ABSTRACT In this study, the proposed linearized inherent strain method for predicting straightening of welded structures is investigated. Thermal elastic-plastic analysis is used to compute inherent strain of a thin flat plate caused by line heating. An accurate gas heat source model is employed in simulating the heating process. Transversal inherent strain is linearized from the computed distortion of the flat plate and applied in the elastic analysis, using higher order Gauss-Legendre (4-nodes shell elements). The accuracy of the proposed method is demonstrated by comparing the angular distortion of both analyses. Furthermore, different plate orientations are taken into account. INTRODUCTION Welding process is one of the most popular assembly method used by many industries such as ships and bridges. However, welding produces many unavoidable problems such as welding residual stress, crack propagation, and welding distortion especially for thin plates and large structures. The welding should be straightened, or the quality of the structure will decrease and the maintenance cost will increase. Welding distortion is caused due to shrinkage during the thermal cycle. It can be separated into the longitudinal shrinkage, transverse shrinkage, and angular distortion, see Fig. 1. In the last decades, ship designers have improved ship performance using thinner and lighter steel plates to reduce the ship weight. However, several problems with welding distortion have appeared as a result of thin plates welding for large structure fabrication. Mechanical and thermal straightening techniques are used to solve this problem. But mechanical techniques are difficult to apply to 3-D structures as ship blocks. Therefore, thermal processes are preferred because it is more economical and more flexible. These techniques create irreversible strain (inherent strain). As discussed by Ueda (1991, 1993), heat straightening consists of applying specific controlled heat patterns to the plastically deformed regions of welded structures in a single or repetitive heating phase and in-plane contraction during the cooling phase. Unfortunately, this method depends most of the cases on the experience of the skilled workers.

ABSTRACT Plates with double curvature are widely used in shipbuilding, and induction heating for plate bending is usually employed in shipyards due to its advantages such as high precision, high efficiency and so on. In this study, induction heating equipment with high frequency and 25KW in power was used to conduct experiments for different heating pattern, and typical bending plates with saddle shape and sail shape were obtained. Meanwhile, Three-coordinate Measuring Machine (TMM) was applied to measure the distribution and magnitude of out-of-plane bending deformation of the considered plates. Then, Thermo-Elasto-Plastic (TEP) FE analysis was carried out to predict the out-ofplane bending deformation generated by induction heating, which has a good agreement with it by measuring. With the integration of computed plastic strains caused by induction heating, elastic FE analysis with heating bending moment was implemented for effective prediction of out-of-plane bending deformation. Computed result of elastic FE analysis agrees well with the result from measurement and TEP FE analysis, while elastic FE analysis consumes less computer resource and computing time. INTRODUCTION The ship hull is made up of a large number of plates with complex curvatures, especially at the bow and stern where there are many double curvature plates such as saddle or sail shape. Thus, plate forming is an essential procedure for shipbuilding, which will be related to the production efficiency and precision of ship structure, as well as fabrication cost and schedule of shipyards (Zhou et al. 2014). Hot forming is an important method of plate bending forming in shipyards. The temperature distribution in the thickness direction is uneven because of local heating the plate, so that the bending moment would be generated to make the plate produce out-of-plane displacement. There are three main ways of hot forming according to heating source forms, including line heating with flame (oxygen-acetylene flame), laser heating and high frequency induction heating. At present, the fore two hot bending forming ways are more common than plate forming by high frequency induction heating, which is still on the early stage in shipyards. However, due to its unique advantages, it has attracted more and more attention. Compared with plate forming by line heating with oxygen-acetylene flame, high frequency induction heating is easier to accurately control the heating region and achieve automation, as well as high efficiency and few pollution (Heo et al. 2010); for plate forming by laser heating, it has low cost, simple equipment, and large heating power. As a result, plate forming by high frequency induction heating has a broad prospect in the efficient and automatic plate bending forming of shipyards.

ABSTRACT This paper mainly proposes simplified prediction procedure of temperature and deformation behavior for ship hull plate by moving thermal process. Maximum temperature Tum , dimensions (breadth b and depth h ) of inherent strain zone (ISZ) are firstly introduced to evaluate thermal forming behavior. Then non-dimensional technological parameters for Tum , b and h are derived based on dimensional analysis, which are subsequently utilized to analyze critical factors through parametric correlation analysis, respectively. Finally, non-dimensional predictions for Tum , b and h are carried out by multi-variable regression, respectively, and utilized to calculate bending angular deformation θ x Inhs based on inherent strain method. Therefore, we can prevent material mechanical degradation from overheating in advance, and improve dimensions of ISZ through adjusting technological parameters. It can be concluded that the proposed procedure can excellently predict Tum , b and h within maximum deviations of 6.95%, 6.63% and 9.70%, respectively, and calculate bending angular deformation θ x with less time to achieve automatic forming. INTRODUCTION Thermal forming process is an effective and economical method for fabricating flat metal plates into three-dimensional complicated shapes (Yu et al., 2001), which are typically utilized for bodies of ocean platform, ship hull and airplane, and rapid prototyping of complex curved surfaces to meet hydrodynamic performance. They cannot be formed at one time by mechanical roll or bending and require much more labor cost. Generally, the dimensions can arrive at more than 10m and the shapes are also mutually different, therefore they cannot be fabricated by batch-type production. They are incrementally fabricated by experienced technicians through adopting oxyacetylene torch as heat source along designed paths to generate non-uniform temperature distribution. Then surrounding cooling regions would prevent the expanding of heated zones to obtain non-uniform shrinkage strain distribution along thickness direction, and thus generate membrane shrinkage and bending angular deformation (Park et al., 2016). But this manual trial-and-error method is largely dependent on experience of each craftsmen resulting in low repeatability and efficiency.

ABSTRACT A development programme founded by the Norwegian Research Council for further increase the competitiveness of the direct electrical heating (DEH) technology was initiated in 2016 and will finish at the end of 2018. The partners in this project have long experience in development, manufacturing, installation of DEH systems and expertise inside all research areas inside DEH. The primary scientific and technological objective is to develop the technology for a low-cost, light-weight and high-efficiency DEH flow assurance system for an expanded application range. The improvements are reduced supply current, losses, weight and costs. Additionally the DEH system should be easier to install and applicable down to water depths of 3000 m. INTRODUCTION DEH is developed for hydrate management of pipelines and uses electrical heating in order to ensure that the pipe content temperature is above plug and wax formation temperature. The method is applicable for continuous heating, heating during shut down and reheating form cooled down pipeline. It has also been used for melting of wax/plugs. This paper considers the basis to determine heat input to the steel pipe and improvements in order to increase the applicability of DEH, i.e. increasing the efficiency of DEH. This activity is one of the work packages for the development programme, which includes: guidelines for mitigation of ac corrosion, increasing the efficiency of DEH, development of wet mateable connector, development of supply power cables, installation techniques of power cable risers and DEH, pipelines for deep-water applications, technical and economic assessments. The optimization of heat input in the steel pipe. Increasing the power frequency from the normal power frequency of 50/60 Hz to a frequency range of 100-200 Hz, provides clear benefits (Lervik et al. ISOPE 2016): reduction of needed DEH-current, which directly considerably reduces the cross-section of the DEH-cable, reduced interference with neighbouring installations, reduced complexity and size of the DEH grounding system, reduced potential practical issues with designing to avoid ac corrosion and thus easing the design of continuous operation.

Abstract Submarine XLPE (cross-linked polyethylene) insulated cables of wet design have been manufactured and delivered by Nexans for more than 40 years, including cables for Direct Electric Heating (DEH) of flowlines for the last 15 years. In a DEH system the cable is strapped (‘piggybacked’) to the flowline, and the operating temperature is high. DEH and XLPE cables are used at ever increasing water depths. The purpose of this paper is to summarize experiences from ageing of wet design cables at different water pressures and give recommendations regarding the use of wet design XLPE cables in the future.

Abstract Hydrate management by direct electric heating (DEH) has been in use for 15 years. The system has been continuously improved and adapted to the specific requirements during the development of new fields. Presently the system is designed for around 5 years of usage during the lifetime of the field. Due to demand for continuously heating, deeper water and reduced costs a promising concept with reduced cable dimensions and reduced risk for ac corrosion is being considered. The development work considers theoretical studies, laboratory tests at relevant pressures and field tests. Accelerated lifetime tests are important regarding qualification of power cable electrical insulation system.

Abstract The manual flame heating has been used in the conventional line heating to form the curved plate. High frequency induction heating could be a good alternative process for the automation of line heating process because of its easiness to control the heat flux. The purpose of this study is to establish the predictive method of the angular distortion caused by the line heating process with high frequency induction heating. The efficiency of high frequency induction heating system was determined by comparing the temperature measurement results and FEA. The proper range of inductor speed was suggested to prevent the degradation of plates with various thicknesses by FEA. The validity of the proper range of the critical heating conditions was verified by mechanical test and microstructure observation for the heated plates. Based on these results, the extensive line heating tests were carried out to evaluate the effect of size, internal restraint and strength of plates on the angular distortion. The predictive equation for the angular distortion was established with a function of heat intensity, bending rigidity, size, variations along the heating line and strength of plates.

Abstract A challenge facing offshore oil production is wax deposition. This has been a major issue for flow assurance in offshore fields, as it leads to increases in operational and remedial costs while suppressing oil production. Wax mitigation technologies including thermal management, wax inhibitors, and pigging were investigated and classified by their approach and application. The mechanism of factors affecting wax deposition, which are related to mitigation technologies, are also presented. Five offshore applications of these technologies are investigated.

Abstract Design of deep foundations within oceanic gas hydrate-bearing sediments (HBS) can be problematic and calls for special attention to incorporate the effect of gas hydrate melting. As naturally occurring gas hydrates in the seabed sediments begin dissociation process due to temperature or pressure changes, the pore pressure increases associated with volume expansion of the gas released during gas hydrate dissociation will likely result in fractures filled with pressurized fluid products open accompanied by softening of soil in gas and water intrusion zone together with seafloor and subsurface sediment motions. In this paper, a numerical approach is described to investigate the effects of gas hydrate dissociation induced by constant heating from a hot wellbore on sediment engineering properties and the radial extent of hydrate dissociation influence zone. The effects of the following process during gas hydrate melting on soil parameters are discussed: thermal stresses; gas exsolution during heating; seepage- induced swelling effects and fracturing. Estimation of hydrate dissociation influence zone employs numerical assessment of fracture formation taking into account of pore seepage of fluid and gas from fractures, which is premised on either (1) development of a pattern of laterally expanding horizontal fractures evenly spaced vertically throughout the hydrate-bearing zone and centered on the wellbore, or (2) development of vertical fractures which will intersect the seafloor to allow released gasses to vent into water column. If the fractures form vertically from the origin of hydrate dissociation, the effects of hydrate melting on sediment parameters for determining deep foundation capacities will be essentially confined within the dissociation front; on the other hand, in the event of horizontal soil fracture formation, the radial extent of dissociation influence zone on soil properties will extend beyond the dissociation front especially for relatively high gas hydrate concentration. Discussion of deep foundation design (tension-leg platform (TLP) piles) in hydrate environment considering effects of hydrate dissociation due to elevated temperature is also presented herein. The potential sediment strength loss and soil loads exerted on the pile resulting from sediment motions induced by fracture growth should be incorporated in the design process.

Abstract As it becomes profitable to extract oil and gas from smaller reservoirs, jumpers (t-offs) connected to the main flowlines become necessary. Hydrate management of these jumpers may be solved by electrical heating systems. This requires development of new subsea electric power components. The most vital component is a transformer qualified for marine applications as this transformer shall be supplied by utilizing the main flowline heating system (DEH).

ABSTRACT A dual-phase (DP) microstructure, which consists of bainite and polygonal ferrite, is effective in achieving low yield to tensile (Y/T) ratio and high uniform elongation in high strength steel. The optimized volume fraction and grain size of polygonal ferrite result in excellent deformability and good low-temperature toughness which are preferred pipe properties for strain-based design (SBD). Moreover, an accelerated cooling condition after controlled-rolling should be controlled to suppress thermal aging during a pipe coating treatment. Based on a trial production result, a total of 5000 metric tons of X70 highly deformable UOE line pipes with 40"OD x 17.5mmWT were manufactured in a commercial mill. All stress-strain curves of the manufactured pipes indicated a round house-type after thermal aging (200°C x 5min). The Y/T ratio was below 0.82, while a uniform elongation was over 8% after the thermal aging.

ABSTRACT In this study, the performance of the sea water cooling system was analyzed by comparatively testing its cooling performance against that of the following methods using diverse sea water heat sources and the existing deep sea water intake systems of the Deep Sea Water Research Center: direct cooling with deep sea water, heat pump cooling with surface sea water and ground sea water, and the existing cooling system. The temperatures of the deep sea water, ground sea water, and surface sea water were approximately 5°C, 13°C, and 20°C, respectively, which indicate that they were excellent heat sources for sea water cooling. The tCO 2 values in the direct cooling, the surface water and ground sea water heat pump cooling after the direct heat exchange of deep water, and the 100% surface water and ground sea water heat pump cooling were approximately 83.6%, 25.6%, 37.3%, 17.1%, and 28.7% lower, respectively, than that in the existing cooling system.

The deck of ship blocks are mainly made of thin plates. A main reason of using thin plates is that deck plates don"t need to support large structural loads and moments. While using thin plates for deck construction, many deformation problems occurs during production process. Especially, out-of-plane deformations between stiffeners are frequent. These deformations are usually straightened by correction heating (flame heating method). After correction heating, the blocks are lifted and moved by cranes to assemble it at dry-dock stage. After this lifting process, out-of-plane deformation again happens frequently. And then, they continuously cause quality and accuracy problems in the final dry-dock process. So, it takes more time for repair and correction working. According to preceding research, the lifting process by cranes would offset the effect on correction heating. This study finds out the remained efficiency of correction heating when tensional loads are added to corrected parts by a lifting. We used inherent strains in calculating the efficiency and established the methodology, where the positions for carlings are. This process makes progress by using correction heating analysis based on FEA (Finite Element Analysis) and it is possible to predict this phenomenon. For getting more accurate positions, besides the structural lifting analysis, welding deformation analysis with upper block and measured data from a serial ship are also referenced. INTRODUCTION During ship building at dry-dock stage, quality problems influences significantly in productivity due to high cost at this stage. During hull structure procedures, quality problems are occurred very widely and unpredictable mostly. But out-of-plane deformations in deck are continuous and common problems. They can be classified into two cases (Fig. 1), one is the shape (Fig. 1(a)) that one-directional out-of-plane deformation and the other (Fig. 1(b)) is jagged out-of-plane deformation. The latter is caused by block shape, boundary condition and temperature differential between deck and atmosphere, on the other hand the former is a welding deformation.

ABSTRACT This study experimented on a heating and cooling system that uses the deep ocean water as a heat source in a laboratory equipped with the water intake system. Experiments on direct cooling using the deep ocean water of yearlong temperatures at 5°C or less were performed. Experiments on heating using a heat pump system were performed with various ocean waters as heat sources including the deep ocean water at 5°C, the surface ocean water at 10°C, and the ground ocean water at 13°C, among others. The comparison results between the conventional cooling systems and the direct cooling system using the deep ocean water revealed that the latter saved approximately 82.7% of the total power consumption and reduced the carbon dioxide exhaust by about 75.6 kgCO 2 . The heating COPs of the surface ocean water and the ground ocean water increased by approximately 21.2% and 28.4% more, respectively, than that of the deep ocean water. INTRODUCTION High oil prices, global warming, and environmental issues all over the world drove the advanced countries to restrict the use of fossil fuels and to develop alternative energy sources. South Korea also needs to implement changes in the face of the rapidly changing international situation. South Korea needs to develop new energy sources that can be immediately applied to the buildings therein, whose energy consumption is approximately only 30% of the total domestic energy consumption rate. While the energy consumption rate for heating remains high in the old buildings, the demand for cooling energy is also steadily increasing due to climate change as well as the improved quality of life of the South Koreans, which allows them to seek greater comfort. Under these circumstances, the advanced countries are actively studying the use of the low-temperature deep waters in their seas and lakes as new energy sources.

ABSTRACT: The present work involves examinations of the microstructure evolution that can occur during welding in the two phase austenite and ferrite region of a high strength low alloy (HSLA) steel that is designed for low temperature applications. This was done by combining in situ heating in a high resolution field emission scanning electron microscope (FESEM) with Electron Backscattered Diffraction (EBSD) measurements. It was found that the designed hot stage is a useful tool to characterize the austenite that forms when heated to 770°C. It was also observed that the austenite transforms to ferrite with increasing holding time at this temperature due to decarburization. INTRODUCTION In recent year's oil and gas production in arctic areas has become an interesting target for oil companies worldwide. An estimate done by the United States Geological Survey indicates that approximately 30% of the remaining gas reserves and 13% of the remaining oil reserves may be located north of the polar circle (Gautier et al., 2009). Oil and gas activities in the Arctic are characterized by extreme challenges from icing conditions and the low temperatures involved. Therefore, robust materials are required to ensure safe and sustainable operations. The base material of HSLA steels may have very good mechanical properties down to −60°C. However, brittle phases, such as martensiteaustenite (M-A) islands, may form during welding (Chen et al, 1984; Akselsen et al, 1987 and 1988, Davis and King, 1994 and 1996) and the existence of these phases increase the probability of brittle fracture with decreasing temperatures. Increased knowledge about the microstructure that forms, and its influence on the materials behavior in these environments, is therefore of utmost importance. In the present work, the microstructure evolution that may occur during welding of an HSLA steel that is designed for low temperature applications is explored.

In plate forming by line heating the usage of water as a cooling source is common. However, the relationship between water-cooling and plate deformation is not well established. This reduces the possibility of automating the process. In order to solve this problem, the influence of the rate of cooling on inherent deformation is first examined. Then, the inherent deformation produced by line heating is studied in detail. Finally, the relationship between inherent deformation and heating condition is recorded into an inherent deformation database. This database can be used to directly predict inherent deformation due to line heating and therefore enable the automation of the process. INTRODUCTION In plate forming by line heating, water-cooling is usually used due to its effectiveness in increasing plate deformation. However, the mechanism of forced cooling such as water cooling is highly complex and it is not fully understood. Therefore, it is necessary to create a method to predict the influence of water-cooling on plate deformation and therefore, enable the usage of automatic machines. Although there have been many papers reporting the line heating method, very few papers are dealing with the effect of water cooling on deformation of plates due to line heating, [e.g. Satoh, Matsui, Terai and Iwamura (1970), Jamg, Kim, Ha and Lee (2005), Ji, Yujun, Zhuoshang, Yanping and Jun (2006), Ha and Jang (2007)]. Not a clear relationship between water-cooling and deformation of plates due to line heating has been found yet. Various attempts have been made to understand the mechanism of heat transfer in pool boiling (the key to explain the influence of water-cooling on line heating process), [e.g. Davidson and Schueler (1960), Han and Griffith (1965), Mikic and Rohsenow (1969), Judd and Hwang (1976), Haramura and Katto (1983), Liu and Wang (2001), Wu, Yang and Yuan (2002), etc.]. However, the calculation of the convection coefficient is a difficult problem and cannot be described by using a single relationship.

ABSTRACT The use of Direct Electrical Heating (DEH) for sub-sea pipelines has become a method for hydrate and wax management control either by itself, or as part of other hydrate management and control techniques. The method is based on resistive heating of the steel pipe by leading electrical AC current in the flowline. DEH has so far only been used in the North Sea, with the first system installed 8 years ago. To date 6 installations are operational with another 4 being implemented. Simulations are carried out to determine whether or not the DEH technology is suitable for the Ichthys Gas Field development. Details of 5 insulated sub-sea flow lines were provided as a basis for the investigation: – To extend the no touch time required after a shutdown, i.e. to avoid depressurization of sub sea system, by keeping flowlines above hydrate formation temperature (this is considered the main objective of the study). – To warm up a cold flowline from seabed temperature to the target temperature above hydrate formation and keep it at this temperature indefinitely. – To melt hydrates after prolonged shutdown. For both these scenarios, the electric power data for the DEH system are determined. Results from the simulations were compared with results from (OLGA) simulations concerning cool-down scenarios. The thermal configurations for the pipelines and the operational conditions have been the governing parameters to provide DEH data. For the application of DEH this method has also been compared with more traditional flow assurance systems regarding topside equipment, and there are obvious advantages concerning required volume and weight. INTRODUCTION The purpose of the study is to evaluate the feasibility of using the Direct Electrical Heating (DEH) technology on subsea flowlines, as part of the Concept Development Phase of the Ichthys Gas Field Development.

The purpose of this study is to establish a control method of the global bending distortion caused by fabrication process for hatch-cover in container carrier. In order to do it, the transitional behavior of global bending distortion in the deck of hatch-cover during fabrication process was measured by 3-dimensional measuring instrument. From the results, the principal factor controlling the global bending distortion was identified as the bending moment associated with the longitudinal shrinkage force and transverse shrinkage caused by welding and flame heating and the change of the centroid axis of hatch-cover in each fabrication process. Therefore, in this study, the predictive equations of the longitudinal shrinkage force and transverse shrinkage caused by welding and flame heating were developed using the comprehensive FEA and experiment. With the predictive equations and the simplified thermo elastic method, the predictive method for the global bending distortion was established and verified by comparing with the measured result. Based on the results, the amount of reverse bending distortion of main stiffeners was determined to prevent the global bending distortion of hatch-cover. INTRODUCTION The hatch-cover used for sustaining the weight of container boxes in container carrier was comprised of large thin plates, which are strengthened by welding stiffeners both longitudinally and transversely to form a box structure. For structural stiffness and self-weight of less 45 ton, the thickness of the main plate is strictly limited to less than 8mm. When the thin panels are welded, residual compressive stress causes "oscillations" in the main plate, which is located between stiffeners and along plate edges. Current fairness requirements for hatch-cover do not permit these distortions. Therefore, hatch-cover was manufactured by "egg crater construction" technique in order to prevent the buckling distortion. This technique is very useful as a distortion control method because the stiffener assembly partitions the plate into small areas that have a higher resistance to buckling (Masubuchi, 1980).

High collapse resistance for withstanding hydraulic pressure is required for line pipes laid in deepwater. Since the collapse resistance is mainly dominated by the compressive yield strength in the circumferential direction (C-YS), the strength distribution in the pipe should be discussed for establishing the methodology of the collapse pressure prediction. This paper deals with the collapse resistance of UOE pipes with and without the thermal aging during anti-corrosion coating, and describes the optimum sampling methods and the mechanical property indicator (Ci) for evaluating the collapse pressure. Based on the measured C-YS, the collapse pressure calculated by finite element analysis (FEA) was compared with the full-scale test results. As the circumferential sampling position, 90° and 180° away from the seam weld are appropriate for the conservative estimation. As the sample diameter, a 50% to 70% ratio for wall thickness is preferable to minimize the prediction error. The proof stress under 0.1% off-set (0.1% PS) gives the linear correlation to the collapse pressure, although the proof stress under 0.2% off-set (0.2% PS) depends on the shape of the stress vs. strain (S-S) curve. The results show that the collapse pressure after coating is predicted by heating the column sample machined from pipes as received. In conclusion, this study indicates the methodology for reliably evaluating the resulting collapse pressure without the full-scale test and the sampling from the coated pipe. INTRODUCTION Intercontinental pipelines are often laid in deepwater above 2000 m like the Mediterranean Sea (Stark, 1995, DeGeer, 2005). In such hostile environments, heavy-walled UOE pipes are used for preventing collapse under the external pressure. The present knowledge widely shows that the collapse resistance is mainly affected by the roundness of the pipe as the dimension and the yield stress (YS) as the mechanical property (Stark, 1995, Toreselletti, 2003). Also shown is that the mechanical properties are changed by the thermal aging during anticorrosion coating (Al-Sharif, 1996, DeGeer, 2004, Tsuru, 2006).

In order to clarify the mechanism of thick plates forming by complex line heating, the distribution characteristics of inherent deformation produced by overlap, parallel and cross heating lines is studied. From this study it is found that the final inherent deformation is not a simple addition of that produced by individual heating. It is also found that the heating sequence has an important role in the production of deformation. Finally, correction factors are proposed to improve the accuracy of the prediction method. When these factors are obtained for a range of cases, deformation can be estimated by elastic analysis using the inherent deformation theory even with complex heating sequences. INTRODUCTION Line heating is an effective method to form curved shell plates with complex three-dimensional geometry. However, line heating process is mostly dependent on the skill of hard-to-find experienced workers. Therefore, automation is highly required. At present, no automatic system that can form a plate without significant human help has been developed. This is because the heat-induced deformation has many complex and uncertain factors, which are obstacles to the accurate prediction required by automatic systems. In forming of thin plates, applying line heating in simple patterns is usually enough to achieve the required deformation of the plate. However, in forming thick plates, it is necessary to apply large amounts of heat. Therefore, a combination of overlap, parallel and cross heating lines on both surfaces of the plate is required. On the other hand, when multiple heating lines are applied, residual stresses caused by a previous heating line affect the inherent deformation of the current heating line making it difficult to predict the deformation by simply superimposing inherent deformations of single heating lines in an elastic analysis. In this paper, the behavior of a thick plate formed by line heating is studied.