Finite element and boundary element methods for the seismic analysis of liquid storage tanks

Abstract

A computer program is developed to analyse axisymmetric liquid storage tanks subjected to lateral ground motion, modelling the interaction between the tank structure and the fluid. The program is designed to handle open and closed axisymmetric tanks of any shape, and in the present study, tanks involving cylindrical polar, spherical and spheroidal curvatures are presented to illustrate possible applications of the program. In the coupled fluid-tank interaction problem formulation, the effects of tank flexibility and liquid sloshing are taken into account. As the first phase of this study, a quadrilateral shell finite element and subsequently a corresponding axisymmetric shell finite element are developed. These shell finite elements are formulated using the shell theory of Koiter (1966) on the two-dimensional plane using curvilinear surface coordinates. The second phase of this study involved the use of an axisymmetric shell element with an axisymmetric boundary element having a cos 0-type variation of the potential and its derivative (i.e. φ and dφ∕dn). The boundary element models the fluid region, and is combined with the axisymmetric shell finite element to model the fluid-tank system as a coupled problem. In order to combine the equations for the fluid region with the equations for the tank structure, an equivalent finite element mass matrix for the fluid region is derived from the boundary element matrices of the fluid region. This equivalent mass matrix is then combined with the shell finite element mass matrix to obtain the mass matrix for the combined fluid-tank system. The finite element matrix equation of motion is then solved for the combined problem. The system of equations of motion for the combined fluid-tank system is solved in the frequency domain via the Fast Fourier Transform. The solution is then obtained in the time domain via the inverse Fast Fourier Transform.