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

The dynamic behavior of a 3D thin flexible structure in inviscid incompressible stationary fluid is studied numerically. A finite element is developed using a combination of classical thin plate theory and finite element analysis, in which the finite elements are rectangular four-noded flat shell with five 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 produces the virtual added-mass matrix of fluid. Calculations are presented to illustrate the dynamic behavior of a rectangular reservoir containing fluid as well as a completely submerged blade.