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


coefficient of empirical formulae is modified for improving the accuracy of assessment results.


Area Ⅲ 2. 2.1 NUMERICAL ANALYSIS PRINCIPLE DIMENSIONS of SHIP


A bulk carrier with 5,000t DWT (deadweight tonnage) is adopted in the collision study, whose overall length, molded breadth and molded depth are 97.0m, 15.8m and 7.5m, respectively. The ship bow model is showed in Figure. 1. The weight of vessel with full and ballast loads are 6,500t and 3,250t, respectively.


Area I Area Ⅳ (a) Ship impact rigid bridge


AreaⅡ


(b) Ship bow


Figure. 2 FE mode of the whole ship and the internal structure of the bow


Figure. 1 Section of the ship bow 2.2 FE MODEL


The explicit finite element method of ANSYS LS- DYNA is adopted to simulate the collision process between vessel and rigid bridge pier, in which the Belytschko-Tsay shell element (Belytschko et al, 2006) is adopted to simulate the plate of ship structure, and the beam element (161) is used for stiffeners. The ‘automatic surface contact’ method is adopted to simulate the contacts between the ship and bridge pier, in which the static coefficient of friction is set as 0.3 and the dynamic coefficient of friction is not accounted for. The mesh size of vessel should be fine enough to obtain reliable results with acceptable computation resource. Tornqvist & Simonsen (2004) and Alsos & Amdahl


(2007)


recommended that the ratio of length to thickness of shell element is between 5 and 10 to capture the local stress and strain area. The fine mesh size at ship bow is around 100mm at ‘Area I’ to consider the structural behaviours of buckling and folding in Figure. 2, whose ratio of length to thickness of shell element is around 8. The gradient mesh sizes (Figure. 2 (a)) are applied for the other part with ‘Area Ⅱ’ 200mm, ‘Area Ⅲ’ 300mm, ‘Area Ⅳ’ 400mm to reduce the element number. The elements with length control are meshed freely by triangle and rectangle shapes. The total number of element is 56757.


The FE model of the ship is presented in Figure. 2. Poisson’s ratio, density and tensile strength of steel material are 0.3, 7,850kg/m3 and 370 MPa, respectively. The yield stress of plastic material model is defined by


  =+ −


yp 0 EEh


EEh (1)


where initial yield stress σ0 is 235 MPa; Young’s modulus E is 2.06×1011 MPa; hardening modulus Eh is 1.18×109 MPa; εp is the plastic strain.


The plastic failure strain of material for bulk carrier is 0.34 according to the element size of the bow structure (Glykas, 2001). Cowper-Symonds formula is adopted to consider the strain rate of material as following (Jones, 1989).


 


0 ' 0


1


=+P C


1


 


 where 0 ’ (2) is the dynamic flow stress relate with plastic


strain rate  , and σ0 is the associated static plastic flow stress. C and P are constant values for ship steel, where C and P are 40.4 s-1 and 5, respectively (Jones, 1989).


In NORSOK N-004 (2004), the anti-collision design of bridge is divided as ductile design, strength design and


A-428


©2019: The Royal Institution of Naval Architects


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