A Localized Variational Principle and Hybrid Element Formulas for Fluid-Structure Coupling Harmonic Vibrations

When solving exterior problems of Helmholtz or Laplace equation, such as potential flow in infinite fluid field, one can not carry out spatial discretization to infinite because the finite element method (FEM) is an approach only used in a finite domain. So an artificial boundary should be introduced to truncate the infinite field into a finite one. However, it is difficult to give appropriate conditions on the artificial boundary. Based on the fluid-structure coupling theory, a localized variational principle is presented in this paper for analyzing fluid-structure interaction problems under harmonic excitations in two-dimensional infinite fluid field. The infinite field is divided into two parts by an auxiliary circle, inside which the structure and its neighboring fluid are computed by FEM, and outside which an analytical solution is used. By means of this variational principle, all governing equations and boundary conditions, especially the continuity on the interface between the numerical and analytical solution as well as their derivatives, are satisfied automatically. At the same time, the numerical solutions are incorporated with the analytical solution via hybrid element formulas derived. A given example for incompressible fluid demonstrates the validity and high efficiency of the proposed approach. In addition, interface of MARC (a general-purpose FEM software) is adopted to improve the efficiency of programming and computation, which provides a new simple way to solve similar problems. This approach can also be extended to a more general situation of 3-D problem in which a closed sphere replaces the 2-D circle as the artificial boundary, and analytical solution of 3-D Helmholtz or Laplace equation replaces 2-D solution. It can be applied in future studies on structure-acoustic problems of submerged structures.