Spurious free displacement-based fluid elements for fluid-structure interaction analysis

Abstract

In this dissertation, liquid sloshing effects in rectangular storage structures with an internal body are investigated for earthquake loadings. A Lagrangian approach is presented, while an Eulerian approach is also studied for the purpose of comparison. In the conventional Eulerian approach, the fluid field is formulated using the velocity potential and the fluid motion is analyzed by solving a boundary value problem. In the Lagrangian approach, however, the fluid as well as the storage structure is modeled by the finite element method, so that fluid-structure interaction may be analyzed effectively. Spurious free 4-node displacement-based fluid elements are developed for sloshing analysis of contained liquid. To remove spurious modes in the free vibration analysis, a combined usage of rotational penalty and mass projection is proposed in conjunction with the one-point reduced integration for a 4-node fluid element. A procedure is also established for determining the required number of elements with rotational penalty, so that low frequency sloshing modes may be retained while the spurious modes can be removed in the free vibration analysis. The performance of the fluid element is examined for several cases of the acoustic vibration of fluid in a rigid cavity and the sloshing in liquid storage structures. Seismic analysis of rectangular liquid storage structures is carried out by the response spectra method with a focus on the fluid-structure interaction including the effects of the wall flexibility and a submerged internal body. Comparison with the results obtained by the Eulerian approach using velocity potential shows that the present method gives good results. It has been also found that the effect of the wall flexibility can increase the forces due to the fluid motion on the wall very significantly.