Session K.pdf - Clarkson University

from each board, going from stem to periphery. The further bend of an ice field resultsin occurrence of a concentric crack with the center on stem and radiusr = 1/α; α = 4ρ g ,D3Ehwhere α – parameter of a bend of an ice plate on the elastic basis, D = –212(1 −ν )cylindrical rigidity of an ice plate, ρ – density of water, g – gravitational acceleration,α – the module of normal ice elasticity, h – thickness of an ice plate, ν – Poisson factorof ice.Formation of a concentric crack does not result in loss of carrying ability of an icecover. First, it is because at big radial sizes ice plates (at the further load) continue bending,and second, with occurrence on coast of a crack of the significant contact pressureinterfering ice breach. Therefore character of connection between loading and a deflectionat kinematic load has a step kind. To each step of the curve loading-deflection correspondsoccurrence of the next concentric crack, and new cracks are formed from peripheryto the center (stem). The bend occurs until there will come a breach of ice on thenearest to stem concentric crack.Because of nonlinearity of the ice cover destruction diagram it is necessary to knowbreaking force value, but it is insufficient information for the description of interactionof the vessel with ice, and it is also necessary to have information on the work necessaryfor ice cover destruction.At modeling of a vessel movement in a continuous ice field, using division of full resistanceinto components we shall consider resistance of destruction of ice R p . Necessarycondition of ice destruction modeling is geometrical similarity of destruction picture inthe plan at which performance the number and an arrangement of ice contact points withthe case at model movement will be identical with natural. Similarity of destruction picturesis determined by similarity of tensely deformed conditions (TDC) of ice plates forwhich definition we shall use differential equation of plates bend, on the elastic basisresulted in a dimensionless form.where wDρgL4∇ w + w =40 , (1)= w L – a dimensionless deflection; L – characteristic linear size in the plan.From the equation (1) follows, that the TDC of an ice cover for a nature and models willbe similar ifAsρn = ρ mandDidem4 =ρgLg = const expression it is possible to transform to(2)DDnmL=L4n4mwhere λ – the module of geometrical similarity.371= λ4, (3)