Abstract

A numerical method is proposed for the seismic response analysis of rectangular and cylindrical tanks accounting for non-linear hydrodynamic effects. The equations of motion are mapped from the physical to the computational domain by means of a change of variable. The numerical solution is then obtained by means of finite differences. The system of second order equations obtained from the finite difference discretization are linearized using the Newton method and solved numerically by means of the biconjugate gradient method. The numerical formulation was applied to study the response of tanks subjected to ground motion records from the Mexico earthquake of 19 September 1985, obtained in Mexico City. Response results are given in terms of wave height on the liquid surface, and shear force and overturning moment at the base wall, and are compared with those obtained for the linear solution.

Abstract

We present a Lagrangian formulation for coupled thermal analysis of quasi and fully incompressible flows and fluid-structure interaction (FSI) problems that has excellent mass preservation features. The success of the formulation lays on a residual-based stabilized expression of the mass balance equation obtained using the Finite Calculus (FIC) method. The governing equations are discretized with the FEM using simplicial elements with equal linear interpolation for the velocities, the pressure and the temperature. The merits of the formulation in terms of reduced mass loss and overall accuracy are verified in the solution of 2D and 3D adiabatic and thermally-coupled quasi-incompressible free-surface flow problems using the Particle Finite Element Method (PFEM). Examples include the sloshing of water in a tank and the falling of a water sphere and a cylinder into a tank containing water.