## 4 Conclusions  
In the present study, the ultimate strength of welded stiffened plates under the predominant action of axial compression was investigated by non-linear finite element analysis using the commercial finite element code ABAQUS. Stiffened plates were employed that were built with three types of stiffener, namely flat-bar stiffener, angle-bar stiffener and tee-bar stiffener, and with various column slenderness ratios provided in the ISSC'2000 VI.2 benchmark calculations. Fabrication-related imperfections, such as initial deflections and residual stresses, are accounted for in the simulations. All calculations are performed by the Arc-length method with the large displacement option switched on. The ultimate strength of the stiffened plates built-up in Steel S315, obtained by the present nonlinear FEA, is in good agreement with the ISSC'2000 VI.2 benchmark calculations. The adopted nonlinear finite element  
Figure 12: The increase ratio of ultimate strength of the stiffened plates plotted against column slenderness ratio.  
method can satisfactorily simulate the buckling behavior and collapse of stiffened plates accounting for initial deflection and welding induced residual stress.  
In addition to the S315 steel, another three grades of steels commonly used in shipbuilding, namely, steels S235, S355 and S390, were employed to investigate the effect of steel grade on the ultimate strength of welded stiffened plates. The comparison of the results shows that: (1) increasing the yield strength of the material (using steels of higher grades) can effectively improve the ultimate strength of stiffened plates, except for those with large column slenderness ratios. For stiffened plates with column slenderness ratios between 0.4 and 0.8, the positive effect (the ratio of the ultimate strength to the yield strength) is somewhat dispersed between 0.2 and 0.8, with an average of 0.4. (2) Welding-induced residual stress may reduce the ultimate strength of the stiffened plates. In comparison with the ultimate strength of stiffened plates without accounting for the welding induced residual stress, the maximum reduction can be 10%. However, the influence of the welding induced residual stress decreases as the column slenderness ratio increases. For stiffened plates with column slenderness ratios smaller than 0.8, the average influence is about 4%.  
A simplified model for the distribution of welding induced stress is adopted in this study, and this model bears a difference from the actual residual stress distribution. A possible approach to obtain more accurate results for the influence of steel grade on the ultimate strength is to simulate the welding induced residual stress by nonlinear FEM analysis of coupled thermo-dynamics.  
Conceptualization, C.L.; Methodology, C.L. & X.Z.; Modeling and Computation, S.D. & T.W., Analysis, C.L. & W.X.; Writing--original draft preparation, X.Z.; Supervision, C.L.; Funding acquisition, C.L. & W.X.  
This research was funded by NSFC, grant number 51679055 & 51779055 and part of the work was carried out under the project grant 0104038.  
The authors would like to thank all the reviewers for their valuable comments.  
The authors declare no conflict of interest.