the bulk cargo was modelled using 8-noded solid elements. In the case of grounding the cargo was modelled using the masses acting directly on the nodes of the mesh representing the cargo deck. It was thus possible to obtain the structural response of the cargo deck which was not over-stiffened as in the case of collision. In the latter case this effect was negligible considering defor-mations of the side and bow parts of the colliding barges. Size of the finite element model varies from 60000 up to 330000 elements, depending on the analysed case. The following material models were applied in the analysis: (i) steel – for modelling of shells, plates and beams; (ii) polyurethane foam – for modelling of filling in the spaces; (iii) model of the sandwich structure; (iv) incompressible model of water; (v) model of loose ground for modelling sand. The material model corresponds: (i) for barge A to steel with yield stress equal to 235 MPa and (ii) for barges B and C yield stress 315 MPa. During grounding hydrodynamic effects are not taken into account. Due to the fact that the inertial effect of water associated with bow part is negligible with respect to the bow part, and the bow part emerges during grounding, the influence of the vertical motion of the associated water is not considered. Hydrodynamic ef-fects occurring between the barge bottom and the river bed is also not accounted for. Model of ground Friction, inertia and deformation of ground under the barge are included in the model. Two material models were used for modelling these phenomena: (i) inelastic material with hysteresis based on the foam model, prop-erties of the model allow to represent the effects of friction between the barge bottom and the river bed; changes of pressures are proportional to the volumetric changes of the elements what corresponds to the sub-stantial part of material resistance, representation of the barge deceleration and associated forces was obtained by forces due to material compression and model of the contact of the bottom and ground (ii) material using the Murnaghan equation (Eq. 2) for solid elements; primar-ily the material model is used for liquids. Model of water In the analysis of collision it is assumed that the influ-ence of water on the investigated phenomena is limited to the inertia effect of added mass of water at non-struck side of the hit barge (collision case). The considered water model include distance of 50 m behind the barge side. Behaviour of water is described by the Murnaghan model ( ) [ ] 1 B p p 0 0 − ρ ρ + = γ (2) where ρ /ρ0 is the ratio of density and initial density; γ = 7; and B is – water bulk modulus. This material model corresponds to the liquid of increased compressi-bility. The model is suitable for representation of hy-drodynamic effects, where the flow velocity is much less than the speed of sound and the effects related to compressibility can be neglected. In the mathematical modelling the considered material model well represents behaviour of the liquid subject to both gravity and iner-tial force. Scenario of collision of two barges All the barges have been subject to the same impact generated by the striking barge which was barge A in all the cases. The struck barge (barges: A, B, C, in turn) goes with the absolute speed of v2=12.0 km/h following the current. The velocity of the current is 4 km/h, water depth is 2.5 m. The striking barge, going with the absolute speed of v1=12 km/h strikes the side of the struck barge in the midship part at the angle of 45°– Fig. 4. Loading condi-tions of both barges: bulk cargo uniformly distributed. Deadweight of struck barges A - 250 t, B and C - 200 t, 内河运输船舶碰撞与搁浅的数值模拟英文文献和中文翻译(4):http://www.751com.cn/fanyi/lunwen_63533.html