## 1 Introduction
Thermal-induced residual stress/warpage is one of the main concerns in the WAAM process. Much research has been performed to resolve this issue. [PERSON] et al. [15] developed the numerical model to study the thermal-induced warpage and proposed the deposition strategy for reduction in buckling of the thin plate. [PERSON] and coworkers [16] performed X-ray diffraction (XRD) and contour method analyses to study the influence of strain hardening and heat treatment on the residual stress and warpage of thin plates. [PERSON] et al. [17] examined the effects of welding speed on material properties of a 6061-T6 aluminum joint. [PERSON] and coworkers [18] studied the influence of the welding speed on microstructure evolution in dissimilar Al/Cu sheets. Analyses suggest that extremely high welding speed could lead to strong laser weldment. [PERSON] et al. [19] investigated the influence of the process parameters for carbon steel welding such as laser power, scanning speed, and focal point position on the welding performance and reliability of weld structure. Numerical analysis has provided insights into the understanding of the process, properties, and performance of AM parts. [PERSON] et al. [6] performed FE simulations to analyze the thermal and stress distributions of WAAM of Al-4046. In their simulations, sequentially coupled thermomechanical constitutive equations were employed. [PERSON] et al. [20] performed sequentially coupled FE simulations to study how the deposition sequence affects the thermal profiles and production of residual stress and distortion. [PERSON] and coworkers [21] conducted FE simulations to understand the effects of the welding sequence on the distortion of stiffened plate panels. [PERSON] et al. [22] conducted a finite element study on the effects of clamping position on the residual stress generation in WAAM. [PERSON] et al. [23] implemented a molten pool model into their numerical model for the study of residual stress in DED of aluminum alloy 2024. In their model, the shape and rate of deposition can be monitored, allowing the feeding rate to be taken into account in WAAM simulation. [PERSON] et al. [24] proposed the modified inherent strain method to investigate the residual distortion of a rectangular contour wall. The proposed model allows the prediction of the inherent strains, which can be applicable to the part model for the DED simulations. [PERSON] et al. [25] developed the numerical model for WAAM of the 2 Cr13 part considering the transient thermal transfer and thermo-elastoplastic coupled behaviors of material. From their combination study of numerical simulation and experimental characterization, the relationship among thermal profiles, microstructure evolutions, and defect production was analyzed. [PERSON] et al. [26] investigated the residual stress and distortion generation of Ti-6 Al-4V and Inconel 718 WAAM components. In their study, the flow of molten metal and the shape and size of molten pool were analyzed. [PERSON] et al. [27] developed the numerical model to analyze the fluid flow and temperature evolution in multilayer deposition of WAAM. In their model, the equations of fluid mechanics and the solid-liquid phase change were incorporated with the molten pool dynamics. The prediction of the shape and size of wire deposition from the numerical simulations was validated by comparison with experiment measurements. The various types of heat source model have also been studied in simulations of the WAAM process. [PERSON] and coworkers [28] implemented the double ellipsoidal and the cylindrical volumetric heat source models to their numerical model to examine thermal profiles and residual stress in the hybrid laser-GMA welding. [PERSON] et al. [29] used the heat source model of Gaussian distribution in direct metal deposition of Ti6 Al4V. The laser absorption coefficient, the shape factor of the Gaussian distributed heat flux, and the laser spot radius were taken into account in the model. [PERSON] et al.