Fluid‐structure interaction analysis by the finite element method–a variational approach

Abstract

SUMMARYWe have developed a finite element method for analysing non-linear and linear fluid-structure interaction problems by working directly from a variational indicator based on Hamilton's principle. We restrict our analyses to inviscid, irrotational and isentropic fluid flows. The variational indicator includes the fluid potential energy due to gravity, which is often ignored. This and the fact that we consider our domain to be variable provide us with the capability to model free surfaces.We demonstrate the effectiveness of both linear and non-linear finite element formulations in analysing a variety of fluid-structure interaction problems.

Response of endlessly long shipping channel due to earthquake

“…As an example case we will assume the ground supported rectangular endlessly long concrete shipping channel, with the length 2L = 5 m and the height Hw = 3 m, where E = 3.4·10 10 Pa, density ρ = 2 540 kg/m 3 . The endlessly long channel surrounding walls have the uniform thickness of 0.25 m. The channel base slab is h = 0.4 m thick.…”

Natural vibrations and stability of a stationary or rotating circular cylindrical shell containing a rotating fluid

“…Representing the symmetric and antisymmetric unknown quantities in (10) in terms of the nodal displacements, we obtain the following expressions for the shell and fluid finite elements…”

“…Later, in [9] a potential-pressure formulation has been proposed for solution of static and dynamic problems and for frequency analysis of acoustic fluids. With a non-linear potential-density formulation developed in [10] one can take into account the fluid flows and gravitational effects on the free surface. However, the application of this approach is restricted to the case of relatively small displacements of the boundary.…”

A Semi-Analytical Coupled Finite Element Formulation for Composite Shells Conveying Fluids

“…For instance, Everstine [7] proposed a velocity potential formulation for a symmetric finite element solution of transient wave propagation problems, while Olson and Bathe [8] proposed a f À u À p finite element formulation in order to eliminate the rigid body mode and enable the solution of static problems. Kock and Olson [9] introduced an Eulerian form of the non-linear velocity potential-density formulation and the significant feature is the derivation of the formulation from a single unified variational principle. Nitikitpaiboon and Bathe [10] extended the work of Olson and Bathe [8] by developing a non-linear u À f À r À l arbitrary Langrangian-Eulerian formulation in which both the velocity potential, f; and the density r are employed.…”