An efficient computational procedure for the dynamic analysis of liquid storage tanks

Abstract

A computationally efficient numerical model is developed in this study for evaluating the dynamic behavior of liquid storage tanks. This model has higher complexity than the Housner model (which corresponds to the simplest and most popular approach for approximating the behavior of rectangular and circular tanks) but still enjoys high computational simplicity to facilitate implementation in practice, while it is applicable to virtually any kind of tank geometry, providing at the same time a high degree of accuracy. In the proposed model, the liquid is assumed to be inviscid, incompressible and irrotational, and its motion is completely characterized by a velocity potential function. Thus, the Continuity and Equilibrium equations characterizing this motion take the form of Laplace and Bernoulli equations, respectively. The Laplace equation is solved through a 2D finite element scheme, and is then combined with the Bernoulli equation through the velocity potential function condensed at the free surface of the liquid. Numerical details for the practical implementation of the proposed scheme are discussed, whereas the approximation is shown to provide results with high accuracy for the dynamic behavior of different type of tanks when compared to the Housner model and a full finite element implementation. As shown in the examples considered the computational efficiency of the proposed model is such that extensive parametric studies can be performed with small numerical effort, which in turn makes the proposed model very attractive not only for analysis purposes but also for the design of liquid storage tanks and other related devices such as tuned liquid dampers.