A Ritz Procedure for Transient Analysis of Dam–Reservoir Interaction

Abstract

A simple and accurate variational formulation is proposed to study the transient dynamic responses of two-dimensional dam–reservoir system. The proposed methodology uses a simple weak formulation with Ritz procedure to reduce the governing partial differential equations of the fluid and structure to a set of ordinary differential equations. An analog procedure is then presented to exactly implement the natural boundary condition of the problem at fluid–structure interface. The Newmark time integration scheme is used to solve the resulting system of ordinary differential equations. To demonstrate the accuracy and efficiency of the proposed formulation, the problem is also solved using the finite element method (FEM). It is found that the proposed method can produce better accuracy than the FEM using less computational time. The technique presented in this investigation is general and can be used to solve various fluid–structure interaction problems.