Trans RINA, Vol 161, Part A4, Intl J Maritime Eng, Oct-Dec 2019


bulk carrier (No. 3, 5 and 7), the elastic deformation coefficient almost decreases linearly as the ship deadweight ton or displacement increases. Thus, it can be estimated that elastic deformation coefficients C1 of the ship can be set to 0.00013, which is used to modify the assessment formula (Eq. (6)). C2 is the elastic deformation coefficients of bridge, and thus is equal to zero when the bridge pier is assumed as rigid.


Table 1 Elastic deformation coefficients of various ship bows (Chen, 2006)


No. 1


2 3 4 5 6 7 8


Ship types 79.54m


passenger ship


5,000t multi- purpose ship


10,000DWT bulk carrier 10,000DWT container ship


35,000DWT bulk carrier


40,000DWT oil tanker


50,000DWT bulk carrier


65,000DWT oil tanker


Displacement (t)


5120 9839


18917 17670 45807 50500 62500 76189


V (m/s) 5.35


5.0 5.0 3.0 5.0 6.7 3.0 5.0


C1( / )m kN 0.000250


0.000120 0.000120 0.000047 0.000093 0.000071 0.000070 0.000022


10 20 30 40 50


The coefficient in Eq. (9) is regressed by least square method. The coefficient of multiple determinations could be used to assess the approximating accuracy of developed formula, which is given by:


R SS = SS


2


R T


(10)


where SST is total sum of squares and SSR is regression sum of squares.


TB-Revised FEM


0 50 100 Ek 150 /MJ


Figure. 10 Comparison between the FE analysis and revised formula from TB requirement


0.2 0.3 0.4 0.5 0.6


Base on FEM Fitting function


The present mainly focuses on the modification method of formula. Since the modification of TB formula in Eq. (9) base on the bulk carrier with 5,000t DWT, which could be used to assess the impact force for similar type and displacement of ship. Actually, there exist many kinds of types, bows and displacements of ship, which would influence the elastic deformation coefficient. The various ships should be systemically investigated for update the formula in TB requirement (TB, 2005) for application. Meanwhile, it is suggested that the elastic deformation coefficient should be expressed as function of dynamic kinetic energy of striking ship.


0 50 100 Ek (MJ)


Figure. 9 Kinetic energy reduction factor by fitting power function


To regression of the kinetic energy reduction factor, more load cases with different initial kinetic energy are also considered in the FE analysis. The kinetic energy reduction factor in Eq. (8) is shown in Figure. 9, which decreases with the increase of initial kinetic energy. A power function is adopted as approximating expression, which is given by:


=   + 5.28 10 ( 116.48) 0.248 6 E −3.38 + (9) 150 200


The results of the fitting function (Eq. (9)) and FE analysis are shown in Figure.10. The coefficients (R2) of multiple determinations are 0.98, which illustrates that the fitting functions give well agreement. The average impact force assessed in the formula of TB requirement by revising elastic deformation coefficient are compared with that in FE analysis as shown in Figure. 10. Their results are also very close. The ratio of the mean value and variance of the revised TB formula to numerical simulation are 0.97 and 1.2%, which indicates that the elastic deformation coefficients assessed in Eq. (9) could significantly improve the accuracy of TB formula.


However, the approximating accuracy of regression method by fitting data significantly depends on the range of design sample data. Although the range of kinetic energy of striking ship is already very wide, Eq. (9) is developed by one ship. The stiffness of ship will be different for various type vessel (Woisin, 1976), which


200 250


©2019: The Royal Institution of Naval Architects


A-433





FA


/MN


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