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The objective of this work is to find and implement a method to calculate a long-term response of the wave-induced bending moment with the non-linear effects accounted within the computational time reasonable for the industrial applications. A general background of the topic as well as the motivation to undertake this study are described in order to outline the starting point of the presented dissertation. As shipbuilding is an industry with a very long history and tradition, a design process throughout the years was based on the experience and modifications of the existing designs by extrapolation to the newly constructed vessels. Nowadays, Classification Societies have undertaken the role of setting up the rules that should be followed to create a new safe design. Evidently, the regulations regarding the assessment of the wave-induced hydrodynamic loads acting on the ship hull are also specified by the Classification Societies. The estimation of hydrodynamic loads is usually provided in the form of empirical formulas derived based on a great variety of existing ship designs and as such, this method is of course highly simplified, [1]. Even though that approach is sufficient for numerous conventional designs, it is not very accurate for more advanced vessels and can lead to improper estimation of acting loads. The solution to that problem offered by Classification Societies, is to apply very high safety factor which would obviously result in not optimised design. An alternative to this approach is to perform a direct hydrodynamic loads calculation which allows to create a safe and optimised design. However, a direct analysis requires of course much longer computational time, very often too long to be acceptable for the industrial applications. Nowadays, since the computational power is increasing and the direct analysis becomes more feasible, a growing interest is directed towards it by many parties. The most common method to evaluate the hydrodynamic loads with direct computations is to perform a frequency domain analysis within the potential flow theory assumptions. This method can provide the solution quite fast, but it is a fully linear approach. If the non-linear effects should be accounted it is necessary to perform calculations in a time domain, yet this type of analysis requires much longer computational time, making this approach impractical for industrial projects. Numerous research studies thus focus on developing the methods that can account for the non-linear effects in an efficient way, providing satisfactory results within reasonable computational time. An attempt to implement such an approximate approach is made within this thesis and the achieved outcome is presented in the following chapters.
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