## 3 Welding Deformation Analysis of Unit Specim  
Based on the results of the butt-welding experiment involving pieces, we aim to establish a method of butt welding thermal elasto-plastic analysis. For this purpose, analysis tools such as welding heat input model and boundary condition were selected through the following process:  
1. Butt welding thermal elasto-plastic analysis was performed using a commercial finite element analysis program (MSC MARC). 2. A 4-node bilinear shell was used for heat transfer analysis, and nine integration points were set to represent linear temperature gradients in the thickness direction, improving the calculation time efficiency of this model in comparison to the solid element analysis. The proposed shell element calculates the temperature distribution by bilinear interpolation in the plane direction. In the thickness direction, temperature gradients are represented by Simpson's rule with up to 11 integral points, assuming linear or quadratic temperature distribution. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **x1** & **x2** & **x3** & **x4** & **x5** & **Average** & **No. of Piece** \\ \hline Specim 1 & 12.79 & 12.07 & 12.43 & 12.81 & 13.18 & 12.66 & 0 \\ Specim 2 & 7.48 & 8.02 & 8.04 & 7.75 & 7.73 & 7.80 & 3 \\ Specim 3 & 3.72 & 3.21 & 3.67 & 2.94 & 3.21 & 3.35 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Experimental results of maximum displacements in x-direction [mm]. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **y1** & **y2** & **y3** & **y1\({}^{\prime}\)** & **y2\({}^{\prime}\)** & **y3\({}^{\prime}\)** & **Average** & **No. of Piece** \\ \hline Specim 1 & 8.63 & 9.02 & 8.58 & 7.61 & 8.24 & 8.28 & 8.39 & 0 \\ Specim 2 & 5.21 & 5.49 & 5.02 & 6.12 & 6.28 & 5.91 & 5.67 & 3 \\ Specim 3 & 3.98 & 4.12 & 4.37 & 5.81 & 5.43 & 4.99 & 4.78 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Experimental results of maximum displacements in y-direction [mm]. A moving heat source was used to simulate three-dimensional effects, such as longitudinal bending deformation and edge effects. To apply the moving heat source to the analysis, the weld beads were generated with the welding speed using the activate elements technique [28]. * The left-right symmetry model was created based on the welding line, and the boundary conditions to prevent rigid motions were applied to the temporary tack welding area for the specimens fixed together with the symmetry boundary conditions. * Temperature-dependent material properties [4] were used for extracting the values for Young's modulus, yield stress, specific heat, conductivity, and thermal expansion coefficient. The temperature-dependent material properties, including tangent modulus, which characterizes the plastic properties of the material, are summarized in Figure 9.
* In general, for manual arc welding, the welding speed, current, and voltage are irregular and influenced by the skill of the operator and the surrounding environment. In this study, a relatively stable manual welding was obtained by monitored and repeated preliminary experiments, so that the welding speed, current, and voltage could be kept within the range of field construction guidelines from Table 1. The welding conditions used in the analysis utilized an average value of these ranges, increasing the analytical time efficiency by reducing the number of steps in the analysis instead of using changes of the weld conditions over time, occurring in the actual welding experiment. The analysis welding conditions used are welding speed of 150 mm/min, welding current of 240 A, and arc voltage of 29 V.
* Based on the experimental results of specimen 1, the similarity between simulated and experimental results was calculated while changing the values of the analysis variables, which is shown in Table 4. The heat flux radius of 135 mm, R135, the analysis parameter value for the highest similarity, was determined as the analysis condition.