Three-dimensional sloshing: a consistent finite element approach

Abstract

This paper presents a new computational methodology based on Legendre's polynomials to predict the slosh and acoustic motion in nearly incompressible fluids in both rigid and flexible structures with free surface. Here, we have used a finite element formulation based on Lagrangian frame of reference to model the fluid motion derived using Hamiltonian equation of the fluid system. We formulated three hexahedral finite elements based on strain fields expressed in terms of extended Legendre's polynomials. Sloshing and acoustic motion of liquid is investigated using these newly formulated elements and inf–sup test is performed on these new elements to check the performance of these elements in modeling sloshing under two severe constraints, namely incompressibility and irrotationality. Comparisons of slosh and acoustic frequencies, and mode shapes with exact solutions are given. Dynamic analysis with earthquake and harmonic kind of forcing function is carried out to validate the formulated hexahedral elements to analyze the sloshing response. Numerical results obtained with these new finite elements, and with the present finite element formulation of the mathematical model agree well with the exact solution and as well as with published experimental literature.