## 4 Comparison with Experimental Results
### Ultimate Strength  
Figure 12 shows the ultimate strength of the curved plates for various flank angles, slenderness ratio, and aspect ratio based on the result of the FE analysis. From these graphs, it can be confirmed that with the increase in flank angle and decrease in slenderness ratio, the ultimate strength of simply supported curved plates increases. However, as outlined above, this trend is different from the experimental results in which the ultimate strength of the curved plates unexpectedly changed at a certain flank angle (5\({}^{\circ}\)), slenderness ratio (2.01) or aspect ratio (1.5). This phenomenon can be explained through the previous studies, as given below. It is well known that the ultimate strength of a curved plate under longitudinal compression loading increases as the flank angle of the curved plate increases. When the compressive load equals the critical buckling stress, the plate starts to buckle. Increasing the axial load further causes an increase in the lateral deflection at the central part of the plate, and the increase in the lateral deflection causes an increase in the membrane stress; this in turn, causes stretching of the surface of plate at the bulged parts near the short edges, as shown in Figure 13[12]. In addition, as shown in Figure 13c,d, an additional membrane stress is generated in a longitudinal direction at the central part of the curved plate when the flank angle is changed from 5\({}^{\circ}\) to 10\({}^{\circ}\). This tensile membrane stress can restrain the lateral deflection of the plates and, as a result, a strength of the curved plate can be significantly improved when that curved plate has a flank angle in excess of 5\({}^{\circ}\). Figure 11: The buckling shapes of curved plates depending on the flank angle: (**a**) FE analysis and (**b**) experiment results. From a comparison with FE analysis, it can be seen that the ultimate strength of a curved plate obtained from experiment is significantly low when the slenderness ratio is 2.01. The collapse behavior and ultimate strength of a thin plate under longitudinal compressive loading is reported in previous studies [13; 14]. In those studies, the secondary buckling after the primary buckling caused a serious decrease in the ultimate strength, accompanied by a change in the buckling mode. This behavior is because of the change in the in-plane stress distribution caused by a large deflection, and it occurs because of the snap-back phenomenon, which happens under conditions such as a specific slenderness ratio, low flank angle, and a certain aspect ratio. In this respect, it can be predicted that the curved plates with a certain slenderness ratio, 2.01, experienced secondary buckling with the increase in compressive load. In addition, a previous study addressed the relationship between the curvature and ultimate strength as the aspect ratio increases [8]. This study found that the curvature increases the ultimate strength of a stiffened curved plate, especially when the plate has an intermediate aspect ratio (1.0 < a/b < 2.0). In this range, the ultimate strength of the stiffened curved plate increases rapidly at an aspect ratio of less than 1.0 and maintains a constant value at aspect ratio in excess of 2.0. Moreover, as the curvature increases, the aspect ratio has a greater effect on the ultimate strength, especially when the aspect ratio is less than 1.0, even though it is generally known that the aspect ratio has little influence on the ultimate strength of a curved plate under a longitudinal compressive load. Therefore, the ultimate strength of a curved plate with an aspect ratio of 1.5 can be regarded as being an unexpected phenomenon because this aspect ratio is the transition point between an  
Figure 12: Ultimate strength of the curved plates based on the results of FE analysis: (**a**) effect of flank angle, (**b**) slenderness ratio, and (**c**) aspect ratio. aspect ratio of 1.0 and 2.0, which determines the behavior characteristics of the ultimate strength of a curved plate.