Simulating Dynamic Motion Of Ship InContact With Elastic Mooring ElementsBy A Nonlinear Algorithm

Abstract

A nonlinear algorithm for simulating dynamic motion of ship in contact with elastic mooring elements was developed. During small time steps all parameters in ship-water-spring system can be taken as linear. Force balance in the system is described by linear second order differential equations for six degrees of freedom. Nonlinearities are taken into account by re-evaluating all affecting forces and mass, damping and stiffness matrices at every time step. Ship is described as a rigid body with three symmetry planes. Water effects are taken into account as added mass and damping coefficients. Solution consists of two parts, which are summed up. In the first part steady, slowly changing and aperiodic forces are taken into account. Such forces are wind, current, ice and second order wave forces. The second part of solution is for first order wave forces. The program can be used to calculate mooring forces and energies caused by ships. Various kinds of affecting parameters can be included at the same time without building up a heavy element model of ship and water around it. So far, on the other hand, the principle of superposition is used. In some situations, for example, in simulating combined effect of waves and current more sophisticated theory should be employed.