## 3 Numerical Modeling
### Fluid-Structure-Soil Interaction
#### 3.2.2 Elements  
The present investigation entails constructing finite element models to represent the fluid-structure and structure-soil systems, which will subsequently be subjected to a comprehensive transient analysis. The present study has employed a displacement-based fluid approximation using FEM to capture the fluid-structure interaction aspects. The general-purpose ANSYS software package has been utilized for this purpose. To simulate the soil/foundation interaction, a 3D solid FEM with viscous boundary conditions has been implemented in the analysis. The phenomenon of interest entails a confluence of two distinct physical interactions: fluid-structure interaction and soil-structure interaction. The present study concerns fluid-structure interaction between a mobile structure and an internal fluid flow. The fluid-structure interaction under investigation pertains to a partially submerged tank. The soil-structure and fluid-structure interaction are complex phenomena, each encompassing complex systems in their own right. In particular, the fluid-structure interaction. After the geometric model of the tank and fluid was created, the modeling was done by simulating the materials and their properties according to the material specifications and boundary conditions. Solid 65 elements were used to model the solid concrete sections separately, while Solid 45 elements were considered to model the soil. The fluid was again modeled using the Fluid 80 elements of the ANSYS11 software [23]. The Solid 65 element is commonly used for the three-dimensional modeling of solids with or without reinforcement. This element can break in tension and pressure. The solid element capability is used when modeling with reinforcement by selecting Solid 65. Other modes include the study of composite reinforcement (e.g., fiberglass) and geological materials (e.g., rock). This element is defined by eight nodes, each with three degrees of freedom. These three degrees of freedom include transmission in the z, y, and x directions, and the material properties are also isotropic. The primary purpose of designing this element in ANSYS11 is to consider the nonlinear properties of materials, which is the difference between this Solid 65 and Solid 45 (Figure 4). This particular element, capable of modeling reinforcement in three dimensions, has been applied independently to various components such as roofs, slabs, columns, and walls. This usage has led to separate property definitions for reinforcement and materials corresponding to these components. The Fluid 80 element, a modification of the three-dimensional structural component known as Solid 45, is used for modeling non-fluid materials within tanks. This element is particularly useful in calculating hydrostatic pressure and fluid-structure interaction scenarios. As illustrated in Figure 4b, this element  
Figure 4: (**a**) Solid 65 geometry was used for the concrete sections. (**b**) Solid 45 geometry was modeled for the solid. (**c**) Prism option for both elements. (**d**) Tetrahedral option for both elements [23]. is characterized by including eight nodes, each possessing three displacement degrees of freedom. The degrees of freedom related to the interaction surface component correspond with the adjacent node degree of freedom of the tank wall, specifically in the direction perpendicular to the tank wall. Additionally, the fluid element incorporates special surface effects, conceptualized as gravity springs that help maintain the surface's position. This is achieved by adding springs to each node and positioning the springs with positive constants at the top of the element. The springs are connected from each node, having positive stiffness at the top nodes and negative stiffness at the bottom nodes. Consequently, they counterbalance the positive and negative impacts on an intermediate node from each other. At the base of the fluid, which the container needs to restrain to prevent settling, the spring ceases to have an effect as it closes off the fluid nodes and the container wall.