## 1 Introduction  
Welded structures are widely used in engineering. The fatigue life of welded joints is of great concern for a number of years. Stress distributions at welds and fatigue behavior of welded joints are continually investigated [1; 2; 3; 4; 5]. Various codes and standards as well as recommended practices (e.g., [6; 7]) are widely adopted for fatigue evaluation of welded joints. The fatigue life of a welded joint is significantly influenced by the stress concentration effect at welded joints [8; 9; 10; 11]. The study of characterizing the stress concentration effects and achieving effective notch stress calculation at welds are important research directions in the field of predicting the fatigue life of welded components. In recent years, meshfree methods are attracting more and more interests in computational mechanics for its advantages such as good self-adaptability. With the rapid development of meshfree techniques, various problems in science and engineering have been solved by meshfree methods [12; 13; 14; 15]. Meshfree methods have been great potential topics and trends in computational mechanics. However, the stress solutions obtained by meshfree methods are often influenced by parameters used in these methods such as shape parameters, dimension of the influence domain and number of field nodes. Especially, the sensitivity of the stress solutions at notch location of weld toe increases significantly due to the presence of stress singularity at geometric discontinuity. As a result, the conventional meshfree methods are not realistic for effectively determining the notch stresses or stress concentration at the weld toe. Fortunately, in order to solve the problem that the conventional finite element method (FEM)-based stress solutions at the weld toe were strongly influenced by the type and size of elements, [PERSON] proposed a mesh-insensitive structural stress method (or named Battelle structural stress method) [16]. Based on the mesh-insensitive structural stress method, the stress concentration factor was consistently characterized and notch stress intensity factor at weld toe was effectively calculated [17]. The equivalent structural stress-based master S-N curve method was then developed to evaluate the fatigue life of weld components [8]. Taking advantage of the mesh-insensitive structural stress method, the mesh-insensitive structural strain method was then proposed extending the mesh-insensitive structural stress method to a low-cycle fatigue regime [18]. Since 2007, the mesh-insensitive structural stress method has been adopted as an alternative fatigue evaluation method for welded components by ASME Section VIII Division 2 Code [19]. In recent years, the theory and engineering application of the mesh-insensitive structural stress method has been carried out continuously [20; 21; 22; 23; 24]. The aim of this study is to propose an improved 2D meshfree radial point interpolation method (RPIM) whose stress solutions are insensitive to parameters such as shape parameters, dimension of the influence domain and number of field nodes by introducing the idea of above mesh-insensitive structural stress method. The essential idea of improved RPIM is that the stress solutions were obtained directly from field nodes forces to avoid using derivatives of shape functions. The novelty of our studies is to provide an approach to apply global weak-form meshfree method in consistently and effectively calculating SCFs and notch stress intensity factors at weld toe. Early meshfree methods originated from the collocation methods in 1930s [25; 26]. The well-known smooth particle hydrodynamics (SPH) method was proposed for solving problems in astrophysics [27; 28]. In recent decades, various meshfree methods have been proposed, such as the element free Galerkin (EFG) method [29], meshfree radial point interpolation method (RPIM) [30; 31], reproducing kernel particle method (RKPM) [32; 33], material point method (MPM) [34; 35], etc.