Three-dimensional modeling of curved structures partially or completely containing and/or submerged in fluid

The dynamic behavior of a three-dimensional flexible structure in inviscid incompressible stationary fluid is studied numerically. A hybrid finite element is developed by using classical thin plate theory and finite element analysis, in which the finite elements are rectangular four-noded flat shell, having 5 degrees of freedom per node. The displacement functions are derived from Sanders' thin shell equations. The velocity potential function and Bernoulli's equation for liquid yield an expression for fluid pressure as a function of nodal displacement of the element and inertial force of the quiescent fluid. An analytical integration of the fluid pressure over the element leads to mass matrix of fluid. Calculations are given to illustrate the dynamic behavior of rectangular reservoir containing fluid, as well as a totally submerged blade.