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Statistical estimation of extreme sloshing impactpressure and its validation based on dynamicbehavior of insulation materialsTo cite this article: Jin-Ho Bae et al 2020 Funct. Compos. Struct. 2 015001

 

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© 2020 The Korean Society for Composite Materials and IOP Publishing Limited

1. Introduction

The International Maritime Organization (IMO) has identified several shape-based liquified natural gas (LNG) cargo containment systems (CCSs) that have been deemed unlikely to achieve the performance targets of either structural safety or economic efficiency, including a boil off gas (BOG), structural stability and safety under a sloshing impact load or/and ocean wave, and even hydrostatic pressure by the LNG. The design of LNG carrier should consider the environmental condition of economic profit by the volume efficiency of LNG CCSs to meet the demand of shipowner. In general, shape-based LNG CCSs can be categorized into four types, namely A, B, C, and membrane-type. In terms of a typical design approach, the membrane-type LNG CCSs as shown in figure 1, have been selected owing to their volume efficiency, structural stability, visibility for safety of vessel operation, and manufacturing technology. Among these advantages, the volume efficiency is the most important factor in terms of the design of an LNG carrier.

In the realistic loading condition of a membrane type LNG CCSs, the significant sloshing impact loading is distinguished as dominant loading state compared with hydrostatic of LNG or thermal stress, considering that the cryogenic state is influencing the material properties being more brittle [2, 3] and the ship operation with a full voyage cause sloshing impact loading on the inner wall as shown in figure 2. In order to obtain dominant loading properly, an estimation method used to calculate the initial loading state and LNG sloshing impact data is referred in this paper with reasonable data [4] included by the size effect, converting time. This approach not only suggests a realistic loading state at the material level of the tests but also indicate that the results will be applied to the design when considering with scalability with its design capacity.

The vast range of LNG sloshing impact loading is driven by dimension of LNG CCSs, the direction of the wave heading, filling ratio of LNG and 6-freedom of a ship. Based on numerous verification studies, statistical estimation methods have rapidly developed in recent decades as a way to verify the sloshing impact load owing to the potentially varying range applied to an inner insulation system [5, 6]. In order to accurately apply these results to the real scale of an insulation system, the extreme sloshing impact load based on the design life of an

J-H Bae et al

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© 2020 The Korean Society for Composite Materials and IOP Publishing Limited

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Funct. Compos. Struct.

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10.1088/2631-6331/ab628c

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Functional Composites and Structures

IOP

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2020

Statistical estimation of extreme sloshing impact pressure and its validation based on dynamic behavior of insulation materials

Jin-Ho Bae1 , Byeong-Kwan Hwang1, Seul-Kee Kim1 and Jae-Myung Lee1,2

1 Department of Naval Architecture and Ocean Engineering, Pusan National University, Busan, Republic of Korea2 Author to whom any correspondence should be addressed.

E-mail: jaemlee@pusan.ac.kr

Keywords: statistical estimation, sloshing impact energy, insulation material, dynamic behavior

AbstractThe design of an insulation material in a liquefied natural gas cargo containment system (LNG CCS) is mainly subjected to dominant sloshing impact loading. The sloshing impact loading, caused by the relative motion between the LNG carrier and the LNG CCS itself, continuously acts on the insulation material during the laden voyage. In the present study, impact tests were conducted on an insulation material consisting of polyurethane foam and plywood. The extreme sloshing impact energy had been set up after considering the sea conditions of wave height, wave period and a design life of 25 years of the LNG carrier. The extreme sloshing impact pressure was calculated using the statistical method of a generalized extreme value distribution (GEVD) combined with the Pierson–Moskowize spectrum and DNV code to obtain the period parameter of GEVD. GEVD was applied as the comparison of dynamic test results of insulation material based on force equilibrium. According to test results, significant sloshing impact pressure was verified as the dominant loading from test results of impact energy 31.66 J causing the overall plastic region of 0.144 mm mm−1.

PAPER2020

RECEIVED 31 July 2019

REVISED

11 December 2019

ACCEPTED FOR PUBLICATION

15 December 2019

PUBLISHED 8 January 2020

https://doi.org/10.1088/2631-6331/ab628cFunct. Compos. Struct. 2 (2020) 015001

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J-H Bae et al

LNG carrier of approximately 25 years was considered. To realize the extreme environment of impact load, a gen-eralized extreme value distribution (GEVD) was adopted.

Kuo et al [7] investigated the structural safety of LNG CCSs using a probabilistic-based framework applied in direct sloshing verification methods. The experiment results of the sloshing impact pressure were inserted as input data to verity the uncertainty of the Gumbel (Type I), Frechet (Type II), and Weibull (Type III) distribu-tions of the statistical models under a GEVD, and a nonlinear structural analysis using the finite element was systemically conducted with coupled tank sloshing and ship motions applied to the insulation system. Moreover, finite element analysis (FEA) was investigated under three variations of the GEVD, which was selected as the esti-mation method of the impact of the initial sloshing load on the integrity assessment of the insulation materials, including a sloshing impact test using the effects of scale, temperature. According to this study, a new sloshing assessment methodology was developed.

Kim [8] conducted an experimental test to investigate the impact of a Weibull distribution on the sloshing impact. The environmental conditions used in this test included a cryogenic temperature of 138 K for the LNG carrier; in addition, the measured pressure data were compared with the proposed statistical method based on the Weibull model, of which the rise time and peak pressure were phenomenologically derived from data set. The

Figure 1. Side view of membrane-type LNG carrier (GTT, Ltd).

Figure 2. Sloshing impact load with a variety of loading ranges in accordance with the relative motion of the LNG and the LNG carrier with 6 degrees of freedom caused by the wave heading.

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experimental results of the sloshing impact, obtained through the fitting, exhibited a compressive state with an impact of 6.84 MPa. This statistical method was considered to achieve a reasonable fitting curve, which is suitable for use in the rise time dataset whose corresponding peak pressure values are within the top 10%.

The insulation system in a membrane type LNG CCS [9] consists of stainless steel 304L at the primary barrier, polyurethane foam (PUF) and plywood with an epoxy resin for the first panel, a rigid and flexible secondary bar-rier, PUF and plywood with an epoxy resin for the second panel, and mastic. The composite of PUF and plywood in the first panel, which receives the sloshing impact load directly, was selected for this study. A sloshing impact experiment of the insulation materials was conducted through a free drop impact test by referring to the follow-ing studies.

Chun et al [10] experimentally confirmed that the use of a free drop impact is a reasonable method for evalu-ating the dynamic mechanical behavior of the insulation materials. A customized impact facility, namely a free drop impact facility, was realized and applied to the investigation of the dynamic behavior. The experiment results on the dynamic behavior determined through test scenarios divided into insulation types MARK III and KC-1 in the membrane of the LNG CCSs show the occurrences of cracking and propagation through the RPUF with respect to the cyclic impact load, which can be used as phenomenological evidence for a nonlinear mechani-cal behavior in its application in the design, as well as in numerical analyses of LNG CCSs.

Reflecting on the above research, this study estimates the initial impact loading using a statistical method applying a Gumbel distribution. The GEVD was found to have a significant impact energy based on the energy conservation law. Impact tests were then conducted using a free drop impact facility for insulation materials con-sisting of PUF and plywood located at the first panel.

2. Statistical estimation

2.1. Estimation of wave periodThe wave period acting on the vessel hull is an important factor for the estimation of the sloshing impact load because of the generated process corresponding to the relative motion between the LNG carrier and the LNG in the CCSs caused by ocean waves. In the following section, the wave period is estimated, and inserted as a variable to convert the sloshing impact pressure into the impact energy of the initial loading condition of the impact facility.

2.1.2. DNV codeA statistical estimation was applied to the dynamic response of the sloshing impact before the impact tests. This research assumes that the frequency of oscillation of the LNG sloshing is the same as the LNG vessel [11] because a realistic environment is extremely complex to achieve. This paper assumes that the ship motions of sway and surge are only caused. The relationship between the resonance frequency and the filling ratio was determined to be the following:

Tres =

√π

B

g

1

tan hÄπ h

B

ä (1)

where h is the filling height of the LNG, B is the breadth and length of the LNC CCS, and g is the acceleration due

to gravity. Table 1 shows the dimension of target LNG CCS in this study.Figure 3 shows the resonance range of the LNG carrier in terms of the filling ratio in the LNG CCS. The filling

level of 90.5% is evidence by the following regulation. In general, the LNG filling ratio is limited to approximately 98% under the international code of the construction and equipment of ships carrying liquefied gases in bulk (IGC code). The boil off gas (BOG) of LNG was conventionally approximated as 0.03%–0.05% per day in LNG CCS. Almost LNG carriers had been shipped to their arrival location within about 15 d as know is well. Addi-tionally, it is known that the lower filling ratio causes more sloshing impact load on the inner wall. The simple relationship of generating BOG reduce the filling ratio of 7.5%, and then, we select the filling level of 90.5%. The solution of equation (1) showed the resonance period of the LNG carrier to be 7–10 s.

2.1.3. Pierson–Moskowize spectrum.Based on the aforementioned vessel frequency, this study assumes that the wave frequency is the same as the vessel frequency. The resonance frequency of the vessel can be defined as under 10 s when a filling ratio of 20% is

Table 1. The main dimension of target LNG CCS in this study.

Breadth Length Height Filling level

38 m 45 m 27 m 90.5 %

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applied based on the results shown in figure 3. Figure 4 shows the governing type of wave that can be generated by wind waves under a period of 30 s. In terms of the wind wave type, the Pierson–Moskowize (PM) spectrum can derive the frequency of the wind wave as well as the wave height from an empirical analysis conducted on an infinite ocean.

S (ω) =αg2

ω5exp

Å−β

(ω0

ω

)4ã

, (2)

where ω = 2πf, f is the frequency of the wave, ω0 = 1.026U10.5, and the empirical constants are α = 8.1 × 10−3 and β = 0.74. Moreover, U10.5 is the wind velocity at a height of 10.5 m from the free surface of the ocean. The period of the wave governed by the wind, cp, is

cp =g

ωp= 1.17U10.5. (3)

The wave height can be calculated using the integral of S(ω).

⟨ζ2⟩=

ˆ ∞

0S (ω)dω = 2.74 × 10−3 (U10.5)

4

g2. (4)

The wave period generated by the wind is expressed in figure 4. The velocity of the wind is regarded as a variable of the wave period and wave height through the linear and nonlinear relations, respectively. This study defines the constraint condition of both outputs, considering that they diverge into infinity when the velocity of the wind increases through this curve. Reasonable constraint conditions for the wind velocity and wave height are indicated in figure 5 in terms of defining the regulations for port entry and ship departure.

2.2. Estimation of extreme impact pressure2.2.1. Extraction of experiment dataMany studies have systemically investigated the sloshing impact based on the geometry and kinetic law of similarity. Hence, this research referenced such studies [12] to estimate the sloshing impact based on an LNG carrier design life of 25 years, and then simply converted it into the impact energy based on the energy conservation law. Figure 6 show the sloshing impact data [12] with considering that the motions of the ship for sway and surge are selected.

2.2.2. Generalized extreme value, or Gumbel distributionAccording to the design life of 25 years is to generate the significant pressures which were calculated by GEVD, namely Gumbel distribution (Type I) with two-parameters (the location parameter and the scale parameter) and the shape parameter of zero. The Gumbel distribution is calculated as follows:

G (x) = exp(− exp

(−x − µ

σ

)), (5)

where µ is the location parameter (−∞ < µ < ∞), and σ is the scale parameter (σ > 0). To estimate the two parameters, the generalized statistics using the first model moment matched the sample moments of the model’s mean µ and variance σ.

Figure 3. The resonance period to LNG filling ratio for a typical membrane LNG tank [6].

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M = µ+ γσ (6)

SD = πσ/√

6 (7)

where M is the mean of the experiment data, SD is the standard deviation of the experiment data, and γ is the Euler’s constant (0.577 72). In accordance with the design life of an LNG carrier, the GEVD was considered through the following equation:

Figure 4. Generation of ocean waves induced by the wave period.

Figure 5. Significant wave height and period under regulation.

Figure 6. The sloshing impact pressure in consideration of the sea condition for wave period and height [12].

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E25 = µ− σ ln

Å− ln

Å1 − 1

N

ãã, (8)

where E25 is the significant impact energy based on the period of sloshing impact generation during 25 years time frame when considering a laden voyage with a return period of N. For this period N, we consider an estimated sloshing impact period of 10 s calculated by PM spectrum. The statistical results based on Gumbel distribution of equation (8) is shown in table 2 according to sloshing impact pressure [8]. The sloshing impact pressure [12] is included of ship motion analysis excited in sway and surge as above mentioned. Moreover, the sea conditions of wave period and wave height were considered in accordance with wave period by PM spectrum results as well as

the wave height in figure 5.

3. Experiment preparation

3.1. Manufacturing of insulation materialPUF is widely used as an insulation material owing to its excellent thermal performance, mechanical properties, and economic feasibility. The density of PUF is generally 135 ± 3 g cm−3, and it contributes to the insulation panel in an LNG CCS with a reasonable thermal conductivity of 0.002 W m−1 K−1 and a strength of 1.4 MPa [13]. A target density of 130 g cm−3 can be achieved through the following method [14]. First, systems of isocyanate, polyol, and an agent blowing (HFC-245fa) were poured into a 3 L container at a weight ratio of 1000:1, 160:50, respectively. To achieve homogeneous mixing, it was mixed using a homogenizer with 4500 rpm for 60 s, and then the solution was poured into an open box with a breadth and length of 320 and 320 mm, respectively. A free forming time of approximately 24 h is assigned as an efficient hardening time for a mixed solution with a temperature of 15 °C. After manufacturing, the PUF was cut into a breadth, length, and height of 50 mm, 50 mm, and 27 mm, respectively. The cutting location should be at the middle because a free forming PUF can be densified near the walls of the box, such as the side walls and bottom due to gravity. Finally, plywood was attached to the top and bottom of the PUF with an epoxy resin, so as to reduce damage from direct impact on the PUF. Figure 7 illustrates the manufacturing process of the final product, and figure 8 shows the dimensions and composition of the material assigned for the final product.

3.2. Impact facilityThe impact test was performed using a free drop impact facility to realize a sloshing impact on the insulation materials as a phenomenological analysis for a fluid-spring back, energy delivery from the main object (impactor) to the subject (the specimen), and various energy ranges on the specimen. The impact facility consists of a steel frame, a square-shaped impactor, a 8.75 kg ballast, and a guideline for vertically throwing the impactor, as depicted in figure 9.

3.3. Impact test scenariosThe impact test scenarios followed the extreme sloshing impact energy estimated statistically, which is under the GEVD. In this test, an impactor with 8.75 kg was used and the impact energy was controlled with a drop height of the impactor. In detail, the inertia effect on the dynamic mechanical behavior of the insulation material under the impactor weight was ignored, and the impact energy was changed depending on the drop height. To obtain reliable test results, the tests were repeated five times for the specimen under the same conditions, with the maximum and minimum results excluded to reduce standard deviation owing to experiment error. Table 3 lists

the range of impact energy levels.

4. Experimental results

4.1. Material characteristicsIn the specimen, the plywood and epoxy resins are thin and have relatively high impact resistance compare to the PUF. Thus, we can assume that the impact responses mainly affected by the dynamic mechanical behaviors

Table 2. The statistical results of GEVD in accordance with sloshing impact pressure [12].

Sea conditions

Period Height Period Height Period Height Period Height

10.0 s 14.71 m 10.5 s 15.1 m 10.5 s 15.1 m 11.5 s 15.58 m

Significant impact pressure by GEVD

2.3554 MPa 2.395 MPa 2.583 MPa 2.537 MPa

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Figure 7. Manufacturing process of PUF and final product along with the specifications of the equipment used.

Figure 8. Specifications of the final product when following the manufacturing process.

Figure 9. Impact facility and its specifications.

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of the PUF. The typical dynamic behavior [1, 6] of PUF under the impact tests is shown in figure 10. Typical behaviors of the PUF were divided into three regions: elastic, plateau (plastic), and densification (plastic) [14]. The dynamic strength of the specimen is the stress at the point of transition from elastic to plastic region. During the plastic deformation it shows plateau region. After all cells in the PUF are fully collapsed it shows densification behavior. The amount of damage is related with the length in the plateau region including the densification region and it reduces the mechanical properties and degrades the thermal performance. Verification of the statistically estimated extreme impact energy and dynamic behavior of the insulation materials was achieved through quantitative comparisons of the occurrence of the plastic region and the length of the plastic region, as mentioned earlier.

Figure 10. Typical dynamic behavior of PUF with the definition of each region.

Figure 11. Test results of (a) strain rate–time relationship (b) dynamic stress–time relationship.

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Figure 12. Dynamic behavior of the insulation material under an impact energy of (a) 0.86, (b) 3.56, (c) 7.96, (d) 14.16, (e) 21.98, (f) 31.66, (g) 38 J and (h) all results.

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4.2. The strain rate over time relationshipFigure 11(a) shows strain rate history after the impactor contacted with the specimen. Initial strain rates are 19.25, 35.5, 53.25, 71, 88.5, 106.25, and 116.5 s−1 in accordance with the drop height of 30, 100, 232, 411, 643, 926, and 1110 mm, respectively. Dynamic stress histories at each impact energy are compared in figure 11(b). Strain rates at the point where the maximum stress occurred in figure 11(b) were observed at 7.62, 9.94, 44.85, 63.18, 81.59, 97.76, 109.81 s−1, respectively, in figure 11(a). Except for the case of impact energy 0.85 J, the strain rates gradually drop with the same gradient.

4.3. Experiment results and verification through statistical analysisIn this study, GEVD was applied in the statistical method for estimating the sloshing impact energy, and an impact test of the insulation material was applied. Figure 12 illustrates the three dynamic mechanical behaviors of the specimen, except for the maximum and minimum behaviors, to reduce the experimental error by the reliability. According to experimental results, the impact energy of 0.875 J seems to show pure elastic behavior and rebound the impactor. The dynamic strengths of 3.56, 7.96, 14.16, 21.98, 31.66, and 38 J are equal to 1.68, 1.87, 1.93, 2.15, 2.32, and 2.49 MPa, respectively. The maximum stress for the case of impact energy 0.85 J, which was included in this test for pure elastic behavior, is 1.03 MPa, and it successfully approached the elastic region under the impact test. The plateau stress fluctuates around 1.75 ± 0.3 MPa for most cases. All the stress–strain curves for each impact energy are compared in figure 12(h). It is observed that all the stress–strain curves in elastic region show similar behavior.

The plateau region for the mechanical behavior under impact is used as the definition of local damage for the insulation materials [15, 16]. The experiment results indicate that the plateau region appear when the impact energy is larger than 3.56 J. However, impact energy of below 3.56 J did not cause a specimen failure because this level of energy does not meet the minimum dynamic stress of 1.68 MPa. The statistically estimated impact pressure of approximately 2.35 MPa obtained by wave period of 10 s and wave height of 14.714 m can potentially make damage to the insulation materials (PUF) because the dynamic strength is around 1.68 MPa which is lower than 2.35 MPa. If the sloshing impact is similar with the impact test scenarios, the PUF cells will be critically damaged and the insulation performance will be degraded with the loss of mechanical performance. When the significant sloshing impact loading caused, the breakage of the PUF will gradually increase, causing degradation of insulation performance and loss of mechanical performance. The test results of dynamic strength and plastic

region are summarized in table 4.

5. Conclusion

This study used a statistical method that applies a Pierson–Moskowize (PM) spectrum and GEVD to estimate the significant impact pressure and verify the dominant loading from the impact test of the insulation material. Impact tests were then conducted on the insulation material, which consists of plywood, PUF, and epoxy resin for the first panel, taking into consideration the location directly impacted by sloshing. In addition, the

Table 3. Test scenarios of impact energy.

Impactor weight Strain rate (s−1) Drop height (mm) Impact energy (J)

A constant weight of 8.75 kg 20 30 0.85

40 100 3.56

60 232 7.96

80 411 14.16

100 643 21.98

120 926 31.66

131 1110 38

Table 4. Test results of dynamic properties of the insulation material.

Impact energy (J) Dynamic strength (MPa) Plastic region (mm mm−1)

0.85 1.03 0.004

3.56 1.68 0.008

7.96 1.87 0.019

14.16 1.93 0.052

21.98 2.15 0.099

31.66 2.32 0.144

38 2.49 0.175

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characteristics of the dynamic behavior of the synthesized insulation materials (except for plywood and epoxy resin) were analyzed based on the typical behavior of PUF. The conclusions of this study are summarized below.

• The wave frequency inducing the sloshing impact is followed by a DNV regulation and PM spectrum under the assumption of wind waves. The sea conditions of wave period and height are designated within 10 s and 15 m, respectively. The sloshing impact data is referred in terms of sea condition. To obtain the significant impact pressure, GEVD is adopted with considering the expectance design of 25 years and generation time of sloshing impact period derived by PM spectrum and DNV code. The statistical results calculate the significant impact pressure from 2.35 to 2.53 MPa.

• The characteristics of the insulation materials are generally categorized according to three states: (i) an elastic region, (ii) a plateau (plastic region), and (iii) densification (plastic region) in accordance with the dynamic behavior of neat PUF (density of approximately 130 kg m−3). The results of the research confirm that elastic and plateau regions are generated under impact tests, and a decrease in stress was observed.

• The dynamic strength of 1.64 MPa appears the plateau in the dynamic behavior of the insulation material. Verification of the significant impact pressure from 2.35 to 2.53 MPa and its application to the insulation design was achieved by identifying that a plateau region was simultaneously caused by the dynamic mechanical behavior.

The statistical estimation can contribute to the safety design of the insulation system located in the inner wall. In detail, the results of the impact test and statistical estimation based on GEVD will be helpful in designing robust and safe of insulation material under sloshing impact loading caused by ship motion of sway and surge conditions.

Acknowledgments

This work was presented at the Korean Society for Composite Materials (KSCM) conference (April 4–6, 2019). This work was supported by the R&D Platform Establishment of Eco-Friendly Hydrogen Propulsion Ship Program (No. 20006632) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea). This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science and ICT (MSIT) (No. 2018R1A2B6007403).

ORCID iDs

Jin-Ho Bae https://orcid.org/0000-0001-7761-6354Jae-Myung Lee https://orcid.org/0000-0002-8096-4306

References

[1] Kim J K, Kim J H, Ahn J H, Kim J D, Park S K, Park K H and Lee J M 2018 Synthesis of nanoparticle-enhanced polyurethane foams and evaluation of mechanical characteristics Composites B 136 28–38

[2] Lee C S, Cho J R, Kim W S, Noh B J, Kim M H and Lee J M 2013 Evaluation of sloshing resistance performance for LNG carrier insulation system based on fluid-structure interaction analysis Int. J. Naval Archit. Ocean Eng. 5 1–20

[3] Kim J H, Park D H, Lee C S, Park K J and Lee J M 2015 Effects of cryogenic thermal cycle and immersion on the mechanical characteristics of phenol-resin bonded plywood Cryogenics 72 90–102

[4] Yamamoto S et al 1993 Study on impact pressure due to sloshing in mid-sized LNG carrier The 3rd Int. Offshore and Polar Engineering Conf. (International Society of Offshore and Polar Engineers)

[5] Saripilli J R and Sen D 2018 Numerical studies on effects of slosh coupling on ship motions and derived slosh loads Appl. Ocean Res. 76 71–87

[6] Souto-lglesias A, Bulian G and Botia-Vera E 2015 A set of canonical problems in sloshing part 2: influence of tank width on impact pressure statistics in regular forced angular motion Ocean Eng. 105 136–59

[7] Kuo J F, Campbell R B, Ding Z, Hoie S M, Rinehart A J, Sandstorm R E, Yung T W, Greer M N and Danaczko M A 2009 LNG tank sloshing assessment methodology-the new generation 19th Int. Offshore and Polar Engineering Conf. (Osaka: ISOPE) pp 1–12

[8] Kim Y 2016 Rapid response calculation of LNG cargo containment system under sloshing load using wavelet transformation Int. J. Naval Archit. Ocean Eng. 5 227–45

[9] Oh D J, Kim N K, Song S W, Kim Y D and Kim M H 2018 Investigation of fatigue performance for new membrane-type LNG CCS at cryogenic temperature Marine Struct. 62 90–105

[10]Chun M S, Kim M H, Kim W S, Kim S H and Lee J M 2009 Experimental investigation on the impact behavior of membrane-type LNG carrier insulation system J. Loss Prevent. Process Ind. 22 901–7

[11]DNV Classification Note, No. 30.9, “Sloshing Analysis of LNG Membrane Tanks”, August 2014[12]Graczyk M, Moan T and Rognebakke O 2006 Probabilistic analysis of characteristic pressure for LNG tanks J. Offshore Mech. Arct. Eng.

128 133–44[13]Park S B, Lee C S, Choi S W, Kim J H, Bang C S and Lee J M 2016 Polymeric foams for cryogenic temperature application: temperature

range for non-recovery and brittle-fracture of microstructure Compos. Struct. 136 258–69

Funct. Compos. Struct. 2 (2020) 015001

12

J-H Bae et al

[14]Park S B, Choi S W, Kim J H, Bang C S and Lee J M 2016 Effect of the blowing agent on the low-temperature mechanical properties of CO2-and HFC-245fa-blown glass-fiber-reinforced polyurethane foams Composites B 93 317–27

[15]Chen W, Lu F and Winfree N 2002 High-strain-rate compressive behavior of a rigid polyurethane foam with various densities Exp. Mech. 42 65–73

[16]Ozkul M H and Mark J E 1994 Ther effect of preloading on the mechanical properties of polymeric foams Polym. Eng. Sci. 34 794–8

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