Finite element and difference formulations of transient fluid-structure problems

A finite element formulation is developed for the two dimensional problem of structural elements in a fluid environment, subjected to high, transient pressures. The emphasis is on short duration loads, so a Lagrangian description is used. The finite element equations for the hydrodynamic fluid are first derived from a conservation of energy approach: it is also indicated how the use of a weak form of the partial differential equations leads to the same form. The equations are then compared to the widely used finite difference equations as developed by Wilkins. It is shown that Wilkins' use of a contour integral to develop the difference formulas also corresponds to the development of a weak form, and that the resulting discrete equations are identical to the finite element equations, both at interior mesh points and along prescribed pressure boundaries. The major difference between the two methods appears to be a matter of form.