## 2 Numerical Model and Adopted FE Techniques
### Verification of the FE Techniques  
To verify the applicability and effectiveness of the employed FE technique, the ultimate strength of the three types of stiffened plates with various stiffeners and dimensions are carried out compared with the results provided in the ISSC'2000 VI.2 benchmark calculations [11].  
The ultimate strength ratio \(\chi\) and the column slenderness ratio \(\lambda\) are introduced for relative analysis, defined as follows:  
\[\chi=\sigma_{U}/\sigma_{Y}\ \text{and}\ \lambda=\sqrt{\frac{\sigma_{Y}}{ \sigma_{E}}}=\frac{a}{\pi\sqrt{I/A}}\sqrt{\frac{\sigma_{Y}}{E}} \tag{7}\]  
where \(\sigma_{U}\) is the ultimate strength, \(\sigma_{E}\) the elastic buckling strength, \(I\) the moment of inertia, \(A\) the cross-section area of the plate of the stiffened plate (i.e., stiffener with attached plate), respectively; while \(\sigma_{Y}\) and \(E\) are the yield stress and Young's modulus of the steel, respectively.  
The results obtained for the ultimate compressive strength, together with those from other benchmark calculations, are presented in Appendix A. Among these calculations, [PERSON] used an analytical method that was based on the Rahman-Hughes' model and Perry-Robertson formula; [PERSON] performed the study using an in-house FE code 'ULSAS' which enables one to simulate collapse behavior of structural members and systems accounting for the influences of yielding and ultra-large deflection; and [PERSON] adopted the commercial FE code ABAQUS for elastic-plastic large deflection analysis.  
The results for the ultimate strength of the three types of stiffened plate with/without welding residual stress are plotted against column slenderness ratio in Figures 5-7. It can be seen that the trend and distribution are in general agreement with those obtained by the ISSC'2000 III.1 calculations.  
In comparison with the calculations by [PERSON] [11], the agreement between the numerical results obtained for the ultimate strength accounting for welding residual stress is better than those without. For a few stiffened plates, the difference is relatively large, namely, 19%. These differences probably resulted from the fact the method accounting for initial deflection and welding residual stress, and also that the nonlinear numerical iteration method adopted in the in-house code ULSAS is different from those used in ABAQUS.  
Figure 4: Assumed residual stress distribution in the fillet weld.  
The differences from the results obtained by [PERSON] [11] are relatively large. This is because the analytical method of [PERSON] was derived based on certain failure modes, and the nonlinear material and geometrical properties of the structures under ultimate state of compression cannot be accurately accounted for. As a result, the method is efficient and easy to apply, while the accuracy is limited. However, despite the relatively large differences, the trend of the ultimate strength versus column slenderness ratio obtained in the present study is similar to that obtained by [PERSON].  
Figure 5: Results for the ultimate strength of flat-bat stiffened plate versus column slenderness ratio compared with the ISSC’2000 Report [11].  
Figure 6: Results for the ultimate strength of angle-bar stiffened plate versus column slenderness ratio compared with the ISSC’2000 Report [11].  
Figure 7: Results for ultimate strength of tee-bar stiffened plate versus column slenderness ratio compared with the ISSC’2000 Report [11].  
According to the verification study, it can be seen that the accuracy of the numerical method is, in general, satisfying, and is suitable for the analysis of ultimate strength of stiffened plates subjected to compressive load.