A Study on Welding Sensitivity Assessment and Deformation Control of International Maritime Organization Type C Liquefied Natural Gas Fuel Tank Support Structures Using the Direct Inherent Strain Method

Abstract

The increasing burden on shipowners and shipping companies due to environmental regulations imposed by the International Maritime Organization (IMO) has led to the adoption of various compliance strategies, including the use of low-sulfur fuel, installation of scrubbers, and the use of liquefied natural gas (LNG) as an alternative fuel. LNG is particularly prevalent in dual-fuel propulsion ships, with the IMO Type C tank being the most commonly used storage facility. The structure of the IMO Type C tank comprises a pressure vessel and supporting saddles, which can be integrated or separate systems. Despite being manufactured within specified tolerances, welding-induced deformation of the tank and saddle is inevitable since the saddle is welded directly onto the hull. In integrated tank–saddle systems, this deformation can lead to cracks in the epoxy resin, which has lower strength and stiffness, as well as burn damage to the resin and wooden blocks from welding heat. In separate tank–saddle systems, installation difficulties can arise due to interference between the fuel tank system and adjacent structures, such as insulation or the fuel preparation room (FPR), resulting from saddle deformation caused by welding. This study analyzes the sensitivity of all weld lines involved in saddle installation using the direct inherent strain (DIS) method. Based on this analysis, the initial welding deformations are evaluated in relation to the welding direction and sequence. Finally, an optimized method for saddle installation is proposed to minimize deformation.

1. Introduction

The enforcement of environmental regulations by the International Maritime Organization (IMO) has significantly increased the operational burdens on shipowners and shipping companies. To comply, solutions such as using low-sulfur oil, installing scrubbers, and utilizing liquefied natural gas (LNG) as a fuel source have been implemented. Among these, LNG is widely adopted in dual-fuel propulsion ships, with a consistent demand for LNG-powered vessels. LNG offers a higher calorific value compared to conventional marine diesel fuel, leading to reduced fuel consumption and operating costs. Additionally, using LNG as an alternative fuel results in a substantial reduction in harmful emissions: 99% of sulfur oxides (SO_X), 80% of nitrogen oxides (NO_X), 20% of carbon dioxide (CO₂), and particulate matter (PM) [1]. While LNG carriers can use the boil-off gas (BOG) from their cargo holds as fuel, other types of merchant ships require dedicated storage for LNG fuel. The IMO Type C fuel tank system, which is the most widely used for LNG storage, consists of a pressure vessel and supporting saddles. These saddles typically feature load-bearing epoxy resin and wooden blocks between the pressure vessel and the support structure. Particularly in integrated tank–saddle systems, cracks may occur in the resin, which has lower strength and stiffness due to deformation and heat generated during the welding of the saddle to the hull. Additionally, burn damage can occur in the resin and wooden blocks. The configuration and installation methods of these fuel tank systems vary based on the ship’s specifications and the shipowner’s requirements. In separate tank–saddle systems, where the saddle is welded to the hull before installing the pressure vessel, welding heat can deform the saddle, necessitating a deformation check before the pressure vessel is installed. This study analyzes the sensitivity of all weld lines during saddle installation and evaluates the initial welding deformations based on welding direction and sequence. An optimized saddle installation method is then proposed based on the results of the welding deformation analysis.

2. Fuel Tank Systems

2.1. Types of Fuel Tank Systems

The International Maritime Organization (IMO) classifies LNG tank systems as shown in Figure 1. These systems can be broadly categorized into two types: independent and membrane. The independent tank system involves mounting a completed tank onto the hull, whereas the membrane tank system involves directly installing an insulation system within the hull.

While Type A and Type B tanks share some structural similarities, Type A tanks are built using conventional methods with significant reinforcement, making them resistant to sloshing but prone to fatigue. These tanks are also heavy and costly to produce. In contrast, Type B tanks benefit from advanced computational analysis techniques, allowing for precise pre-construction model testing. This detailed analysis facilitates the consideration of stress, fatigue life, and crack propagation characteristics, resulting in the application of a partial secondary barrier.

The IMO Type C independent tank system, classified as a pressure vessel, includes single-cylinder and bi-lobe or tri-lobe configurations, where two or three cylinders are combined. The IMO Type C fuel tank system is designed conservatively, following the ASME BPVC (The American Society of Mechanical Engineers, Boiler, and Pressure Vessel Code) Sec. VIII and the IGF code, thus excluding considerations for leakage. Therefore, it does not require a secondary barrier needed for other tanks [3,4,5]. Since the insulation system of the IMO Type C tanks is installed externally, it must be protected from external impacts. Additionally, they must be constructed to prevent insulation material delamination and cracking due to differences in thermal contraction rates between the tank material and the insulation material. Although Figure 1 indicates that the allowable pressure for Type C tanks ranges from 2 to 10 bars, this variation stems from differences in the values presented by the IMO and IGF codes. In practice, depending on the construction method, these tanks can withstand pressures exceeding several hundred bars. However, compliance with the relevant codes or rules is essential for their intended use. The IMO Type C fuel tank system is in high demand, particularly for LNG propulsion ships, due to its versatility and reliability.

Membrane-type tanks are the most widely used cargo hold type in LNG ships due to their high volumetric efficiency and low boil-off rate, making them highly competitive. However, the insulation material used in membrane tanks has low strength, necessitating measures to counter sloshing. Additionally, since the insulation system is installed through bonding, attention to adhesion quality is crucial.

2.2. IMO Type C Fuel Tank System

The saddle, which supports the pressure vessel, is installed on the hull. The pressure vessel stores the liquefied natural gas, and the upper platform transfers fuel to the fuel preparation room (FPR) for engine supply. To accommodate the thermal contraction of the cryogenic fuel, the saddle is divided into fixed and sliding types.

Between the saddle and the pressure vessel, wooden blocks and resin perform a load-bearing role, supporting the pressure vessel. Minor deformations occurring during the fabrication, transportation, and installation of the fuel tank system are compensated by the tolerance between the wooden block and the saddle. This tolerance is typically about 20 mm, and resin is filled in this space and cured, as shown in Figure 2.

Several studies have been conducted on IMO Type C tanks, focusing on various aspects such as material strength and selection [6,7], structural strength evaluations [8,9,10], sloshing issues [11], design pressure analysis [12], and thermal insulation performance assessments [13] for pressure vessels. In addition, these studies cover structural and fatigue strength evaluations of the lower support structures, particularly the saddles [14,15]. However, no research has addressed the issue of welding deformation or its control in the saddle. Thus, this study focuses on evaluating welding deformation in saddles, based on observations from the shipyard, and identifying relevant trends.

3. Evaluation Overview

3.1. Evaluation Target and Analysis Model

The target of this evaluation is a 1750 CBM LNG fuel tank system with a diameter of 9 m and a length of 29 m. The materials used in the fuel tank system are listed in

Table 1. Material specifications for each component in the fuel tank.

Item	Material
Pressure vessel	9% nickel
Wooden block	Laminated wood
Load bearing	Epoxy resin
Saddle	DH36
Seat (hull part)	DH36

. The weld bead shape and welding procedure specification (WPS) applied to the manufacture of the fuel tank system are simplified considering a current of 260 (A), voltage of 31 (V), and speed of 27 (cm/min). Welding deformation analysis was performed using the general-purpose nonlinear finite element software MSC Marc 2023. The finite element model and boundary conditions used in the analysis are shown in Figure 3. Points ① and ② represent the initial positions of the symmetric boundary and free edge at the centerline of the saddle arch in the FE model, while points ③ and ④ denote the corresponding positions at the end of the saddle arch. The elements used are 4-node shell elements, with each element sized at 50 mm × 50 mm. The analysis model utilizes 1/4 symmetry, with a symmetry boundary condition applied to the cut surface. The bottom of the hull seat is welded to align with the longitudinal/transverse reinforcement lines on the underside of the hull’s upper deck, and a fixed boundary condition was applied.

3.2. Evaluation Method

For the analysis method to evaluate welding deformation, the thermo-elasto-plastic method (TEP) [16], the equivalent load method [17], and the equivalent thermal strain method (ETS) [18,19,20,21,22,23] are used, which is an enhancement of the equivalent load method. Each of these methods offers unique approaches and can be adapted or improved to effectively assess welding deformation.

The TEP method, which employs 3D solid elements, is a high-fidelity analysis method that closely simulates reality by considering various welding-related parameters such as welding speed, sequence, direction, heat input, arc shape, melting temperature, ambient temperature, heat transfer through conduction, heat loss through convection and radiation, and constraint conditions. However, the TEP method presents challenges, including the complexity of modeling intricate structures, increased element count, and lengthy calculation times due to the use of 3D solid elements. Additionally, recalculating the entire model to account for element creation corresponding to a single weld bead and reduced convergence due to excessive element deformation from high heat input further complicates the process. Despite advancements in computational capabilities, performing welding deformation analysis on large structures using the TEP method remains impractical due to the significant time required.

Moreover, deriving the optimal welding sequence using the TEP method involves performing a considerable number of analyses [24]. In this study, the full model of the saddle includes 72 weld lines that are welded to the hull seat. If all weld lines are welded sequentially, the number of welding sequence scenarios can be calculated using Equation (1), and the analyses required to derive the optimal sequence amount to approximately 2.89125 scenarios—a practically impossible number. This study only accounts for the number of weld lines, excluding various parameters related to welding, such as speed, ambient temperature, and convection coefficients. The total number of analysis cases, including these parameters, can be calculated using Equation (2).

$$Weld sequence=w!\times 2^w (w\ge 1 and integer)$$

(1)

$$Total combination=w!\times 2^w\times f\{v, T, h,\dots ,etc.\}$$

(2)

where w represents the number of weld lines, and 2 represents the possible directions of welding progress. v is the welding speed, T is the ambient temperature, and h is the convection coefficient—parameters related to welding. The function f{v, T, h, …, etc.} represents the conditions for each parameter, as expressed in Equation (3).

$$f\{v, T, h,\dots ,etc.\}={\displaystyle \prod _{i=1}^n}{p}_i$$

(3)

where p_i represents welding parameters such as v, T, h, etc., and n is the number of conditions for each parameter. Consequently, considering the welding sequence and parameters that influence welding deformation requires a substantial number of evaluations to determine the condition that results in minimal welding deformation.

The equivalent load method calculates the load corresponding to the weld deformation and applies it to the analysis model. By using inherent strain obtained through the TEP method to calculate the inherent deformation and then determining the equivalent load, results similar to those from the TEP method can be achieved, although the process is complex. Additionally, while the input data for welding analysis are scalar (welding heat input), the equivalent load used in the equivalent load method is a vector, making it difficult to apply to various structural shapes, such as curved plates.

The ETS method implements the actual welding angle deformation in finite element analysis based on experimental measurements of welding angle deformation relative to plate thickness and leg length, using a virtual temperature and a virtual thermal shrinkage rate [5]. The ETS method, while effective, inputs data for analysis to the nodes of the designated weld line path in bulk, making it challenging to implement sequential welding on both sides of the web in fillet welding.

In this study, a novel approach using the direct inherent strain (DIS) method is explored, differing from existing analysis methods. The DIS method can be applied not only to butt welding but also to sequential welding, such as fillet welding, by converting the data input from the ETS method into inherent strain for elements corresponding to the welding region [25].

3.3. Sensitivity Evaluation

Before deriving the optimal welding sequence through welding deformation analysis, the sensitivity of each weld line was evaluated based on the deformation that occurs when welding is performed at each position, as shown in Figure 4. The sensitivity evaluation was conducted using the post-sequence method [13]. The post-sequence method is an analysis approach for determining the optimal welding sequence, analyzing the impact of each weld line on deformation by performing welding deformation analysis as many times as the number of weld lines. This method identifies the welding sequence that results in the least deformation.

3.4. Welding Deformation Analysis Conditions

There are several methods for installing the LNG fuel tank system:

• Welding the saddle to the hull first, followed by mounting the pressure vessel.
• Temporarily mounting the pressure vessel on the saddle, welding the saddle to the hull, and then fully mounting the pressure vessel.
• Installing an integrated tank–saddle fuel tank system.

The objective of this welding deformation analysis is to evaluate the impact of welding heat on saddle deformation. To achieve this, the study focused on method (1), where the saddle is installed independently, without additional constraints, leading to the most significant welding deformations. In this scenario, welding sequence scenarios were developed based on the results of sensitivity analysis and feedback from field experts. The resulting saddle deformations were then compared to determine the optimal welding sequence.

4. Results and Discussion

4.1. Sensitivity Evaluation Results

Sensitivity rankings were established by comparing the degree to which each weld line, specifically X1 through X7 (corresponding to the bracket weld line) and Y1 through Y6 (corresponding to the web frame weld line), contributed to the overall deformation of the saddle. The sensitivity ranking was based either on the maximum deformation of the saddle or the degree to which the ends of the saddle arch (points ③ and ④) induced deformation either inside or outside the saddle.

In this study, emphasis was placed on the latter approach—ranking sensitivity based on the directionality of the saddle’s deformation. This approach aligns with field experience, where deformation along the width of the saddle arch’s ends posed challenges during pressure vessel installation. For clarity, the signs of the average Y displacement data in

Table 2. Sensitivity assessment results and derived welding order considering displacement direction.

Target	Weld Line	Y Disp. [mm]		Ave. Difference of Y Disp. ③, ④ [mm]	Sensitivity Ranking	Absolute δ/δ min	Welding Sequence
		③	④				Most Inward Deformation
X1	w/o X1	−0.156	−0.156	−0.013	5	1.2	X7	Y3
	X1	−0.143	−0.143
X2	w/o X2	−0.166	−0.166	−0.021	8	1.9	Y6	Y4
	X2	−0.145	−0.145
X3	w/o X3	−0.152	−0.152	−0.020	7	1.8	X6	Y2
	X3	−0.132	−0.132
X4	w/o X4	−0.121	−0.121	−0.029	9	2.7	X5	Y1
	X4	−0.093	−0.093
X5	w/o X5	−0.111	−0.111	−0.011	4	1.0	X1	X4
	X5	−0.100	−0.100
X6	w/o X6	−0.105	−0.105	0.022	3	2.0	Y5	X2
	X6	−0.127	−0.127
X7	w/o X7	−0.088	−0.088	0.349	1	32.5	X3	X3
	X7	−0.438	−0.438
Y1	w/o Y1	−0.166	−0.166	−0.046	10	4.3	X2	Y5
	Y1	−0.120	−0.120
Y2	w/o Y2	−0.154	−0.154	−0.054	11	5.0	X4	X1
	Y2	−0.100	−0.100
Y3	w/o Y3	−0.141	−0.141	−0.067	13	6.3	Y1	X5
	Y3	−0.074	−0.074
Y4	w/o Y4	−0.121	−0.122	−0.062	12	5.7	Y2	X6
	Y4	−0.060	−0.060
Y5	w/o Y5	−0.112	−0.112	−0.020	6	1.8	Y4	Y6
	Y5	−0.092	−0.092
Y6	w/o Y6	−0.179	−0.179	0.168	2	15.6	Y3	X7
	Y6	−0.347	−0.347

(and subsequent tables) were inverted to better illustrate the deformation direction of the attached model. In this context, a positive (‘+’) Y displacement indicates outward deformation of the saddle, while a negative (‘−’) Y displacement signifies inward deformation.

The sensitivity evaluation results indicate that the X7, Y6, and X6 weld lines exhibit the highest sensitivity in that order. These three weld lines significantly influence the outward deformation of the saddle arch ends (points ③ and ④ in Figure 3). Notably, among these, the weld line positioned farther from the center of the saddle causes greater outward deformation.

When evaluated based on the magnitude of deformation regardless of direction, the deformation observed during the X7 bracket welding and Y6 web frame welding was approximately 33 times and 16 times larger, respectively, than that observed during the X5 bracket welding, which exhibited the smallest deformation. The X7 bracket and Y6 web frame are the two weld lines with the highest sensitivity, located at the outermost side of the saddle and spanning the widest distance to the adjacent bracket. The deformation patterns for the Y3 welding case (lowest sensitivity), the X5 welding case (smallest final deformation), and the X7 welding case (highest sensitivity and final deformation) are illustrated in Figure 5. For clarity, the elements corresponding to the web frame of the seat and saddle were deactivated.

No significant change in deformation was observed before and after welding of the Y3 web frame and X5 bracket. However, substantial deformation was noted in the outward direction of the saddle following welding at the X7 bracket. This confirms the tendency for the saddle to deform outward from the weld line on the saddle’s outer side, consistent with the high sensitivity identified in

Table 3. Welding deformation according to the derived welding sequence.

Scenario	Y Displacement [mm]		Average of Y Displacement ③, ④ [mm]
	③	④
Most inward deformation	−2.293830	−2.293810	−2.293820
Most outward deformation	1.938490	1.938510	1.938500

. The welding deformation results for scenarios expected to cause maximum inward and outward deformations, derived from Table 2 through sensitivity analysis, are presented in Table 3 and Figure 6.

4.2. Welding Deformation Analysis Results

Sensitivity analysis identified welding sequences that were expected to cause the maximum inward and outward deformations. However, these sequences proved to be impractical due to poor workability, making them unsuitable for implementation. Consequently, twelve new welding sequence scenarios were developed, incorporating the results of the sensitivity analysis and insights from field experts, as shown in

Table 4. Welding scenarios for welding deformation analysis and workability.

Welding Sequence	SC1	SC2	SC3	SC4	SC5	SC6	SC7	SC8	SC9	SC10	SC11	SC12
1	X7_o	X1_o	Y6	Y1	X7_o	X1_o	Y6	Y1	X7_o	X1_o	X1_o	X7_o
2	X7_i	Y1	Y5	Y2	X7_i	X2_i	Y5	Y2	X7_i	X2_i	Y6	X7_i
3	Y6	X2_i	Y4	Y3	X6_o	X2_o	Y4	Y3	X6_o	X2_o	X2_i	Y1
4	X6_o	X2_o	Y3	Y4	X6_i	X3_i	Y3	Y4	X6_i	X3_i	X2_o	X6_o
5	X6_i	Y2	Y2	Y5	X5_o	X3_o	Y2	Y5	X5_o	X3_o	Y5	X6_i
6	Y5	X3_i	Y1	Y6	X5_i	X4_i	Y1	Y6	X5_i	X4_i	X3_i	Y2
7	X5_o	X3_o	X7_o	X1_o	X4_o	X4_o	X1_o	X7_o	X4_o	X4_o	X3_o	X5_o
8	X5_i	Y3	X7_i	X2_i	X4_i	X5_i	X2_i	X7_i	X4_i	X5_i	Y4	X5_i
9	Y4	X4_i	X6_o	X2_o	X3_o	X5_o	X2_o	X6_o	X3_o	X5_o	X4_i	Y3
10	X4_o	X4_o	X6_i	X3_i	X3_i	X6_i	X3_i	X6_i	X3_i	X6_i	X4_o	X4_o
11	X4_i	Y4	X5_o	X3_o	X2_o	X6_o	X3_o	X5_o	X2_o	X6_o	Y3	X4_i
12	Y3	X5_i	X5_i	X4_i	X2_i	X7_i	X4_i	X5_i	X2_i	X7_i	X5_i	Y4
13	X3_o	X5_o	X4_o	X4_o	X1_o	X7_o	X4_o	X4_o	X1_o	X7_o	X5_o	X3_o
14	X3_i	Y5	X4_i	X5_i	Y6	Y1	X5_i	X4_i	Y1	Y6	Y2	X3_i
15	Y2	X6_i	X3_o	X5_o	Y5	Y2	X5_o	X3_o	Y2	Y5	X6_i	Y5
16	X2_o	X6_o	X3_i	X6_i	Y4	Y3	X6_i	X3_i	Y3	Y4	X6_o	X2_o
17	X2_i	Y6	X2_o	X6_o	Y3	Y4	X6_o	X2_o	Y4	Y3	Y1	X2_i
18	Y2	X7_i	X2_i	X7_i	Y2	Y5	X7_i	X2_i	Y5	Y2	X7_i	Y6
19	X1_o	X7_o	X1_o	X7_o	Y1	Y6	X7_o	X1_o	Y6	Y1	X7_o	X1_o
Workability	Very good			Normal			Good			Very bad

o: outside, i: inside.

. These scenarios were deemed feasible for implementation after consultation with field workers. Unlike the post-sequence method, this analysis took a more realistic approach by considering the left-to-right order of fillet welding.

Saddle welding work often necessitates frequent movement by workers to access the hull seat’s top plate. This increased movement can lead to worker fatigue, which may negatively impact welding quality and necessitate repairs. Consequently, workability refers to the extent to which work costs are consumed due to these factors.

• Scenarios 1 and 2: These scenarios offer excellent workability, as the saddle’s bracket and web frame are welded alternately in the same direction.
• Scenarios 3, 4, 5, and 6: These scenarios have average workability. While the bracket and web frame are welded in the same direction, the work path is retraced after welding the bracket or web frame, and welding is then performed again in the same direction.
• Scenarios 7, 8, 9, and 10: These scenarios also exhibit good workability, where the bracket or web frame is welded in sequence, and the remaining welding is completed by retracing the previously covered work path.
• Scenarios 11 and 12: These scenarios have the poorest workability, as the bracket and web frame are alternately welded at precisely opposite positions.

Before analyzing the welding deformation results, it is essential to validate the model used in the analysis. Dimensional changes resulting from converting the 3D solid model provided by the field into a 2D shell model have been accounted for. Additionally, to calculate the eccentricity and origin based on the analysis results, the center and radius of the arch in the analysis model were recalculated, as shown in Figure 7.

The analysis results for each scenario are summarized in

Table 5. Y displacement of the designated points of each scenario.

Y Displacement [mm]	Position
	①	②	③	④
SC1	0	0	1.031	1.031
SC2	0	0	−2.775	−2.775
SC3	0	0	0.312	0.312
SC4	0	0	−1.584	−1.584
SC5	0	0	1.154	1.154
SC6	0	0	−2.873	−2.873
SC7	0	0	0.299	0.299
SC8	0	0	−1.572	−1.572
SC9	0	0	1.128	1.128
SC10	0	0	−2.848	−2.848
SC11	0	0	0.180	0.180
SC12	0	0	0.168	0.168

and

Table 6. Z displacement of the designated points of each scenario.

Z Displacement [mm]	Position
	①	②	③	④	③’	④’
SC1	−1.664	−1.695	−0.227	−0.227	1.437	1.468
SC2	−0.102	−0.076	−2.658	−2.658	−2.556	−2.582
SC3	−0.814	−0.834	−0.185	−0.185	0.630	0.649
SC4	−0.101	−0.107	−1.561	−1.561	−1.460	−1.454
SC5	−1.907	−1.908	−0.298	−0.298	1.609	1.610
SC6	−0.117	−0.090	−3.037	−3.037	−2.920	−2.947
SC7	−0.806	−0.824	−0.191	−0.191	0.615	0.633
SC8	−0.109	−0.118	−1.554	−1.554	−1.445	−1.437
SC9	−1.901	−1.904	−0.313	−0.313	1.588	1.590
SC10	−0.124	−0.095	−3.022	−3.022	−2.897	−2.926
SC11	−0.170	−0.133	−0.300	−0.300	−0.129	−0.167
SC12	−0.073	−0.083	−0.427	−0.427	−0.353	−0.343

. The Z displacement of points ③ and ④ is represented as relative Z displacements ③’ and ④’, taking into account the Z displacement of points ① and ② as the analysis progresses.

The Y-direction deformation results indicate that the ends of the saddle where the pressure vessel is installed (points ③ and ④) deform either outward or inward, depending on the welding scenario. As expected, due to the transverse shrinkage in the bracket and web frame during welding, negative Z-direction deformation occurs at all points from ① to ④. However, the relative Z displacements ③’ and ④’, when adjusted for the Z displacement of points ① and ②, show variations depending on the welding scenario. This suggests that the final deformation of the saddle arch could resemble either a horizontal ellipse or a vertical ellipse, as depicted in Figure 8.

Using the new coordinates ①’ through ④’ for points ① through ④, where displacement occurred (as shown in Table 5 and Table 6), the dimensions of the ellipses passing through points ①’–③’ and ②’–④’ are listed in

Table 7. The specification of the deformed arch of the saddle in each scenario.

Scenario	Ellipse Shape	a ①’–③’ [mm]	b ①’–③’ [mm]	e ①’–③’	Ovality ①’–③’ [%]	a ②’–④’ [mm]	b ②’–④’ [mm]	e ②’–④’	Ovality ②’–④’ [%]
SC1	Vertical	5019.523	4996.500	0.096	0.229	5019.554	4996.251	0.096	0.232
SC2	Horizontal	5017.960	5048.928	0.111	0.309	5017.934	5049.140	0.111	0.311
SC3	Vertical	5018.673	5009.220	0.061	0.094	5018.693	5009.060	0.062	0.096
SC4	Horizontal	5017.959	5035.330	0.083	0.173	5017.965	5035.281	0.083	0.173
SC5	Vertical	5019.766	4993.746	0.102	0.259	5019.767	4993.737	0.102	0.259
SC6	Horizontal	5017.975	5050.798	0.114	0.327	5017.948	5051.018	0.114	0.330
SC7	Vertical	5018.665	5009.415	0.061	0.092	5018.682	5009.277	0.061	0.094
SC8	Horizontal	5017.967	5035.134	0.083	0.171	5017.976	5035.063	0.082	0.170
SC9	Vertical	5019.760	4994.059	0.101	0.256	5019.762	4994.037	0.101	0.256
SC10	Horizontal	5017.983	5050.473	0.113	0.324	5017.954	5050.709	0.114	0.326
SC11	Vertical	5018.029	5015.851	0.029	0.022	5017.992	5016.150	0.027	0.018
SC12	Vertical	5017.932	5017.114	0.018	0.008	5017.942	5017.035	0.019	0.009

.

The eccentricity and ovality of the ellipse formed by the deformed saddle arch were calculated using Equations (4) and (5).

$$e=\sqrt{1-{[{\displaystyle \frac{\min \left(a, b\right)}{\max \left(a, b\right)}}]}^2}$$

(4)

$$u={\displaystyle \frac{[max(a, b)-min(a, b\left)\right]}{D}}\times 100\%$$

(5)

Here, a and b represent the lengths of the minor and major axes of the ellipse, e denotes the eccentricity, u the ovality, and D the initial diameter of the saddle model. Although the deformed shape of the saddle arch varies slightly between scenarios, the differences in eccentricity and ovality are minimal. These values suggest that the saddle arch’s deformed shape is nearly circular. However, the pressure vessel is installed in a configuration closer to a tangent at the center of the saddle arch, as shown in Figure 9, rather than being concentric with the saddle. Therefore, from the perspective of pressure vessel installation, the positions of the upper ends ③ and ④ of the saddle are more critical than the saddle arch’s ovality. The scenarios that most clearly illustrate the arch transitioning into a vertical or horizontal ellipse after welding are shown in Figure 10, providing insight into the potential placement of the pressure vessel, as depicted in Figure 9.

If points ③ and ④ deform inwardly, this could lead to interference and collision issues during the installation of the pressure vessel. Typically, a tolerance of about 20 mm is maintained between the saddle and the wooden block of the pressure vessel, with resin applied in this space. To ensure that the resin is applied with sufficient thickness to effectively bear the load and avoid issues during pressure vessel installation, excessive inward deformation of the saddle should be avoided. Conversely, if points ③ and ④ deform outwardly, the pressure vessel may tilt during installation, and the increased resin usage could raise material costs.

In both cases—whether the saddle ends deform inwardly or outwardly—installing the anti-floating device (AFD) on the upper plate at the saddle ends may become challenging. In particular, interference between the AFD and the fuel tank insulation, as shown in Figure 11, is a recurring quality issue, even when the pressure vessel, saddle, and AFD are manufactured within tolerance. This issue is exacerbated by the manual application of sprayed polyurethane foam (SPF) insulation on the pressure vessel, making quality control more difficult. Therefore, installation methods that lead to excessive deformation compared to the initial design should be avoided. The displacement tracking results for points ③ and ④ during welding, used to assess the impact of the welding sequence, are summarized in

Table 8. Displacement tendency according to different welding sequences for SC1, SC2, and SC3.

Welding Sequence	Weld Line	Average of Y-Displacement ③, ④ [mm]	Weld Line	Average of Y-Displacement ③, ④ [mm]	Weld Line	Average of Y-Displacement ③, ④ [mm]
	SC1		SC2		SC3
0	-	0.000	-	0.000	-	0.000
1	X7_outside	−0.500	X1_outside	0.005	Y6	0.011
2	X7_inside	0.287	Y1	0.310	Y5	−0.196
3	Y6	0.058	X2_inside	0.441	Y4	−0.336
4	X6_outside	−0.059	X2_outside	0.456	Y3	−0.421
5	X6_inside	−0.240	Y2	0.775	Y2	−0.466
6	Y5	−0.415	X3_inside	0.918	Y1	−0.495
7	X5_outside	−0.489	X3_outside	0.998	X7_outside	−0.380
8	X5_inside	−0.592	Y3	1.303	X7_inside	−0.241
9	Y4	−0.702	X4_inside	1.458	X6_outside	−0.229
10	X4_outside	−0.742	X4_outside	1.553	X6_inside	−0.223
11	X4_inside	−0.810	Y4	1.791	X5_outside	−0.223
12	Y3	−0.871	X5_inside	1.905	X5_inside	−0.232
13	X3_outside	−0.894	X5_outside	2.002	X4_outside	−0.237
14	X3_inside	−0.927	Y5	2.188	X4_inside	−0.255
15	Y2	−0.961	X6_inside	2.281	X3_outside	−0.263
16	X2_outside	−0.976	X6_outside	2.367	X3_inside	−0.276
17	X2_inside	−0.995	Y6	2.514	X2_outside	−0.287
18	Y1	−1.019	X7_inside	2.634	X2_inside	−0.300
19	X1_outside	−1.031	X7_outside	2.775	X1_outside	−0.312

,

Table 9. Displacement tendency according to different welding sequences for SC4, SC5, and SC6.

Welding Sequence	Weld Line	Ave. of Y-Disp. ③, ④ [mm]	Weld Line	Ave. of Y-Disp. ③, ④ [mm]	Weld Line	Ave. of Y-Disp. ③, ④ [mm]
	SC4		SC5		SC6
0	-	0.000	-	-		0.000
1	Y1	0.244	X7_outside	Y1	X7_outside	0.244
2	Y2	0.537	X7_inside	Y2	X7_inside	0.537
3	Y3	0.824	X6_outside	Y3	X6_outside	0.824
4	Y4	1.059	X6_inside	Y4	X6_inside	1.059
5	Y5	1.245	X5_outside	Y5	X5_outside	1.245
6	Y6	1.394	X5_inside	Y6	X5_inside	1.394
7	X1_outside	1.379	X4_outside	X1_outside	X4_outside	1.379
8	X2_inside	1.363	X4_inside	X2_inside	X4_inside	1.363
9	X2_outside	1.352	X3_outside	X2_outside	X3_outside	1.352
10	X3_inside	1.336	X3_inside	X3_inside	X3_inside	1.336
11	X3_outside	1.328	X2_outside	X3_outside	X2_outside	1.328
12	X4_inside	1.308	X2_inside	X4_inside	X2_inside	1.308
13	X4_outside	1.301	X1_outside	X4_outside	X1_outside	1.301
14	X5_inside	1.294	Y6	X5_inside	Y6	1.294
15	X5_outside	1.294	Y5	X5_outside	Y5	1.294
16	X6_inside	1.306	Y4	X6_inside	Y4	1.306
17	X6_outside	1.319	Y3	X6_outside	Y3	1.319
18	X7_inside	1.444	Y2	X7_inside	Y2	1.444
19	X7_outside	1.584	Y1	X7_outside	Y1	1.584

,

Table 10. Displacement tendency according to different welding sequences for SC7, SC8, and SC9.

Welding Sequence	Weld Line	Ave. of Y-Disp. ③, ④ [mm]	Weld Line	Ave. of Y-Disp. ③, ④ [mm]	Weld Line	Ave. of Y-Disp. ③, ④ [mm]
	SC7		SC8		SC9
0	-	0.000	-	-	0.000	-
1	Y6	0.011	Y1	Y6	0.011	Y1
2	Y5	−0.196	Y2	Y5	−0.196	Y2
3	Y4	−0.336	Y3	Y4	−0.336	Y3
4	Y3	−0.421	Y4	Y3	−0.421	Y4
5	Y2	−0.466	Y5	Y2	−0.466	Y5
6	Y1	−0.495	Y6	Y1	−0.495	Y6
7	X1_outside	−0.509	X7_outside	X1_outside	−0.509	X7_outside
8	X2_inside	−0.526	X7_inside	X2_inside	−0.526	X7_inside
9	X2_outside	−0.536	X6_outside	X2_outside	−0.536	X6_outside
10	X3_inside	−0.552	X6_inside	X3_inside	−0.552	X6_inside
11	X3_outside	−0.560	X5_outside	X3_outside	−0.560	X5_outside
12	X4_inside	−0.580	X5_inside	X4_inside	−0.580	X5_inside
13	X4_outside	−0.587	X4_outside	X4_outside	−0.587	X4_outside
14	X5_inside	−0.594	X4_inside	X5_inside	−0.594	X4_inside
15	X5_outside	−0.594	X3_outside	X5_outside	−0.594	X3_outside
16	X6_inside	−0.582	X3_inside	X6_inside	−0.582	X3_inside
17	X6_outside	−0.569	X2_outside	X6_outside	−0.569	X2_outside
18	X7_inside	−0.440	X2_inside	X7_inside	−0.440	X2_inside
19	X7_outside	−0.299	X1_outside	X7_outside	−0.299	X1_outside

and

Table 11. Displacement tendency according to different welding sequences for SC10, SC11, and SC12.

Welding Sequence	Weld Line	Ave. of Y-Disp. ③, ④ [mm]	Weld Line	Ave. of Y-Disp. ③, ④ [mm]	Weld Line	Ave. of Y-Disp. ③, ④ [mm]
	SC10		SC11		SC12
0	-	0.000	-	-	0.000	-
1	X1_outside	0.005	X1_outside	X1_outside	0.005	X1_outside
2	X2_inside	0.390	Y6	X2_inside	0.390	Y6
3	X2_outside	0.431	X2_inside	X2_outside	0.431	X2_inside
4	X3_inside	0.925	X2_outside	X3_inside	0.925	X2_outside
5	X3_outside	1.102	Y5	X3_outside	1.102	Y5
6	X4_inside	1.483	X3_inside	X4_inside	1.483	X3_inside
7	X4_outside	1.628	X3_outside	X4_outside	1.628	X3_outside
8	X5_inside	1.953	Y4	X5_inside	1.953	Y4
9	X5_outside	2.142	X4_inside	X5_outside	2.142	X4_inside
10	X6_inside	2.382	X4_outside	X6_inside	2.382	X4_outside
11	X6_outside	2.550	Y3	X6_outside	2.550	Y3
12	X7_inside	2.665	X5_inside	X7_inside	2.665	X5_inside
13	X7_outside	2.892	X5_outside	X7_outside	2.892	X5_outside
14	Y6	2.940	Y2	Y6	2.940	Y2
15	Y5	2.936	X6_inside	Y5	2.936	X6_inside
16	Y4	2.917	X6_outside	Y4	2.917	X6_outside
17	Y3	2.892	Y1	Y3	2.892	Y1
18	Y2	2.870	X7_inside	Y2	2.870	X7_inside
19	Y1	2.848	X7_outside	Y1	2.848	X7_outside

and Figure 12.

As summarized in Table 5 and Table 6, differences in the width-direction behavior of points ③ and ④ can be observed for each scenario. To enhance visibility and provide a more detailed behavior analysis, certain scenarios have been grouped; they are represented in Figure 13, Figure 14, Figure 15 and Figure 16.

Figure 13 illustrates the behavior for scenarios where the web frame is welded after the bracket. In Scenarios 5 and 9, where the bracket is welded from the outside toward the inside of the saddle, deformation occurred inward at points ③ and ④. Conversely, in Scenarios 6 and 10, deformation occurred outward at the same points. These results indicate that the final deformation due to web frame welding is not significantly affected by the welding direction, as the structural stiffness of the saddle is already increased by the prior bracket welding.

Figure 14a shows the behavior when the bracket and web frame are welded sequentially. In Scenario 1, where the bracket and web frame are alternately welded toward the inside of the saddle, deformation occurred inward at points ③ and ④. In the opposite case, Scenario 2, deformation occurred outward at the same points. This pattern is consistent with the behavior observed in Figure 13. Figure 14b depicts scenarios where the bracket is welded after the web frame. In Scenarios 3 and 7, where the web frame is welded from the outside toward the inside of the saddle, deformation occurred inward at points ③ and ④. Conversely, in Scenarios 4 and 8, deformation occurred outward at the same points. These scenarios confirm that the final deformation due to bracket welding is not significantly affected by the welding direction, as the structural stiffness of the saddle is increased by the web frame welding. This phenomenon mirrors what was observed in Figure 13, where significant deformation occurred during X7 welding, which was identified as highly sensitive.

Figure 14c shows the behavior in Scenarios 11 and 12, where the bracket and web frame are alternately welded from the inside to the outside and vice versa. These scenarios induce minimal deformation, as the structural stiffness of the saddle increases early in the welding process due to boundary conditions forming on either side of the saddle as welding progresses. However, the workability is poor because these scenarios involve alternating welding between opposite sides. Despite this, the deformation behavior in Scenarios 1, 5, 9, and 12, shown in Figure 15, deviated from the results of the sensitivity analysis.

These scenarios involve welding the X7 weld line first. During X7_outside welding, the X7 bracket would typically deform outward, causing outward deformation at points ③ and ④, but inward deformation was observed instead. This discrepancy is related to the position of the X7 bracket and the thickness of the seat top plate where the bracket is welded. During X7_outside welding, the deformation of the outermost seat top plate and the X7 bracket was observed to decrease due to the angular deformation formed by the two plates during welding, as shown in Figure 16.

However, since the edge of the seat top plate is free, larger deformation occurs outward from the seat top plate. Additionally, the seat top plate has greater structural stiffness than the bracket due to its thickness. Therefore, the force driving inward deformation of the saddle structure due to upward deformation of the seat top plate is stronger than the force driving outward deformation by the X7 bracket. As a result, during X7_outside welding, the reaction force from the seat suppresses the deformation of the X7 bracket and the outer seat top plate, with the reaction force from the seat being greater, as shown in Figure 17.

For these reasons, when the X7 weld line is welded first, points ③ and ④ deform inward. This does not contradict the finding from the sensitivity analysis that the X7 weld line is the most sensitive. This conclusion is further supported by the deformation tendencies in other scenarios. Summarizing the behavior observed in Figure 13 and Figure 14, when welding proceeds inward, points ③ and ④ deform inward, and when welding proceeds outward, these points deform outward. This is related to the longitudinal and transverse shrinkage, as well as the angular deformation caused by welding. In Scenario 5, where the largest inward deformation occurs at points ③ and ④, and in Scenario 6, where the largest outward deformation occurs, the welding heat input conditions were adjusted to isolate the effects of longitudinal shrinkage, transverse shrinkage, and angular deformation. The results, compared with the original analysis, are shown in

Table 12. Deformation behavior in weld heat input conditions that cause longitudinal shrinkage, transverse shrinkage and angular distortion only.

Welding Heat Input Condition	Step	SC5 Ave. of Y-Dis. ③, ④ [mm]	SC6 Ave. of Y-Dis. ③, ④ [mm]	Remark
Combined (original)	After bracket welding	−1.11	2.89	SC5: Weld brackets (1st) and web frames (2nd) inward of the saddle SC6: Weld brackets (1st) and web frames (2nd) outward of the saddle
	After web frame welding	−1.15	2.87
Only Longi. shrinkage	After bracket welding	−0.32	0.98
	After web frame welding	−0.38	0.98
Only Trans. shrinkage	After bracket welding	−0.75	2.17
	After web frame welding	−0.80	2.14
Only Ang. distortion	After bracket welding	−0.37	0.78
	After web frame welding	−0.36	0.78

, with deformation patterns for each case illustrated in Figure 18.

The results in Table 12 show that most deformation occurs during bracket welding. Once bracket welding is complete, the increased structural stiffness of the saddle due to strong constraints results in negligible additional deformation during web frame welding. This observation aligns with the explanation provided in Figure 13. When a welding heat input condition that induces only angular deformation is applied, out-of-plane deformation occurs due to bracket welding, but it is localized and has a minimal impact on deformation at points ③ and ④. When a condition that induces only longitudinal shrinkage is applied, in-plane deformation of the seat top plate due to bracket weld shrinkage is observed, but the impact on points ③ and ④ remains small. However, when a condition that induces only transverse shrinkage is applied, the impact on deformation at points ③ and ④ is greatest, as transverse shrinkage affects the entire weld regardless of the base metal’s influence.

The final displacement of points ③ and ④ across the twelve scenarios is summarized in

Table 13. Transverse displacement of the designated points of each scenario.

Scenario	Average of Y-Displacement ③, ④ [mm, anticlastic]	Brackets’ Welding Direction (X)	Web Frame’s Welding Direction (Y)	Absolute δ/δ min	Work-Ability	Remark
SC12	−0.168	Inward	Outward	1.000	Very bad	Small Displacement ↑ | | | | | | ↓ Large displacement
SC11	−0.180	Outward	Inward	1.071	Very bad
SC07	−0.299	Outward	Inward	1.775	Good
SC03	−0.312	Inward	Inward	1.855	Normal
SC01	−1.031	Inward	Inward	6.124	Very good
SC09	−1.128	Inward	Outward	6.703	Good
SC05	−1.154	Inward	Inward	6.857	Normal
SC08	1.572	Inward	Outward	9.335	Good
SC04	1.584	Outward	Outward	9.412	Normal
SC02	2.775	Outward	Outward	16.486	Very good
SC10	2.848	Outward	Inward	16.917	Good
SC06	2.873	Outward	Outward	17.066	Normal

. This table quantitatively indicates the direction of welding progress and the degree of deformation for each welding sequence scenario, with workability qualitatively classified as previously discussed. As noted earlier, from the perspective of pressure vessel installation, the displacement of points ③ and ④ is crucial, so the results are summarized based on the displacement of these points.

Based on the deformation amount and workability, the summary is as follows:

• Scenarios 1 and 2 offer the best workability but result in moderate-to-large deformation.
• Scenarios 3, 4, 5, and 6 provide good workability, with deformation ranging from moderate to maximum.
• Scenarios 7, 8, 9, and 10 have average workability, inducing deformation from small to large.
• Scenarios 11 and 12 exhibit the worst workability but cause the least deformation.

These findings suggest that the welding scenario can be selected based on the most critical factors to manage. Given the characteristics of the saddle, a certain degree of deformation can be accommodated through resin application. Therefore, Scenarios 1 and 3 are considered appropriate, as they offer good workability and do not result in significant deformation. However, these scenarios cause inward deformation of the saddle. If there is concern about interference between the pressure vessel’s insulation and the saddle’s AFD, Scenario 8 may be appropriate. However, for different structures, such as the dynamic positioning (DP) system of a ship or the material passing hole (MPH) located on the LNG ship’s liquid dome cover, the criteria for selecting a welding sequence would differ.

The azimuth thruster, which requires perfect roundness and flatness for 360-degree rotation and waterproofing, must be welded to the hull with high precision. Similarly, the MPH, which must be bolted to the MPH cover, requires a high level of flatness to prevent leaks of cold air or vaporized natural gas, which could lead to a major accident. If the evaluation targets of this study were the azimuth thruster or the MPH, and the results were similar to those in Table 13, Scenario 12 would be the preferred welding sequence, regardless of workability.

As previously mentioned, a tolerance of approximately 20 mm is applied between the saddle and the wooden block of the pressure vessel during fuel tank installation. Therefore, the welding deformation predicted through numerical analysis may not have a significant impact on pressure vessel installation. However, these results are based on theoretical models, while in practice, all components of the fuel tank system are subject to manufacturing tolerances, and issues have been encountered during actual installation. While it is impossible to predict all potential onsite challenges, the results of this study can help avoid the most severe problems. Additionally, the findings of this study may be useful in selecting welding construction methods for similar structures, not limited to the saddle structure of the fuel tank system.

5. Conclusions

This study has examined the deformation behavior associated with welding during the installation of the support structure for the IMO Type C LNG fuel tank system. The primary objective was to assess the impact of saddle welding deformation that occurs when the saddle is installed on the hull seat in a separate tank–saddle LNG fuel tank system. The key findings are summarized as follows:

• Sensitivity analysis of all weld lines on the saddle’s bracket and web frame revealed that the weld lines located on the outer side of the saddle exhibit the highest sensitivity to welding deformation.
• Based on the sensitivity analysis, twelve welding sequence scenarios were developed for sequential fillet welding. The study confirmed the differences in deformation behavior and the extent of saddle deformation depending on the welding direction and sequence.
• A quantitative and qualitative classification of welding deformation and workability was provided, offering a range of options tailored to specific needs.

In future research, the DIS method applied in this study will be extended to various structures to further verify its effectiveness. Additionally, new iterations of the DIS method, incorporating different welding techniques, will be developed to propose solutions that better align with the practical conditions and needs of shipyards.