their linear and nonlinear combinations as well as the joint probability density functions of multiple random variables having an impact on these loads.
The method presented in this dissertation is based on efficient multi-voyage simulations of properly correlated hull-girder loads. It relies on a comprehensive statistical model from which nine relevant variables that have an impact on the hull-girder load spectral densities can be simulated or sampled using the rejection sampling technique. These nine variables are: significant wave height, zero crossing wave period, prevailing wind and wave direction, ship's relative heading with respect to waves, ship's location, season of the year, ship's speed, voluntary and involuntary speed reductions in severe sea states and the ship's loading condition. The rejection sampling can significantly decrease the number of sea state and operational profile combinations that have to be considered in the long-term analysis. Non-stationary wave elevations during the ship's entire life are treated as a sequence of different short-term weakly stationary Gaussian stochastic processes, each of which is two hours long. Hull girder sectional loads during each short-term period are efficiently simulated from the load spectral densities taking into account their relative phase differences. Multi-voyage long time series of various load combinations, including the nonlinear ones, are obtained and their correlation structure and other statistical properties are examined. Nonlinearities in the vertical bending moment (VBM) and the hydroelastic response of the ship in the form of springing and whipping are also included in the simulation. Slamming events are determined from the linear motion analysis and the subsequent whipping response of the structure is simulated in time domain using a combination of trapezoidal and finite element methods to numerically solve dynamic Timoshenko beam problem. Nonlinearities have a significant effect on the simulation time. However, neglecting the super and subharmonics of small amplitudes significantly reduces simulation time while retaining reasonable accuracy. This makes it possible to use simulation even at the initial stages of ship design process.
Although some assumptions are necessary when calculating the loads on a ship structure, the main advantages of the simulation method are that it doesn't make assumptions about the statistical nature of these loads, and it enables nonlinear combinations of linear and nonlinear loads even when their theoretical short-term probability distributions don't exist.
Three different ship types; container ship, tanker and bulk carrier, navigating in the North Atlantic, North Pacific, and between Europe and Asia are used to demonstrate the capabilities of the simulation method in three different areas of hull-girder structural analysis: load combinations, extreme value, and fatigue analysis. Correlation structure between all six sectional loads is examined as well as some linear and nonlinear load combinations. The effect of ship route, damping ratio, slamming extent, hydroelasticity, and nonlinearities on the long-term exceedance probabilities of the VBM are also examined. Finally, the fatigue behavior of a selected container ship is studied on all three routes. The total fatigue damage caused by the vertical bending stresses is separated into damage caused by low- and high-frequency VBM components. The high-frequency part is further divided into the damage caused by linear springing, nonlinearities (including nonlinear springing), and whipping.
Linear springing does not have a significant effect on the long-term exceedance probabilities of the VBM, but has a significant effect on the fatigue life of the structure. Nonlinearities, on the other hand, have a significant effect on the exceedance probabilities of the VBM and its extreme values as well as on the fatigue life of the structure. Damping ratio has a relatively significant effect on the nonlinear component of the VBM, but does not significantly affect the long-term exceedance probabilities of the total VBM since the damping effects are only pronounced in moderate sea states with steep waves. Nonlinearities are also largest in these sea states.
Whipping alone has a relatively small effect on the exceedance probabilities of the VBM and also on the fatigue life of the post-Panamax container ship analyzed in this work. This is attributed to the lack of strong positive correlation in time between whipping peaks and the peaks of the global VBM. More research is needed on studying the phase relationship between these peaks for different ship types, sizes and routes.
Simulation method results agree very well with the full-scale measurements taken on board ships in service in terms of linear and nonlinear VBM exceedance probabilities and fatigue life predictions. For ships studied in this work, the simulation outperforms some existing and commonly used long-term methods in terms of accuracy.