## 2 Target Structures and Crack Scenarios  
Most hull girder collapse accidents caused by cracks occur in container ships, with these cracks typically propagating from the side shells. The target structure in this study is the outer side shell of a 9300 TEU container ship, composed of high-tensile steel (AH32) and located in the midship section. The analysis considers two structural components: (1) a plate, located between longitudinal stiffeners and transverse frames and (2) a stiffened panel, located between longitudinal girders and transverse frames. Tables 1 and 2 present the material properties and dimensions of the target structure.  
Cracks are generally classified as longitudinal (horizontal), transverse, vertical, or oblique (angular) cracks [9; 31; 32]. For angular cracks, the use of different layouts of geometry according to crack size and direction may introduce uncertainties by the element shape and size in FE modeling. This study examines longitudinal, transverse, and combined (bidirectional) cracks. To analyze the effect of crack size relative to the structural dimensions, three levels of crack sizes (minor, moderate, and major) were selected randomly. In all  
\begin{table}
\begin{tabular}{c c} \hline
**Description** & **Dimension** \\ \hline Yield strength, \(\sigma_{\text{Y}}\) & 315 MPa \\ Elastic modulus, E & 205,800 MPa \\ \hline \end{tabular}
\end{table}
Table 1: Material properties of target structure.  
\begin{table}
\begin{tabular}{c c} \hline
**Description** & **Dimension** \\ \hline Plate length, L & 4200 mm \\ Plate breadth, b & 860 mm \\ Plate thickness, t\({}_{\text{p}}\) & 16 mm \\ Panel breadth, B & 6880 mm \\ Number of stiffeners & 7 \\ Web height, h\({}_{\text{w}}\) & 300 mm \\ Web thickness, t\({}_{\text{w}}\) & 11 mm \\ Flange breadth, b\({}_{\text{f}}\) & 90 mm \\ Flange thickness, t\({}_{\text{f}}\) & 16 mm \\ Plate aspect ratio & 4.884 \\ Plate slenderness ratio & 2.103 \\ Radius of gyration & 98.268 mm \\ Column slenderness ratio & 0.532 \\ \hline \end{tabular}
\end{table}
Table 2: Structural dimensions of target structure.  
cases, the cracks were modeled as through-thickness defects, meaning that the crack depth was equal to the full thickness of the plate or web where the crack was located.  
Crack types were as follows:  
* A longitudinal crack is a crack in the plate length direction.
* A transverse crack is a crack in the breadth (for plates) or web height (for webs) direction.
* A combined crack is a crack in the longitudinal and transverse directions.  
Crack sizes were as follows:  
* A longitudinal crack extends 10%, 25%, and 50% of the plate length.
* A transverse crack extends 10%, 25%, and 50% of the plate breadth (or web height).  
As illustrated in Figure 1, longitudinal and transverse cracks were assumed to be located at the center of the structure, while a combined crack was considered to propagate from the midpoint of one side of the structure. For transverse and combined cracks in the stiffened panels, both the plate and the web stiffener developed cracks in the transverse and vertical directions. In the case of a longitudinal crack, the plate and the web were completely disconnected at the crack region by assigning independent nodes to each part, ensuring that the structural discontinuity caused by the crack was properly represented.