# Understanding the Seismic Resilience of Metallic Cylindrical Tanks Through Parametric Analysis
## 2 Finite Element Modeling, Analysis and Verification
### FEM of Manos and Clough Experimental Tank [42]  
The tank model used in the experiments was a 1/3 scale model of a steel prototype with a radius of 1.83 m and a total height of 1.83 m. The tank was filled with water (density of 1000 kg/m\({}^{3}\)) to a height of 1.53 m. The tank was constructed from aluminum with a density of 2700 kg/m\({}^{3}\), an elastic modulus of 71,000 MPa, and a yield stress of 100 MPa. The thickness of the aluminum bottom plate and the shell section near the bottom was 0.002 m, while the second shell course had a thickness of 0.0013 m. A steel wind girder, shaped in an L configuration, was placed on top of the second shell course. The geometry of the tank is shown in Figure 1a.  
In the experiment, the shaking table motion was derived from the horizontal component of the El Centro 1940 earthquake with a peak acceleration of 0.50 g. The motion was scaled with respect to time by a factor of \(1/\sqrt{3}\) to meet similitude requirements. For the numerical verifications, the same tank model with an open top, anchored support, and resting on a rigid foundation was used. The numerical model retained the same dimensions and material properties as the experimental tank. During model development, the effect of element size and formulation, for both the tank and the fluid, was carefully investigated and adjusted to accurately capture the fluid-structure interaction. The tank was discretized using four-noded, fully integrated shell elements with two integration points through the thickness. The resulting finite element model consisted of 5793 nodes, 890 shell elements, and 4320 solid elements, as shown in Figure 1b. An explicit nonlinear transient analysis was performed to replicate the experimental test. The time histories of pressure (excluding hydrostatic pressure) at three specific locations (at \(R=1.83\) m with heights of 0.05 m, 0.45 m, and 0.86 m above the tank base) during the experiment were presented in Figure 2. These results were used to verify the numerical model and compare the simulated pressures with the experimentally observed values. Pressure is a key parameter in the study of storage tanks because it plays a crucial role in evaluating the dynamic response of the tank to seismic loading. Figure 2 presents a comparison of the pressure distribution at three different levels along the height of the tank: at the base, one-third of the height, and approximately half the height. This comparison is crucial, as it captures the pressure variation along the tank wall during seismic loading, offering valuable insights into the fluid-structure interaction over time. By showing the overlap between the experimental results and the numerically evaluated data, the figure clearly demonstrates that the numerical model successfully replicates the actual behavior of the fluid inside the tank. The pressure profiles at these three heights highlight the nonlinear behavior of the fluid's displacement. The significant variation in pressure over time, especially at higher fluid levels, emphasizes the complex dynamics involved in fluid motion during seismic events. The agreement between the experimental and numerical results confirms that the model effectively captures the real-world fluid behavior. This validation is key to understanding the dynamic response of the tank under seismic loading and supports the accuracy of the proposed numerical methods. In summary, Figure 2 summarizes these findings, illustrating the alignment between experimental and numerical data across different fluid heights, and reinforces the robustness of the methodology used in this research.  
Figure 1: [PERSON] and [PERSON] experimental tank dimensions (**a**); and finite element model (**b**).