Beam Structural Modelling in Hydroelastic Analysis of Ultra Large Container Ships

Abstract

Ultra large container ships are very sensitive to the wave load of quartering seas due to considerably reduced torsional stiffness caused by large deck openings. As a result, their natural frequencies can fall into the range of encounter frequencies in an ordinary sea spectrum. Therefore, the wave induced hydroelastic response of large container ships becomes an important issue in structural design. Mathematical hydroelastic model incorporates structural, hydrostatic and hydrodynamic parts (Senjanovic et al. 2007, 2008a, 2009b, 2010b). Beam structural model is preferable in the early design stage and for determining global response, while for more detailed analyses 3D FEM model has to be used. The hydroelastic analysis is performed by the modal superposition method, which requires dry natural vibrations of the structure to be determined. For each mode dynamic coefficients (added mass and damping) and wave load are calculated based on velocity potential. The governing equation of ship motion in rough sea specified for the impulsive (slamming) load as a transient problem is solved in time domain. The motion equation is also given for the case of harmonic wave excitation (springing), which is solved in the frequency domain. In the chapter, methodology of the ship hydroelastic analysis is described, and position and role of the beam structural model is explained. Beam finite element for coupled horizontal and torsional vibrations, that includes warping of ship cross-section, is constructed. Shear influence on both bending and torsion is taken into account. The strip element method is used for determination of normal and shear stress flows, and stiffness moduli, i.e. shear area, torsional modulus, shear inertia modulus (as a novelty), and warping modulus. In the modelling of large container ships it is important to appropriately account for the contribution of transverse bulkheads to hull stiffness and the behavior of relatively short engine room structure. In the former case, the equivalent torsional modulus is determined by increasing ordinary (St. Venant) value, depending on the ratio of the strain energy of a bulkhead and corresponding hull portion. Equivalent torsional modulus of the engine room structure is also determined utilizing the energy approach. It is assumed that a short closed structure behaves as an open one with the contribution of decks. Application of the beam structural model for ship hydroelastic analysis is illustrated in case of a very large container ship. Correlation of dry natural vibrations analysis results for the beam model with those for 3D FEM model shows very good agreement. Hydroelastic analysis emphasizes peak values of transfer functions of displacements and sectional forces