engleski

Comparative study of hydroelastic response of large container ships determined by different formulations of restoring stiffness in FEM technique

Nowadays, great effort is put into investigation of fluid – structure interaction (FSI), both from hydrodynamic and structural point of view. This fact is very important for ship structural design, since its real dynamic behavior, instead of quasi-static, is considered as relevant one. This fact is even more prominent in the case of Ultra Large Container Ships (ULCS), since the FSI effects, namely springing and whipping, are even more pronounced due to increasing vessel size and speed and reduced torsional stiffness. In order to analyze such physical phenomena one has to apply hydroelasticity theory capable for mathematical modeling of complex wave – ship interaction problems. Hydroelastic mathematical model is composed of structural, hydrodynamic and hydrostatic model. The governing modal matrix differential equation for coupled motions and vibrations is solved in frequency domain by the modal superposition method. One of the complex issues related to the hydroelasticity analysis is restoring stiffness, which is determined within hydrostatic model. Three current restoring stiffness formulations for homogenous body are recognized: consistent, complete and unified one which is in the case of thin-walled structures identical to the complete one. Each component of the current restoring stiffness formulations is determined by the integration of shape functions in FEM technique over the structural elements (beam, triangle, quadratic elements). Such approach is applied as more accurate one comparing to the Gauss point integration commonly used for the determination of hydrostatic part of the restoring stiffness. Special approach needed to include lumped mass (mass elements) as well as geometric stiffness into the restoring stiffness is recognized and developed. Derived geometric stiffness consists of three constituents, ordinary one and two additional in plane terms needed to satisfy ship stability conditions and is based on the application of membrane shape functions both for membrane and deflection d.o.f. with neglected rotational d.o.f. Program RESTAN was coded based on the developed theory and its application was tested in the case of the regular thin - wall barge. Also restoring stiffness analysis of real life ship was performed and the influence of different restoring stiffnesses formulations (consistent one with distributed mass, consistent one with lumped mass and complete one) on ship response was illustrated. Finally, consistent restoring stiffness with distributed mass or lumped mass, as well as complete one can be used with different level of accuracy. Some numerical instability related to the complete restoring stiffness formulation induced by the geometric stiffness has been indentified.

container ship; hydroelasticity; finite element method; restoring stiffness; geometric stiffness; ship response

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