engleski

Advanced beam model for hydroelastic analysis of container ships

Combination of the beam structural model with the 3D hydrodynamic model is a rational choice for hydroelastic analysis of large container ships in the early design stage since the detailed technical documentation is not available yet. Main problem of container ship response is coupling between horizontal bending and torsion. In order to increase accuracy of the hydroelastic analysis an advanced beam structural model is developed, which takes into account both shear influence on bending and torsion, [1]. The strip element method is used for determining normal and shear stress flows, and stiffness moduli, i.e. shear area, torsional modulus, shear inertia modulus, and warping modulus, [2]. Their values are calculated by program STIFF. Few formulations of the modal restoring stiffness are known starting from simple one to more complex (Price, Newman, Malenica, Molin etc.).Nowadays three of them are actual, as shown in Table 1. Huang & Riggs formulation, Eq. (1), started from geometric stiffness with additional hydrostatic terms obtained by linearization of the governing equations. It is generally valid for ship and offshore structure. By applying zero strain constraint Eq. (1) is reduced to Eq. (2) valid only for rigid body modes. The exactly the same set of formulas, Eq. (2), is obtained by a direct derivation in which rigid body and elastic modes are treated in the same manner. It is shown that Eq. (2) is valid for an elastic body with low initial stresses. Eq. (3) is obtained by comprising Eq. (2) with geometric stiffness in order to achieve general formulation. Hence, two additional terms are obtained comparing to Eq. (1), and their contribution has to be investigated, [3]. For hydroelastic response (springing in the frequency domain and transient in the time domain) program HYELACS has been developed by comprising program DYANA for beam structural model and HYDROSTAR for 3D hydrodynamic response. Numerical procedure is checked by correlation analysis of the calculated and measured results for a segmented barge, which is recently used as a benchmark for such analyses. Modeling of ship structure by a beam is illustrated in case of 7800 TEU container ships. Two main problems arise, i.e. contribution of transverse bulkheads to torsional hull stiffness, and 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 strain energy ration of a bulkhead and corresponding hull portion [4]. A similar energy approach is used for determining equivalent torsional modulus of relatively short engine room structure. It is assumed that a short closed structure behaves as an open one with contribution of decks, [5]. In addition distortion of engine room structure is analysed, which is caused by different shear stress distribution at boundary of transverse bulkhead, i.e. from closed engine room and open hull side. The bulkhead distortion is used as the boundary condition for bending of the deck girder, as a beam on elastic support. Hence, the total normal stress in deck girder consists of two parts: one due to restrained warping and another due to bending imposed with distortion. Determination of stress concentration is a prerogative for fatigue analysis. The advanced beam theory is checked in the case of prismatic pontoon with ship-like cross-section, for which purpose 3D FEM analysis is performed. It is found that shear centre and twist centre are two different points due to shear influence on torsion. Dry natural vibrations of the advanced beam model and 3D FEM model of the complete ship show very good agreement. Hydroelastic response emphasizes peak values of transfer functions due to resonances at the encounter frequency. Transfer function of sectional forces have to converge to zero value as the encounter frequency approaches to zero, as in the case of rigid body analysis. This is achieved by applying the consistent restoring stiffness.

Hydroelasticity; Container ship; Beam model

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