The Theoretical Study And Numerical Computation Of A Large Ship’s Elastic Deformation When In Waves

With the all-round development of China’s comprehensive strength, the shipbuilding industry has become more and more important. In economics, shipping will be in the dominant position in the field of international freight in future as a kind of the most effective mode of transport. In military, the protection of our ocean territory needs us to constantly update maritime weaponry to deal with the escalating regional security situation. So the research of shipbuilding becomes more and more important. Then the simulation of many characteristics of the body of a ship when sailing in ocean is a essential part of the above research. This paper will focus on the research of the deformation of a ship caused by the crash of waves.Firstly, based on the theory of fluid dynamics and solid mechanics, the fluid-solid coupling model of a ship’s movement in the sea is built. Then the stress analysis of the bottom of the hull of a ship at sea is conducted. A mathematical model which addresses the vibration of the body of a ship in vertical direction is obtained. The main part of the model is a second-order non-linear partial differential equation.Secondly, in order to get the analytical solution of the partial differential equation obtained above, this paper gives the initial condition and the boundary condition of the partial differential equation. Perturbation method is used to expand the non-linear partial differential equation above. Based on superposition principle and homogeneitisation principle, the analytical solution of the hull’s vibration is obtained by separation of variables.Then, the added mass which is an important parameter in the slice theory is obtained by using the Green function method to make preparation for the numerical simulation. Meanwhile, a formula for numerical simulation is obtained by using the second-order difference method to discrete above zero-order and one-order partial differential equations.Finally, this paper takes the ship 907 steel as an example to get the material parameter involved in the numerical simulation. Then when separately assuming that the incident waves are sinusoidal, double sine or random waves, the real-time simulation of the deformation of a ship is conducted by using the added mass and the numerical simulation formula. And the real-time deformation of the hull along the direction of the length of a ship is obtained.The innovations of this article are:1) The fluid-solid coupling model of a ship’s moving in the sea is built, which iseasy to use and compute.2) The zero-order and one-order partial differential equation of the non-linearpartial differential equation are obtained by using small-area parameterexpansion method. The analytical solution of the zero-order equation of ahull’s vibration is obtained.3) The approximate numerical solution of a ship’s non-linear deformation inwaves is obtained.