## 3 Development of Methodology Using Finite Element Analysis  
### Review of FEA Packages  
To evaluate the blast resistance performance through numerical analysis, the evaluator must first understand the loading effect of blasts on the structure; it is also necessary to understand the structure's behavior when subject to blast loading [20; 21; 22; 23; 24; 25]. Since the numerical analysis of explosions concerns structural behavior that manifests in a significantly short period of time, there are additional considerations that differ from typical static and dynamic numerical analyses [3; 26; 27; 28; 29; 30; 31; 32].  
There are mainly two types of computer software for analyzing the response of structures subject to blast loading: uncoupled analysis and coupled analysis. First, considering uncoupled analysis, the structure is assumed to be a rigid body and the blast pressure acting on the structure is obtained,  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Protection** & **Construction** & **Damage Aspect** & **Damage Aspect** \\
**Level** & **Method** & & **Aspect** \\ \hline \multirow{2}{*}{A} & Elastic design & \multirow{2}{*}{Microcrack} & \multirow{2}{*}{0\(\sim\)2\({}^{\circ}\)} \\  & (Working stress design) & & \\ \multirow{2}{*}{B} & Elasto-plastic design & \multirow{2}{*}{Protection for human lives and interior possible (crack, crush)} & \multirow{2}{*}{2\(\sim\)6\({}^{\circ}\)} \\  & & & \\ \multirow{2}{*}{C} & Plastic design & Severe collapse (separation of \\ \multirow{2}{*}{C} & (limit design) & concrete form the reinforcement bar) & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Design consideration of the protective facilities.  
Figure 3: Rotation angle at its supports.  
after which the blast pressure is applied to the structure as a load and the structure's response is calculated. As the interactions between the structure and blast pressure are not considered and the structure is assumed to be a rigid body, this method tends to overestimate the blast loading. In coupled analysis, the ground or air, the medium that transfers the blast pressure is modeled and the blast pressure load and corresponding structural response is calculated through a fluid-structure interaction analysis. While this method can obtain more accurate structural responses, it has the disadvantage of being a lengthy analysis.  
Commonly used commercial programs in this field include AUTODYN, DYNA3D, LS-DYNA, ABAQUS, BLASTX, CTH, FEFLO, FOIL, SHARC, ALE3D, and CONWEP, among which AUTODYN and LS-DYNA are the most used in Korea. LS-DYNA is based on structural element (solid) analysis and has the advantages of solid collision analysis at low/medium speeds, large deformation/large displacement analysis, nonlinear analysis, and drop test analysis [33]. AUTODYN, a representative analysis program capable of coupling fluids and solids, has the advantages of large deformation/large displacement analysis and nonlinear analysis, in addition to the analysis of shockwave transmission according to fluid characteristics, structural behavior according to solid/fluid coupling, and high-speed shock. Hence, LS-DYNA can be used for uncoupled analysis, whereas AUTODYN can perform coupled analysis. The results of coupled analysis for structural responses to blast loading are typically more accurate. Therefore, this study will use the AUTODYN software package to model an actual K9 artillery position and evaluate its degree of protection.