Probabilistic Method for Predicting Ship Collision Damage

where j is the number of webs counted from the striking point. The elongation in adjacent webs is:ej= w j − w j+22s( 1) + L − L(16)sand the elongation in the struck web is:e20 i = w − w1)2i( + L − L(17)iWith these elongation and deformation results, the rupture criteria given in equations (9) and (10) are applied to all deformedwebs. The total elongation on the L i side is:eti= e+n∑e0 i ji(18)j=1and the energy absorbed in membrane tension and web deformation is:Ei= T eiti+ Pn∑wfj=1wji(19)For right angle collisions, T i always equals T m as calculated in equation (6). In oblique angle collisions, T i equals T m if L i ison the side behind the strike. Based on experimental data, Rosenblatt [1975] suggests using ½ T m ahead of the strike and thisis used in SIMCOL.For double hull ships, if the web frames are distorted because of bending, shearing and buckling of supporting struts, thedeformed web frames push the inner skin into membrane tension as shown in Figure 4 (right), and the right angle collisionmechanism is applied to the inner hull. Inner skin integrity is checked using equations (9) and (10), and the energy absorbedin inner-skin membrane tension is calculated using equation (6).In the simulation, the energy absorbed in membrane tension and web deformation during the time step is:∆ KE n = ( E1,n+ 1 + E2,n+1)− ( E1n+ E2,n)(20)Considering the friction force, F f , shown in Figure 6, and assuming the dynamic coefficient of friction is a constant value of0.15, the reacting forces and moments are:∆KEFηnFξnMnn= N= F= N ( wnfn( llξnn + 1n + 1nn+1( E=( w1, n+1n + 1= −Fd + F l− w ) + Fnηnnn+ E2 , n+1nfn− ln)= 0.15F− lηn[(w − w ) + 0.15 l − l ]In addition to the friction force, another longitudinal force, F R , the force to propagate the yielding zone, is considered, asshown in Figure 6. McDermott [1974] provides an expression for this force:11n + 1) − ( E( ll1n− w ) + 0.15 lln+1n+1n+1− ln+ E− l2, nnn− ln)− l= N)n+1nn + 1n(21)