## 2 Method
### Welding Simulation  
The simulation method utilized in this paper consists of two approaches. Initially, the fast response method was utilized for screening purposes. This approach integrates the new heat source model for keyhole mode laser welding presented in [34] with the Convex Volumetric Shrinkage (CVS) method for welding distortion simulation presented in [35]. The combined approach focuses on accurately simulating weld-induced distortions while ensuring computational efficiency. First, the heat input during welding is modeled using a combination of a Gaussian surface heat source and an upside-down cone to represent the \"nail head\" and the keyhole regions, respectively. The Gaussian heat source simulates the diffusive surface heat distribution, while the cone simulates the deeper penetration caused by the laser's keyhole effect. The heat input is governed by the following equations:  
\[Q_{s}=\eta f_{s}Q,\ Q_{c}=\eta(1-f_{s})Q \tag{1}\]  
where \(Q\) is the total power, \(f_{s}\) is the surface heat fraction, and \(\eta\) represents the efficiency.  
Next, the Convex Volumetric Shrinkage (CVS) method is employed to simulate the residual distortion induced by welding. The CVS method consists of three main steps: First, a steady-state thermal analysis is performed to calculate the temperature distribution along the weld path using a moving reference frame. The temperature above the melting point is used to identify the melt zone. Second, the melted zone is determined by identifying all nodes with temperatures above the melting point. A convex hull is generated around these points to define the region of melted material. Thirdly, the melted zone is subjected to volumetric shrinkage as the material cools. This step assumes linear elastic shrinkage to predict the residual stresses and distortions. The temperature drop from the melting point to room temperature is applied uniformly to the nodes within the melted zone. This combination of a new heat source model with the CVS method provides an efficient, hence accurate, approach to simulate welding processes. This method is validated against experimental data, showing agreement in both weld bead geometry and residual distortions [34]. The CVS method significantly reduces computational time compared to full transient thermo-elasto-plastic simulations, making it suitable for applications requiring numerous simulations, such as variation analysis. To implement the above approach, a FEM simulation model was established, simulating the welding outcome with the above approach and screening the locating points.  
The second approach involves full thermoplastic and transient simulation solving the heat transfer and the mechanical deformation at time steps for simulation of weld sequences and path directions. This method is also extensively validated by performing simulation and physical experiments [36]. The welding path is introduced to the model as a set of points of the geometry mesh, where the weld is applied and the direction of the weld path is set as the starting and end points in this set. Furthermore, the weld sequence is introduced by creating different sets of points representing the weld segments and applying the welding heat path to the segments in an orderly fashion. To represent the fixturing during the welding, the boundary conditions are applied to the nodes, locking the rotations and the translations in a given direction. The positioning system is introduced as six boundary conditions for each part included in the assembly. After welding is performed, the springback is calculated by negating the calculated after-weld displacement in the position of boundary conditions while the assembly is held in a measurement fixture. Figure 1 visualizes a model setup for welding experimentation, visualizing the weld paths, their sequences, and the locating schemes represented by the fixturing points.