• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.60-68
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• 1991

The updated Lagrangian Finite Element Method is introduced to analyse rigid body-fluid impact problem which is characterized by incompressible Navier-Stokes equations and impact-contact conditions between free surface and rigid body. For the convenience of numerical computation, velocity fields are splinted into vicous and pressure parts, and then the governing equations and boundary conditions are decomposed in accordance with the decomposition. However, Viscous stresses acting an the solid boundaries are neglected on the assumption that very small velocity gradients may occur during extremely small time interval of the impact. Four coded quadrilateral elements are used to discretize the space domain and the fully explicit time-marching algorithm is employed with a reasonably small time step. At the beginning of each time step, contact velocity of the rigid body is computed from the momentum balance between the body and the fluid. The velocity field is then computed to satisfy the discretized equations of motions and incompressibility and contact constraints as well as an exact free surface boundary condition. At the end of each time step, the fluid domain is updated from the velocity field. In the present time stepping numerical analysis, behaviour of the free surface near the body can be observed without any difficulty which is very important in the water impact problem. The applicability of the algorithm is illustrated by a wedge type falling body problem. The numerical solutions for time-varying pressure distributions and impact loadings acting ion the surface are obtained.