Solution of the dam-reservoir interaction problem using a combination of FEM, BEM with particular integrals, modal analysis and substructuring

Abstract

This paper presents a new analysis procedure, which is a combination of the finite element method, the boundary element method with particular integrals, modal analysis and substructuring. The difficulty of the nonsymmetric matrix generally introduced from the boundary element method with nonsymmetric and full matrix at the interface between the finite element and the boundary element methods, is overcome by using the described procedure. A new boundary integral equation, which adopts a frequency-independent fundamental solution, is derived for solving the scalar wave equation. Modal analysis of the dam without the reservoir is first addressed. Then, the modal added-mass and added-loads are calculated by using the boundary element method with particular integrals, to solve the Helmholtz equation along with the boundary conditions, which are functions of modal shapes and generalized coordinates. After obtaining the modal added-mass and added-loads, the dam-reservoir system can be reformed in terms of modal shapes — with the reservoir empty — to obtain the natural frequencies, modal shapes and responses of the total system. Using this procedure, not only can the number of degress-of-freedom of the nonsymmetric, full matrix be significantly reduced, but there is no need to recalculate the properties of the dam without the reservoir when the level of the water changes.