## 2 Methods
\[f_{f}=\frac{2}{1+C_{r}/C_{f}},f_{r}=\frac{2}{1+C_{f}/C_{r}}, \tag{7}\]  
where: \(Q_{s}\) is the heat distribution of the welding heat source; \(q_{f}(x,y,z)\) is the first half of the ellipsoid heat distribution amount at a point \((x,y,z)\); \(q_{r}(x,y,z)\) is the second half of the ellipsoid heat distribution amount at a point \((x,y,z)\); \(a\) is the half width of the distributed heat source; \(b\) is the welding heat source depth; \(c_{f}\) is the length of the first half of the ellipsoid; \(c_{r}\) is the length of the other half of the ellipsoid; \(f_{r}\) is the strength distribution on the first half of the ellipsoid; \(f_{r}\) is the strength distribution on the other half of the ellipsoid; and \(x,y,\) and \(z\) are the moving coordinates of the heat source. Since the welding heat source in MSC.MARC software adopts the ellipsoid Gaussian heat source distribution model depicted in Figure 2, the welding simulation for a moving straight line and for a heat source applied in a single direction can be directly used in a simulation study. However, if the heat source spreads in a non-linear pattern or does not conform to the ellipsoid Gaussian normal distribution, another subroutine should be designed and inserted in MSC.MARC to play the role of this heat source [19]. Our research studies the simulation of single-V butt welding using two steel plates 300 \(\times\) 125 \(\times\) 6 mm of type SUS304 with a 60\({}^{\circ}\) groove angle. The dimensions of the plates follow the specifications in AWS D1.62007--Structural Welding Code--Stainless Steel for a horizontal sample plate welding simulation, as shown [20]. Since the geometric shape of the welding pieces is quite simple, inserting a 2D drafting frame designed by Solidwork into MSC.MARC was sufficient to build a grid plan. After a 2D grid was generated for all four sides, additional mesh density was added to the area of the welding bead, as shown in Figure 3a,b. Because welding deformation can be partially inhibited by adding jigs to the workpieces, this applied downward pressure is also incorporated into the simulation (Figure 4). Note that the jig model is considered a rigid body. Figure 3: \(Cont.\)  
\[q(x,y)=\frac{3Q_{s}}{\pi u_{a}^{2}}e^{(\frac{-3x^{2}}{\pi^{2}})} \tag{2}\]0 Ellipsoid Gaussian heat source distribution model. The simulation assumptions for this article are as follows: (1) the thermal and mechanical characteristics of the welding test pieces of type JIS SUS304 are equal in all directions [21]; (2) the welding filler material is of the same type as the test pieces [22]; (3) the jigs used to inhibit deformation are steel jigs; and (4) the influence of gravity is ignored. Note that two independent plates are used for the simulation analysis. When a high-calorie welding filler is directly applied to the workpieces, the working plates are easily separated due to thermal deformation problems and cause divergence in the simulation analysis. So, we use a pre-welding spot at both ends of the welding bead to stabilize the simulation analysis for the two separate test pieces, which is similar to the procedure during actual welding. Figure 5 shows the pre-welding spots to attach the two pieces together, and Figure 6 represents the stabilization welding spots inserted into the simulation model, which is a key point in the numerical analysis. In general, the deformation produced on the welded plates is in a saddle-bulge shape vertically and has a twisted formation horizontally, as shown in \[q(x,y)=\frac{3Q_{s}}{\pi u_{a}^{2}}e^{(\frac{-3x^{2}}{\pi^{2}})} \tag{2}\]1 This study mainly implemented 6 mm thick SUS304 steel plates as realistic test pieces for CO\({}_{2}\) GMAW. Table 1 presents the practical welding parameters for the test workpiece with and without jig constraints. Variation in the parameters is due to the manual nature of the welding process. Table 2 shows the simulation parameters of the welding heat source for the test workpiece.