# Understanding the Seismic Resilience of Metallic Cylindrical Tanks Through Parametric Analysis
## 2 Finite Element Modeling, Analysis and Verification  
The analysis of the seismic behavior of steel tanks using the finite element method (FEM) involves addressing an FSI problem, which presents several challenges. One of the main difficulties in solving this problem is the need for specialized finite element (FE) formulations capable of handling the large distortions in computational meshes that arise during simulations of dynamic fluid-structure interactions. To address this issue, several FE formulations for FSI problems are discussed and experimentally validated for use in this research. Particular emphasis is placed on the ALE method, as it is widely regarded as the most effective approach for solving FSI problems in fluid-structure simulations. The ALE method, which allows for the handling of mesh deformations, was specifically chosen for the analyses conducted in this study due to its ability to accurately model the behavior of both the fluid and the tank structure under seismic loads. This method ensures that the evolving geometry of the system during seismic excitation is properly captured, allowing for more accurate predictions of the tank's response to seismic events. In this research, the general-purpose FE code LS-DYNA is employed to study the FSI problem of deformable steel tanks, which are completely filled with fluid and subjected to seismic loading at the base. The interactions between the fluid and the structure are modeled using the ALE method, which is well suited for handling large deformations in both the fluid and the structure. This method enables an accurate representation of the fluid's behavior and the tank's deformation under seismic excitation. The use of the LS-DYNA FE code allows for the incorporation of both material and geometric nonlinearities, providing a more realistic simulation of the tank's dynamic response. Additionally, LS-DYNA performs dynamic analyses using an explicit time integration scheme based on the central difference method, which is particularly effective for simulating high-speed dynamic events like seismic loading. This combination of advanced modeling techniquesand robust numerical methods ensures a comprehensive and accurate assessment of the seismic response of steel tanks under extreme conditions. Numerical techniques for simulating tank-fluid interaction problems are highly effective tools for evaluating the seismic response of these systems, as they can significantly reduce the need for time-consuming, costly experimental tests, which are typically conducted under specific boundary and excitation conditions. Once validated against experimental data, numerical simulations can serve as reliable design tools to assess various system configurations subjected to different earthquake ground motions. In this study, experimental tests are used as reference solutions for validating the tank models then used in the parametric evaluation of the resilience. Before developing the FEMs for the case study tanks, the chosen modeling approach is verified by comparing the results of FE analyses with experimental data obtained from two separate tests. The first test is the pioneering work by [PERSON] [41], which involved a small-scale tank model. As a continuation of this research, [PERSON] and [PERSON] [42] conducted a series of experiments on the same model subjected to three different scaled earthquake motions with varying boundary and soil conditions. This study focuses solely on a model tank with an open top, anchored support, and a rigid foundation. The second experimental test considered is presented in [PERSON] [43], which describes a shake table test performed on an open-top cylindrical tank. [PERSON]'s work also includes numerical results, allowing for a direct comparison between the experimentally observed behavior and the predictions obtained from an LS-DYNA model developed according to the previously described modeling approach.