## 1 Introduction  
While carrying out welding work on the hull block joint, a plate jig, referred to as temporary piece, is generally used to correct misalignment and prevent welding deformation [1]. However, because the deformations cannot be prevented and the weight increases if pieces become larger than a specific size, each shipyard uses a standardized piece, with specific shape and size. Figure 1 shows the working area of a temporary piece in the block assembly stage, Figure 2 shows the working area in the block direction stage, and Figure 3 presents technical drawings for representative standardized temporary pieces and strong-back. In each shipyard, some hundred thousand temporary pieces are used in a year, according to its scale, and the production time required for piece installation, removal, grinding, and work completion also mounts to some hundred thousand hours. A survey found that around 38,000 temporary pieces are used for only one unit of a 50,000 deadweight tonnage (DWT) tanker [2]. Furthermore, quality accuracy control of the hull block, by controlling deformations caused by welding, is very important for improving the productivity in the assembly and erection stages. Therefore, reduced usage of temporary piece, while maintaining a welding quality of hull block, is required. Interest in the optimization of butt joint welding has generated many analytical and experimental studies [3; 4; 5; 6]. Furthermore, the studies have been made to reduce residual stresses and deformations of fillet weld joints. [PERSON] et al. carried out a numerical simulation for reducing longitudinal residual stress and deformation using a local preheating technique [7]. The authors analyzed the correlation between residual stress and deformation according to preheating temperature and inter-pass time. Recently, efforts to precisely evaluate the residual stress and deformation of the butt-welded joint welding are performed in the same way as in the previous studies [8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21  
have been aided by finite element analysis, thanks to the development of increasingly more powerful computers. However, most of the research done has been limited to a range of simple welded joint model levels [8; 9]. Finite element simulations of the welding deformation of large structures, such as aircraft fuselages and hull blocks, have the downside of generating a quite large deviation from the real welding deformations in spite of large calculation times, due to considering the nonlinearity of materials [10]. It is known that the accuracy of the simulation result is largely relying on an appropriate consideration of the weld area affected by heat [11; 12; 13]. [PERSON] et al. explained a laser beam welding (LBW) model to predict the geometry of the resulting joint when welding thin Inconel 718 plates used in the aerospace industry [14]. [PERSON] et al. and [PERSON] et al. carried out simulations of the welding deformation by the assembly sequence of reinforced plate of hull body, by combining the equivalent load method and finite element method based on the inherent strain [15; 16]. [PERSON] et al. proposed an equivalent strain method, based on inherent strain for curved double bottom ship block [17]. [PERSON] et al. modified the inherent strain method to include the friction stir welding process [18]. This method expedited calculation time by simplifying a complicated thermal elasto-plastic analysis by using the inherent strain theory. However, this method has limitations in deciding the size and distribution area of inherent deformations. Furthermore, it requires an inconvenient process of obtaining a degree of restraint, each time, if external restraint condition is changed. Meanwhile, several studies have focused on the welding deformation itself. [PERSON] et al. clarified the generation mechanism of angular distortion in fillet welded joints through numerical simulations and experiments [19]. [PERSON] et al.