FSI methods for seismic analysis of sloshing tank problems

The long-period components in earthquake ground motions, which attenuate gradually with distance, can induce sloshing waves in the liquid containment tanks although they are located far away from the seismic source. The resulting sloshing waves generate additional forces impacting the wall and roof of the tanks and may cause extensive damage on the tank structure. Numerous examples of tank damages due to sloshing of fluid have been observed during many earthquakes. Nevertheless, the effect of sloshing is usually primitively considered in most of the seismic design codes of tanks. On the other hand, the derivation of an analytical solution for the sloshing response of a liquid storage tank subjected to harmonic excitation includes many assumptions and simplifications. Most of the analytical solutions in the recent literature assumed the containing liquid to be invicid, incompressible and irrotational, and the tank structure to be an isotropic elastic plate with uniform stiffness, mass and thickness. Even though, experimental works are necessary to study the actual behavior of the system, they are time consuming, very costly and performed only for specific boundary and excitation conditions. However, appropriate numerical simulation using fluid structure interaction techniques can be used to predict the hydrodynamic forces due to the high-speed impacts of sloshing liquid on a tank wall and roof. These simulations can reduce the number of experimental tests. The nonlinear finite element techniques with either Lagrangian and/or Eulerian formulations may be employed as a numerical method to model sloshing problems. But, most of the Lagrangian formulations used to solve such problems have failed due to high mesh distortion of the fluid. The arbitrary Lagrangian Eulerian techniques are capable of keeping mesh integrity during the motion of the tank. In this study, an explicit nonlinear finite element analysis method with ALE algorithm is developed and sloshing phenomenon is analyzed. The analysis capabilities of the method are explained on a technical level. Although, the developed numerical procedure is applicable to deformable structures, the accuracy of the method is validated with the existing analytical formulation derived from potential flow theory as well as the experimental data carried out on rigid tanks when subjected to harmonic and earthquake ground motions. High consistency between numerical and experimental results in terms of peak level timing, shape and amplitude of sloshing waves is obtained not only for non-resonant excitation but also for resonant frequency motion.