Temperature-stress-time methodology for flat-patterning ETFE cushions in use for large-span building structures

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Temperature-stress-time methodology for flat-patterning ETFE cushions in use for large-span building structures Jianhui Hua,b,c, Wujun Chena,c, , Yipo Lia, Yegao Que, Bing Zhaoa, Deqing Yangd,c ⁎

a

Space Structures Research Center, Shanghai Jiao Tong University, Shanghai 200240, China Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505, Japan c State Key Laboratory of Ocean Engineering, Shanghai 200240, China d Collaborative Innovation Center for Advanced Ship and Deep-Sea Exploration, Shanghai 200240, China e State Key Laboratory of Mechanical System and Vibration, Shanghai 200240, China b

ARTICLE INFO

ABSTRACT

Keywords: Creep model Engineering structures ETFE cushion Flat-patterning Large-span structures Membrane structure Structural behavior Temperature-stress-time methodology

Ethylene tetrafluoroethylene (ETFE) cushion structures with excellent building aesthetics and reasonable structural behavior can be utilized as roofs and facades of large-span building structures. The form and force of such structures interact due to structural flexibility and complexity. The determination of a suitable form needs form-finding and cutting pattern for conventional ETFE cushions, which incorporates complex theoretical analysis and fabrications. To obtain a structural form without complex cutting pattern, a flat-patterning ETFE cushion is proposed based on creep properties of polymer materials. This methodology facilitates to achieve desired forms using creep models of ETFE foils. Moreover, time-temperature superposition of polymer materials is employed to improve this method. Therefore, this paper focuses on a modified creep model of ETFE foils and utilizes it to assess form and force of flat-patterning ETFE cushion structures. The Bailey-Norton model with Modified Time Hardening effect results in a creep model that describes creep strains at high temperature. To integrate this model into software, a multi-linear model is used where parameters are determined with experimental results. The related numerical simulations demonstrate the suitability of reproducing creep strains. For structural analysis, two typical cushions with inverse temperatures and pressures are simulated with multi-linear models. It is found that the maximum stress and strain exist near middle area of long edges and propagate towards cushion center. The final deformations of two cushions are 21.2 mm and 19.4 mm; the ratios of heights to edge length are larger than the engineering ratio of 1/8, resulting in a suitable structural form. A further ratio of stress to yield stress suggests the easy operation to achieve desired forms for small pressure at high temperature than large pressure at low temperature. In general, the proposed method to reveal form and structural behavior is useful for promoting utilizations of flat-patterning ETFE cushions.

1. Introduction The ethylene tetrafluoroethylene (ETFE) cushion buildings used as roofs and facades of large-span building structures, such as recent Dalian Sports Center Stadium and Guangzhou South Railway Station (see Fig. 1), have attracted considerable attention in recent decades due to excellent building performance and reasonable structural behavior [1,2]. Typical building performance is composed of light, thermal, environment and sustainability. The light level inside such buildings is high due to 95% light transmittance of ETFE foils [3]. The adjustment of light level with surface treatment can meet various demands. One useful utilization is to generate images in the front of buildings with active pressure control [4]. For thermal performance, the enclosed air

⁎

between ETFE layers increases insulation properties and thus reduces energy consumption. The incorporation of high-performance membrane materials further improves building thermal performance [5]. As for sustainability, Monticelli et al. demonstrated that utilizing 100% recyclable ETFE foils is essential for natural environment [6,7]. Moreover, sustainability of ETFE buildings can be enhanced in a way of buildings integrated photovoltaics that use solar energy to compensate building energy consumption [8,10]. The integrations of ETFE foils and flexible/organic photovoltaics have validated possible feasibility and potential. Therefore, overall building performance matches the criteria of sustainable buildings. These building characteristics distinguish ETFE buildings from other traditional buildings and related research is indispensable for evaluating building performance.

Corresponding author at: Space Structures Research Center, Shanghai Jiao Tong University, Shanghai 200240, China. E-mail addresses: [email protected], [email protected] (J. Hu), [email protected] (W. Chen).

https://doi.org/10.1016/j.engstruct.2019.109607 Received 31 March 2019; Received in revised form 5 July 2019; Accepted 29 August 2019 0141-0296/ © 2019 Published by Elsevier Ltd.

Please cite this article as: Jianhui Hu, et al., Engineering Structures, https://doi.org/10.1016/j.engstruct.2019.109607

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Fig. 1. Recent ETFE building projects: Dalian Sports Center Stadium and Guangzhou South Railway Station [9].

The accomplishment of building performance requires proper structural form and behavior. The conventional design and analysis of ETFE structures incorporate form-finding, structural analysis and cutting pattern [11,12]. Generally, theoretical form-finding is complex due to geometrical nonlinearity and commercial software gives approximate forms [13,14]. Moreover, theoretical and numerical forms need to be translated to plan forms due to limited width of ETFE foils. The discrepancy between designing and cutting forms exist and thus real structural behavior is not in line with design one [15]. Considering creep and hardening of polymer materials [16], one novel and easy method is proposed to find approximate forms of ETFE cushions since complicated cutting pattern is not necessary. The feasibility of this method is validated with experimental and numerical analysis. Kawabata and Moriyama combined dynamic viscoelastic and creep experiments to introduce corrective function of time and stress [17]. Bartle and Gosling extended an analytical expression of large deformation to predict form and stress distributions of un-patterned square ETFE cushions [18]. Kawabata et al. investigated structural design of membrane structure using plastic stretch and heat shrink of ETFE films [19]. Chen et al. proposed a new approach for form finding of flat-patterning ETFE cushions and found that plastic strain originated at 2 kPa at room temperature [20]. However, it is pointed out that this method requires high pressure and that structural behavior is not fully-revealed. The uniaxial constitutive models of ETFE foils are indispensable to assess structural behavior [12]. Using the Peirce model to calculate stress and strain distributions of ETFE structures is helpful to understand structural behavior of ETFE structures [20]. However, the analysis ignores creep effects of over-pressure inside ETFE cushions on structural forms. In fact, the real process of flat-patterning ETFE cushion includes inflation and pressure maintenance, meaning that a creep model is essential to achieve desired forms and evaluate structural behavior [19,21]. The Kelvin-Voigt models can describe nonlinear strains with a series of complex combination of springs and dampers [22]. However, these models are not easy use for determining structural behavior of ETFE cushions. Therefore, a proper creep model of ETFE foils is indispensable to estimate structural behavior and achieve desired forms in the creep process [16]. Furthermore, it is possible to modify this method with time-temperature superposition [23]. For such superposition, creep strains at low stress level and high temperature can be identical for creep strains at high stress and low temperature, suggesting that conventional methods at room temperature and high stress can be replaced with high temperature and low stress. The use of this superposition has been validated for polycarbonates [24] and plastic materials [25], giving credits for ETFE foils. However, corresponding creep models are not available after a survey of the literature. Therefore, this paper focuses on proper creep models of ETFE foils at room and high temperatures and utilizes it to reveal forms and structural behavior of ETFE cushions. The composition of this paper is organized as follows. Creep models based on Bailey-Norton equations are improved with Modified Time

Hardening effect, and are validated with experimental and numerical results in Section 2. In Section 3, material experiments and simulations are performed as the basis for structural analysis. The following Section concerns numerical simulations using creep models for two typical cushions to evaluate form characteristics and structural behavior. Finally, typical observations and useful values are summarized in the Conclusions. 2. Creep models In general, the Kelvin-Voigt models including spring and damper elements that correspond to elastic and viscous properties are used to simulate creep properties of polymer materials. However, utilizing these models to calculate structural behavior is hard due to multiple undetermined parameters. To relate creep strain, stress and time, a modified creep model based on Bailey-Norton constitutive equation is presented in this study; this model can clearly express basic mechanism in the creep process. 2.1. Bailey-Norton models The uniaxial creep properties of polymer materials at given stress, time and temperature can be expressed in a following function. cr

(1)

= f ( , t, T )

It is assumed that the interactions between stress, time and temperature can be ignored and a new function is achieved. cr

(2)

= f1 ( ) f2 (t ) f3 (T )

A superposition of the f1, f2 and f3 that can be determined with experiments generates an expression for creep strains of polymer materials. cr

= C exp(

H/RT ) t m

n

(3)

For a given temperature, the expression is the Bailey-Norton equation and given in a power law function as follows [26]. cr

(4)

= A nt m

where A, n and m are constants related to temperature. The derivative of this equation with respect to time is often referred to as the timehardening formulation of power law creep, expressed as: cr

= mA1/ m

n/m (

cr )

(m 1)/ m

(5)

This function describes strain hardening in power law. The NortonBailey law can also be given as follows, especially suitable when primary and secondary creep strains are significant for the strain values. cr

=A

n m

t

(6)

where A′, n′ and m′ are material parameters. The function shows that creep rate is associated with stress and time at a temperature, which 2

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corresponds to the following theoretical function in ANSYS. cr

= C1

C4 T

C2 t C3 e

algorithm is used to get values with iterative process. The characteristic points from experimental curves are chosen since stress-strain curves are nonlinear. A weighted method that points near turning area need more than linear and nonlinear parts can ensure suitable results. As initial values of C1, C2 and C3 play an important role in the convergence process, an approximate approach is expressed as follows.

(7)

where C1 is a correction factor and C2, C3 and C4 are constants in relation with stress, time and temperature. Integrating Eq. (7) with time can obtain creep strains in the form of stress, time and temperature. cr

= C1

C2 t C3+ 1e

C4 T /(C3

• Set a stress value, the creep strain and time are in the power func-

(8)

+ 1)

Therefore, the total creep strain is the sum of loading strain and creep strain. (9)

•

This creep model modified with time hardening theory shows that creep strain increases nonlinearly with time.

•

total

=

loading

+

cr

=

loading

+ C1

C2 t C3+ 1e

C4 T /(C3

+ 1)

2.2. Parameter determination

3. Material experiments and simulations

The total creep includes loading that generated by stress from 0 MPa until pre-stress and cr that generated due to time and pre-stress effects. To determine material parameters, three issues are worth noting.

3.1. Material experiments The ETFE foils are 200-NJ-1600-NT foils from Asahi Glass Co. Ltd, where 250, NJ, 1600 and NT are thickness, grade, roll width and surface treatment [29]. Standard rectangular specimens with 100 mm × 25 mm are made with a standard cutting machine. The experimental conditions for creep experiments are room and high temperatures (24 °C and 60 °C), stress of 8 MPa and creep time of 24 h [30,31]. The reasons to choose the two temperatures are that these two temperatures represent room temperature and high temperature that are used to compare differences between the conventional method and a new method considering temperature effects. Moreover, these temperatures are chosen based on the temperature range of the high temperature chamber where material experiments are carried out. Furthermore, these temperatures are typical for actual utilizations of ETFE cushions. Mechanical tests are carried out on a single axis servo-hydraulic test machine with computer control and acquisition. Rectangular specimens are preloaded with 0.1 N to ensure the removal of slack. For each test, displacements and loads are measured with integrated standard MTS displacement and force transducers, see Fig. 3. The strain-time curves of ETFE foils at 8 MPa and 60 °C are shown in Fig. 2. The loading speed for these experiments is 1%/min according to the ISO standards and the experimental procedure for ETFE cushion structures. To combine loading stress-strain and creep curves, a simplified multi-linear model is proposed to characterize homogeneous hardening material properties. The characteristic points in stress-strain curves are

• The pre-stress needs to exceed the first yield stress to produce nonreversible strains [27]. • The parameter determination needs to subcontract loading strains since experimental strains are total ones (see Fig. 2). • The cross-sectional area of ETFE specimens changes in the loading process under large strain condition. The true stress-strain curves are necessary for obtaining reasonable values.

The functions to get true stress and strain from engineering stress and strain are expressed as follows [28]. true

= ln(1 +

true

=

eng )

eng (1 +

(10)

eng )

where true and true are true strain and stress while eng and eng are engineering strain and stress. The temperature control in the experiments is employed to ensure a constant temperature. For this reason, temperature parameter in Eq. (9) is set to zero and results in the following function. cr

= C1

C2 t C3+ 1/(C 3

tion. The tendency of the function should follow experimental curves, indicating that C3 + 1 is in the range of 0–1 and thus C3 in the range of −1 to 0. Set a specific time, the creep strain and stress are also the power function and thus the C2 needs to be larger than 1 and in the order of 10. Based on C2 and C3, creep strains (10−2−10−1), and σ and t in the orders of 107 and 105, the range of C1 should be within 10−20.

(11)

+ 1)

The new equation needs to be fitted using specific mathematical tools to obtain parameter values. In this study, the fitting function organizer is suitable to solve this problem, where Levenberg-Marquardt

0.10

0.25 0.08

ε

0.15

cr

Creep strain

Strain

0.20

0.10

ε

loading

0.05

0.00

0.06

0.04

0.02

8MPa 0

20000

40000

60000

80000

0.00

100000

Time/s

0

20000

40000

60000

Time/s

Fig. 2. Illustration of total stains and experimental creep-time curves at 60 °C and 8 MPa. 3

80000

100000

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Fig. 3. Creep photos for ETFE foils: loading machine and specimen.

20

25

15

Stress/MPa

Stress/MPa

20 15 10

0 0.00

5

Experiment Multilinear model

5 0.05

0.10

0.15

Strain

0.20

0.25

10

0.30

0 0.00

Experiment Multilinear model 0.05

0.10

0.15

0.20

0.25

0.30

Strain

Fig. 4. Stress-strain curves of ETFE foils at 25 °C and 60 °C.

Fig. 5. Strain distribution and comparisons of ETFE foils at 60 °C and 8 MPa.

required to be identified. The typical stress-strain curves show two points and the intervals between these specific points need at least three points to show linear and nonlinear properties. The resulting points from stress-strain curves are depicted in Fig. 4.

The numerical model is established in accordance with ETFE specimens. The shell 181 element is utilized to simulate ETFE foils due to non-pressure and non-moment properties, which is suitable for large strain and creep analysis of membrane materials. The boundary conditions of numerical models are fixed with only one direction movement for pre-stress and strain. The loading stress is distributed at one end to avoid stress concentration. The mesh of the specimens is rectangular for matching rectangular specimens. The option of smart size is chosen to generate suitable mesh quality. The final mesh includes 1210 elements and 1288 nodes. Then, C1, C2, C3 are input in the software to define material properties.

3.2. Numerical validation The essential utilization of the proposed model is to calculate and analyze creep properties of ETFE foils at different temperature, stress and time. To validate this model, numerical simulations based on software ANSYS are performed with obtained parameters. 4

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fastening aluminum extruder. To measure structural behavior and ensure simple symmetrical structural behavior, the ETFE cushion is fixed vertically to aluminum frame using bolts. Additionally, two holes are placed to connect pressure system for controlling inflation. The pressure control system, crucial for ETFE cushion structures, includes pressure monitoring and control parts, shown in Fig. 7. Such system is mainly combined of software, air blower, one-way valve, pressure sensor. Since the current control system cannot meet the control accuracy of small cushion volume, one major modification is the addition of a 50L air vessel. The working principle of the system is that the sensor detects the pressure inside the ETFE cushions and sends it back to the controller to check. The blower begins to work when the pressure value is lower than the given one and stops inflating when the pressure reaches to the given pressure. The displacement measuring equipment is laser displacement sensor as equipment cannot be put into the temperature chamber for high temperature experiments. The sensors measure three points on cushion surface with one in the center and two symmetrical distribution along the vertical direction (see Fig. 6). The measuring range of the sensors (Type HG-C1050, Panasonic Co. Ltd.) is larger than preliminary numerical analysis with a maximum displacement of about 20 mm. The temperature-stress-time effects can be divided into two categories, i.e., high stress at low temperature and low stress at high temperature. In this study, the basic parameters for two typical cushions are 24 °C/24 kPa for CUSHION 1 and 60 °C/12 kPa for CUSHION 2 which are determined with a preliminary analysis. To perform structural experiments, the inflation rate needs to consider temperature- and ratedependent material properties. The inflation rate of ETFE cushions can match 1%/min material experiments and justify the utilization of corresponding material properties. Some preliminary numerical analysis shows that 10% and 7% strains are for the two cushions in the inflation process. Therefore, a 10-min and 7-min inflations are suitable to reach these strains. The cushions are then maintained at a constant inner pressure for 24 h to generate creep deformation and achieve desired forms. Fig. 7 shows the photos for room and high temperature experiments. The experimental deformations of the two cushions are compared with numerical analysis to validate the suitability of creep models. Then, the detailed stress and strain distributions are analyzed and quantified to understand form characteristics and structural behavior.

Two steps in the simulation are used to perform nonlinear analysis according to real engineering application. In the first step, the raterelated option needs to be tuned off not to consider viscous properties. However, this step can affect the total time step and thus a small time interval (1e-8) is given in this step. For the second step, the rate-related option needs to open to consider time effect and the time period is set as 86,400 s (24 h). Based on these settings, strain distribution and displacement of ETFE foils at 60 °C and 8 MPa are given in Fig. 5. To compare experimental and numerical results, the displacement at the specimen center is used to analyze material properties. A good agreement is found for experimental and numerical results. The tendency and characteristics points match well and a maximum deviation is within 6%. Therefore, it is suitable for using this creep model to determine structural behavior and form of flat-patterning ETFE structures. 4. Structural experiments and simulations Generally, form methods of ETFE cushions include three-dimensional method and flat-patterning approach. The three-dimensional method is composed of form-finding, structural analysis and cutting pattern. The accurate structural behavior strongly depends on form and cutting patterns. For flat-patterning ETFE cushions, the main idea is to use creep properties of ETFE foils after yield point. Moreover, pressure maintenance for a specific period can achieve desired forms, where creep strain propagates with time. Although desired forms can be obtained with plastic deformation, inner pressure is much larger than conventional ETFE cushions. The structural behavior in the creep process is also not available due to the lack of suitable creep models. This section concerns a structural form and accordingly structural behavior of flat-patterned ETFE cushions. 4.1. Structural experiments This study employs rectangular ETFE cushions that are better in structural behavior and fabrication compared with triangular and circular types. To carry out high temperature experiments, the dimensions of an available temperature chamber (200 mm × 600 mm) need to be considered. The allowance space for aluminum frame and equipment is necessary before determining cushion dimensions. For this reason, cushion dimension is selected as 135 mm × 380 mm where two layers are welded at the perimeter, illustrated in Fig. 6. An EPDM is used for

Fig. 6. Schematic illustration and photos of ETFE cushion at 24 °C and 60 °C. 5

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Fig. 7. Experimental photos for 24 °C and 60 °C.

4.2. Numerical analysis

The final stress and strain distributions are depicted in Fig. 9. It is interesting to find that the maximum stress and strain exist near the middle part of long edges. The maximum stress tends to increase towards cushion center. For specific values, the maximum stress of 13.6 MPa is slightly larger than the first yield stress of 13.5 MPa, meaning that partial ETFE cushion is in plastic region after creep experiments. The center height of 21.2 mm results in a ratio of height to edge (21.2/135 = 0.157), which is larger than the engineering ratio of 1/8. For CUSHION 2, the displacement distribution shown in Fig. 8 again indicates good agreement between experimental and numerical results, validating the suitable creep models for calculating structural behavior of ETFE cushions. Moreover, it is shown that low stress at high temperature is easy to operate compared with high stress at low temperature. The displacement at cushions center is 19.4 mm after a 24 h creep experiment. The relative ratio of (19.4/135 = 0.141) is larger than the engineering ratio of 1/8, resulting in an approximate suitable form. The stress and strain distributions of ETFE cushions are indispensable to analyze structural behavior. The maximum stress of 7.61 MPa is larger than the first yield stress of 4.23 MPa (see Fig. 10). For comparisons between CUSHION 1 and CUSHION 2. These two cushions represent two different effects but similar superposition on form characteristics and structural behavior. The comparisons address forms and related structural behavior. For forms, two displacements and relative ratios of heights to edges are larger than engineering ratios, which demonstrates the superposition effect of temperature and stress on structural behavior. For stress and strain, the comparisons between absolute stresses are not proper to reveal basic characteristics as stress-strain curves of ETFE foils depend on temperature and high temperature corresponds to low yield stress. In this study, the relative percentage with respect to yield stress is used to do the comparisons.

The numerical model is rectangular ETFE cushion with dimensions of 135 mm × 380 mm. The reason for selecting this model is to be in line with experimental prototypes. The ETFE foils fixed with aluminum extruders indicate that fixed boundary conditions are suitable for numerical simulations. The experiments for vertical cushions indicate that upper and bottom layers are the same and thus one layer is enough to demonstrate structural behavior. The mesh type is also rectangular element. As for material properties, a reduction to consider differences between uniaxial and biaxial properties is employed and the ratio value is 0.3 [32,33]. In this paper, this reduction factor is used to determine C1, C2 and C3 in the creep model (see Table 1). In fact, the real process of flat-patterning ETFE cushion includes inflation and pressure maintenance, which requires two steps to simulate this process. The specific operations are similar as material numerical models. The first step needs to close rate-related options to simplify inflation process where inner pressure increases from 0 k Pa to a set pressure. Then, the second step requires to open rate-related option to consider time effects (86,400 s). To take inflation time period into consideration, a small time value (1e−8) is given in the calculation. After iterations, stress, strain and deformation are obtained and analyzed as follows. 4.3. Two ETFE cushions Two typical ETFE cushions are considered to show temperaturestress-time effects, i.e., high stress at low temperature (CUSHION 1: 24 °C/24 kPa) and low stress at high temperature (CUSHION 2: 60 °C/ 12 kPa). The structural behavior is compared with experimental results. For CUSHION 1. The experimental and numerical displacements are illustrated in Fig. 8. The reason to explain variations in experimental curves is that the pressure in ETFE cushion prototype is not easy to control due to the small volume in comparisons with conventional ones. This is why a 50L air vessel is added to mitigate this problem. However, the tendencies are similar and differences between experimental and numerical are within a maximum difference of about 10% at the end of the creep experiments.

=

C1

C2

C3

Coefficient

24 °C 60 °C

9.124e-24 4.345e-12

2.725 1.176

−0.704 −0.882

0.987 0.982

yield yield

× 100%

(12)

where η is a relative ratio. The resulting stress ratios of 0.7% and 79% indicate that high temperature can facilitate form and structural behavior. Therefore, structural forms and related structural behavior are revealed using multi-linear creep models. The flat-patterning ETFE cushions that require simple pattern and easy to achieve a desired structural form can promote design and construction of ETFE cushions.

Table 1 Material properties of creep models at two temperatures. Parameter

max

6

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2.5

1.5

Creep displacement/mm

Creep displacement/mm

1.8

1.2 0.9 0.6

Experiment Simulation

0.3 0.0

0

20000

40000

60000

Time/s

80000

100000

2.0 1.5 1.0

Experiment Simulation

0.5 0.0

0

20000

40000

60000

Time/s

Fig. 8. Creep strain curves of CUSHION 1 and CUSHION 2.

Fig. 9. Stress and strain distributions of CUSHION 1 after creep process.

Fig. 10. Stress and strain distributions of CUSHION 2 after creep process. 7

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5. Conclusions [8]

This paper focuses on a creep model of ETFE foils and utilizes it to assess form and related structural behavior of flat-patterning ETFE cushions structures. Two typical cushions with high stress at low temperature and low stress at high temperature are investigated with experiments and numerical simulations. Typical observations and useful values are summarized as follows.

• •

•

[9] [10] [11]

The Bailey-Norton model with Modified Time Hardening effect results in a creep model that describes creep strains at high temperature. A multi-linear model for reproducing creep strains is used and validated with numerical simulations. For structural analysis, two typical cushions with inverse temperatures and pressures are simulated with multi-linear models. The maximum stress and strain exist near middle area of long edges and propagate towards cushion center. The ratios of heights to edge length are larger than the engineering ratio of 1/8, resulting in a suitable structural form. A further ratio of stress to yield stress suggests the easy operation to achieve desired forms for small pressure at high temperature than large pressure at low temperature.

[12]

[13] [14] [15] [16] [17]

In general, these observations and values are indispensable for structural forms and behavior of flat-patterning ETFE cushion. The proposed temperature-stress-time methodology is useful for promoting utilizations of flat-patterning ETFE cushions.

[18] [19]

Acknowledgement

[20]

The work was supported by International Research Fellow of Japan Society for the Promotion of Science (Postdoctoral Fellowships for Research in Japan (Standard)) and JSPS KAKENHI (Grant Number: JP18F18345), National Natural Science Foundation of China (Nos. 51608320, 51778362 and 51478264) and project funded by China Postdoctoral Science Foundation (Nos. 2017T100298 and 2016M591677). The authors are grateful to the editors and anonymous reviewers for professional comments and suggestions in improving the quality of the paper.

[21] [22] [23] [24] [25]

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