## 1 Introduction  
Fatigue has been researched for decades as one of the most common failure modes of mechanical structures. The fatigue damage assessment approaches of welded structures include the hot spot stress method, effective notch stress method, etc. The hot spot stress is related to the overall geometry and load conditions of the welded structure, but does not include the stress concentration caused by local factors, such as weld size and welding defects [1, 2]. [PERSON] et al. [3] used the hot spot stress method to calculate the hot spot stress value at the welding toe, and a modified S-N curve, considering the thickness effect of the main board, was proposed to predict the fatigue life of the sample. [PERSON] et al. [4] compared the hot spot stress calculation result with the nominal stress from shell elements in a welded bogie frame, and their results showed that the hot spot stress is higher than the nominal stress. [PERSON] et al. [5] clarified the limitations of the hot spot stress method. These researchers proposed that the hot spot stress method could effectively evaluate toe failure based on the geometric discontinuity of the welding structure, but could not appraise the fatigue failure caused by defects on the weld root and inside the weld. This method is suitable for the fatigue analysis of the toe of nonstandard structural details and complex welding joints. The effective notch stress method uses a specific radius to replace the notch at the weld root and toe and calculates the effective notch stress at the weld toe and weld root by the finite element method (FEM). This approach avoids the occurrence of singular stress values at the sharp gap and can be used for fatigue evaluation at the weld root and toe [6; 7]. It can also determine whether fatigue failure occurs at the weld root or toe by assessing principal stress. [PERSON] et al. [8] estimated the fatigue life of welded joints, and their results indicated that this method can rationalize the thickness effect observed in these joints. [PERSON] et al. [9; 10] obtained the stress concentration coefficient of a welded joint gap by using a formula method and numerical method. These researchers obtained an S-N curve with a lower slope than the FAT225 curve recommended by the International Welding Society (IIW). At present, if the effective notch stress method or hot spot stress method is adopted for the analysis of a car body, then the required grid division of the weld area is exceedingly small, leading to an excessively large number of grids at the weld area. Furthermore, an abrupt change in the grid size in the transition area between large and small grids may occur, which is inappropriate in engineering. This method is not sensitive to the grid and has a high calculation accuracy. The effects of stress concentration, plate thickness, and load mode on fatigue life can be considered simultaneously [11]. [PERSON] [12] used the structural stress method to predict the fatigue life of the welded structure of rail vehicles. The calculation steps were complicated, and the resulting data could not be directly mapped to each node in the weld model. The nominal stress method has been broadly used in fatigue assessment [13; 14; 15; 16]. This method references a defined component cross-section and neglects the local peak stresses resulting from geometrical notches or load applications. The fatigue strength of a structure can be directly estimated according to the nominal structural stress and the S-N curve corresponding to different notch grades. This method has three advantages when using the FEM to solve engineering problems: the methodology is straightforward; the mesh quality requirement is low; the nominal stress value is accessible. However, the dispersion between the fatigue life and nominal stress amplitude is large, and it is difficult to obtain accurate prediction results. The multiaxial stress method [17; 18] is more comprehensive and accurate than the uniaxial stress method.