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,
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