engleski

Hydroelastic analysis of large container ships by beam structural model

The importance of mathematical models for ship hydroelastic analysis grows with the design of ever larger container ships which have specific design and exploitation characteristics. Compared with other merchant ships, they are characterized by relatively lower torsional stiffness, which in combination with encounter sea states related to their higher speed of approximately 27 knots can cause resonance effects. Generally, harmonic hydroelastic problem can be solved at different level of complexity and accuracy, i.e. by coupling 1D FEM structural model with 3D BEM hydrodynamic model, or by coupling fine mesh 3D FEM model with an appropriate hydrodynamic model. The former approach seems to be appropriate for preliminary design stage when the detailed design of ship structure is not known yet, while the later one should be used for final strength checks. Within EU FP7 project Tools for Ultra Large Container Ships (TULCS) a sophisticated beam structural model for its application in ship hydroelastic analysis has been developed. Hydroelastic model is bases on modal superposition method, and coupling is realized by transmitting nodal displacements from beam model to the wetted surface. Beam structural model takes into account shear influence on torsion, following analogy with shear influence on bending. Unique and from an engineering point of view relatively simple procedure for taking into account contribution of transverse bulkheads and engine room structure has been also developed. For determination of ship cross-section parameters necessary for vibration analysis a special software STIFF has been developed and used, while for hydroelastic analysis program HYELACS is applied. Beside above mentioned beam structural model, it includes also 3D hydrodynamic model based on potential flow theory and encounter frequency approximation. Consistent restoring stiffness for ship structures has been derived based on variational principle and method of virtual displacements is included into hydrostatic part of hydroelastic model. Theoretical contributions are illustrated within two numerical examples which include complete hydroelastic analyses of 7800 TEU and 11400 TEU container ships. In both cases, the validation of advanced beam model is checked by correlation analysis with vibration response of the fine 3D FEM models and excellent agreement is achieved, both in case of vertical and coupled horizontal and torsional vibrations. In addition, ship hydroelastic response assessed by sophisticated beam model is compared with the results of fully coupled 3D FEM + 3D BEM hydroelastic analysis. The obtained transfer functions of sectional forces confirm that the developed model is very useful numerical tool for the designer and represents a reasonable choice for determining wave load effects on ULCS, in early design stage.

Container ship; Hydroelasticity; Finite element method; Beam model; Restoring stiffness; Ship response

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