Optimizing Winding Angles of Reinforced Thermoplastic Pipes Based on Progressive Failure Criterion

WANG Yangyang, LOU Min, *, ZENG Xin, DONG Wenyi, and WANG Sen

Optimizing Winding Angles of Reinforced Thermoplastic Pipes Based on Progressive Failure Criterion

WANG Yangyang1), 2), LOU Min1), 2), *, ZENG Xin3), DONG Wenyi4), and WANG Sen5)

1) School of Petroleum Engineering, China University of Petroleum (East China), Qingdao 266580, China 2) Key Laboratory of Unconventional Oil & Gas Development (China University of Petroleum (East China)), Ministry of Education, Qingdao 266580, China 3) Zoomlion Heavy Industry Science & Technology Co., Ltd., Changsha 410013, China 4) China Offshore Oil Engineering (Qingdao) Co., Ltd., Qingdao 266520, China 5) Weihai Nacheon Pipeline Co., Ltd., Weihai 264400, China

This paper examines a scheme to optimize the multiple winding angles of reinforced thermoplastic pipes (RTPs) under internal and external pressures. To consider the nonlinear mechanical behavior of the material under changes of winding angle due to deformation, we use three-dimensional (3D) thick-walled cylinder theory with the 3D Hashin failure criterion and theory of the evolution of damage to composite materials, to formulate a model that analyzes the progressive failure of RTPs. The accuracy of the model was verified by experiments. A model to optimize the multiple winding angles of the RTPs was then established using the model for progressive failure analysis and a multi-island genetic algorithm. The optimal scheme for winding angles of RTPs capable of withstanding the maximum internal/external pressure was obtained. The simulation results showed that the ply number of the reinforced layer has a prominent nonlinear effect on the internal and external pressure capacity of the RTPs. Compared with RTPs with a single angle of ±55?, the multiple winding angle overlay scheme based on the multi-angle optimization model improved the internal and external pressure capacity of the RTPs, and the improvement in the external pressure capacity was significantly better than the internal pressure carrying capacity.

reinforced thermoplastic pipes; 3D thick-walled cylinder theory; multi-island genetic algorithm; pressure capacity

1 Introduction

Composite pipes have several advantages over conventional steel pipes such as better corrosion and fatigue resistance, higher stiffness to weight ratio, and lower maintenance cost. Therefore, in recent years, composite pipes have been increasingly used instead of conventional carbon steel pipes in the oil and gas industries (Kaddour.,2003). With further advancements in fiber and thermoplastic materials, reinforced thermoplastic pipes (RTPs) have been used in marine engineering (Lou., 2020). Thistechnologycombineshigh-performancematerialswithhigh-strength reinforcement materials to create a coiled, high-pressure piping system that can be used in a variety of applications (Conley., 2010; Kuang., 2015).

The load-bearing capacity of composite pipes under internal and external pressure is a primary concern for designing offshore pipes. Overestimating this capacity can lead to catastrophic failure of pipes, whereas underestimating the amount of product that can be transported reduces production and increases cost (Kuang., 2017). Fun-damental research has been performed on the edge effects,shearcharacterization,engineeringproperties,crack extension, and thermal stresses of fiber-reinforced composites by Hsu and Herakovich (1977), Herakovich (1984) and Pindera and Herakovich (1986). It is difficult to predict the pressure capacity of composite pipes because of the anisotropy of the materials. Experimental failure analyses (So- den., 1978, 1989; Spencer and Hull, 1978; Ellyin., 1997; Antoniou., 2009) have been conducted on pipes with different winding angles, and an optimum winding angle of 55? has been recommended for thin pipes subjected to internal pressure or biaxial loads with a hoop-to-axial stress ratio of 2:1.Xing. (2015) studied the deformation and stresses of a thick filament-wound composite cylinder with a multi-angle winding pattern subjected to a combined load consisting of axial loading and internal and external pressures.Kruijer. (2005) and Bai. (2011, 2012) studied the burst capacity of RTPs under internal pressure through experimental, numerical, and theoretical approaches. The results of a numerical model and finite element model yielded significant errors compared with the experimental results, which could have been caused by the nonlinear behavior of polyethylene (PE). Melo. (2011) used the Tsai-Hill criterion and Hoffman criterion in a numerical simulation to determine the failure pressure of the first layer of composite pipes as the burst pressure. Rafiee (2013, 2016) performed experimental analyses of glass fiber-wound tubes of different diameters (300, 500, 600, 700, 800, 900, and 1000mm), and compared them with an established progressive failure model to verify the effectiveness. With shear deformation and pre-buckling deformation, a 2D mathematical model for composite pipes was developed to analyze the collapse of a RTP pipe under pure external pressure, a pure bending moment, or combined external pressure and bending moment by Bai. (2015).

Rafiee. (Rafiee, 2017; Rafiee, 2018, 2019, 2020; Rafiee and Habibagahi, 2018a, 2018b; Rafiee and Sharifi, 2019; Rafiee and Abbasi, 2020; Rafiee and Ghor- banhosseini, 2020) analyzed the effect of the winding angle on the mechanical performance of glass fiber-reinforced plastic pipes according to different behaviors such as creep, fatigue, and deformation. The optimal winding angle ofRTPs is usually selected based on experiments with a single winding angle, where ±55? is generally considered the optimal winding angle (Bakaiyan., 2009; Onder., 2009; Ansari., 2010; Tamer, 2019). Recent experimental studies have shown that compared with a single-winding structure, a multi-angle winding structure can improve the mechanical properties of RTPs (Skinner, 2006; Antoniou., 2009). Xing. (2015) proved that the winding process of multi-angle fibers can improve the rate of use of a material and its working pressure. Kuang. (2015) developed a finite element model in Abaqus/Standard to study the anti-buckling performance of RTPs under external pressure and bending at different lamination angles. The results showed that the mechanical properties of RTPs can be improved using a multi-angle lamination-reinforced system.

Research on the multi-angle winding in RTPs remains limited to the use of finite element software to analyze the mechanical performance under simple loads. Relevant studies have considered only axial and annular stresses on the RTPs in the 2D plane. Difficulties also persist in solving the 3D stress and displacement fields of RTPs as well as selecting the failure criterion in the multi-angle optimization process. This paper formulates a mechanical model of RTPs based on the theory of a 3D thick-walled cylinder, and by considering changes in the winding angle caused by deformation and nonlinear mechanical behavior of thermoplastic materials. Combined with the 3D Hashin failure criterion and damage evolution theory of composite materials, a model to analyze the progressive failure of RTPs was established to examine their maximum internal/external pressure. The numerical simulations were compared with experimental results to verify the accuracy of the theoretical model. This model was then used with the multi-island genetic algorithm (MIGA) to establish a model to optimize the multiple winding angles in RTPs under maximum internal and external pressures. The results show that the multi-angle optimization model can significantly improve the pressure bearing capacity of RTP.

2 Numerical Model

The RTPs studied in this paper were made of a PE matrix and fiberglass was used as the reinforcement material, as shown in Fig.1 (Lou., 2020). The reinforced layers consisted of fiberglass embedded in the polymer matrix wrapped around the inner PE liner at a specified angle (, the winding angle). The layers were bonded by heating, and were fused to form a filament-wound fiber-reinforced composite pipe. The functional units were not considered in the mechanical model because they were used only for signal transmission and did not affect the overall mechanical properties of the RTPs.

Fig.1 Structural diagram of an RTP.

2.1 Constitutive Relation

A simplified model of a typical RTP, featuring the inner PE liner, a reinforced layer, and a protective layer from inside to outside, is shown in Fig.2. The cylindrical coordinate system is designated as (,,), where,, andare the axial, circumferential, and radial directions of the RTP, respectively. The material coordinate system of the tap layer is designated as (,,), whereis the winding direction of the fiber,is the direction vertical to the fiber wire in a plane, andis the normal direction of the tape layer. The two coordinate systems have the same coordinate direction ofandis the angle between the directionsand.

When the RTP is subjected to an axial symmetric load with internal pressureq, external pressureq, axial forceT, and torqueM, deformation along three directions occurs. The radial, annular, and axial displacements are(),(,), and(), respectively.

When the pipe is subjected to axisymmetric loads, the equation of geometric strain can be simplified as follows:

Fig.2 Mechanical model of a flexible thermoplastic composite pipe.

whereε,ε,ε,γ,γ, andγrepresent the strain components.

According to the geometric conditions of the RTP, the equilibrium equation for each layer can be simplified as follows:

According to Xing(2015), the positive axial stress-strain relationship of each layer of the reinforced layer is given by:

The positive axial stress-strain relationship of the PE material is given by:

whereE,E, andErepresent the tensile modulus of the reinforced layer in different directions, andrepresents the elastic modulus of the PE material.andrepresents the Poisson ratio and shear modulus of the reinforced layer, respectively.

The axial eccentric stress-strain relationship can be expressed as follows:

where=cos() and=sin().

According to the conservation of strain-related energy, the following expression can be obtained:

The overall stress-strain relationship can be written as follows:

According to the equilibrium and geometric strain equations, the general expressions of the axial and annular displacements can be obtained as follows:

Radial displacement can then be expressed as follows:

where

The expression for strain varies with the value ofS:

WhenS=1, it corresponds to an isotropic material:

WhenS= 2:

WhenS≠1 andS≠2:

The boundary conditions of the inner and outer surfaces can be expressed as follows:

The following expression can be obtained from the boundary and continuity conditions:

Torque balance:

Axial balance:

Then, the entire stress and strain fields can be obtained:

where [] is the stiffness matrix, [] is the matrix of the displacement parameters, and [] is the load matrix.

When RTPs are subjected to an internal pressure loadqand external pressureq, the RTP is subjected to the axial loadqπ02and –qπr2because its two ends are closed. The winding angles before and after deformation are shown in Fig.3.

Fig.3 Change in the winding angle before and after deformation.

According to Eq. (5), the shear deformation of theth layer of the reinforced layers of the RTP can be expressed as follows:

Therefore, the change in the winding angle caused by deformation can be expressed as follows:

2.2 Progressive Failure Criterion

In this paper, the 3D Hashin failure criterion is used as the failure criterion of a single-layer plate. The relevant expressions are shown in Eqs. (25)–(31):

Fiber stretching pattern (σ>0):

Fiber compression pattern (σ<0):

Matrix tensile failure (σ>0):

Matrix compression failure (σ<0):

Fiber matrix shear failure:

Tensile lamination failure (σ>0):

Compression layering failure (σ<0):

whereσ,σ,σ,τ,τ, andτare the components of normal stress and shear stress in each direction, andX,X,Y,Y,Z,Z,S,S, andSare the limit parameters of strength in the composite monolayer plate.

The degradation of materials by damage is a gradual process, as shown in Fig.4.σandδare the equivalent stress and equivalent strain of the material, respectively. When the material stress reaches the ultimate strength0, the material does not immediately fail, though the stiffness degrades. The specific form of degradation depends on the value of:=0 implies linear degradation,=1, 2, 3, ···,corresponds to exponential degradation, and=∞ is degradation that causes immediate damage. The progressive damage model refers to the modes of linear degradation developed by Chang and Larry (1991), Chang andLiu (1991), and Camanho and Matthews (1999). As shown in Table 1, the specific form of degradation in the performance-related parameters are determined as shown in Table 2.

Fig.4 Process of the damage evolution.

Table 1 Degradation modes of the material properties

Table 2 Degradation parameters of the material properties

Table 2 illustrates the stiffness reduction coefficient (SCR) of the material. The performance-related parameter of the material is the product of its initial performance and SCR. When the SCR is one, the performance parameter of the material is constant.

2.3 RTP Optimization Model

Using the progressive failure model described above, the genetic algorithm is used to establish the optimization model to optimize the multiple winding angles of RTPs.

1) Objective function

According to different internal and external pressures, the objective function of the optimization can be divided into maximum internal and external pressure loads borne by the RTPs; however, but there is only one objective function for each optimization.

2) Design variables

The winding angle of the reinforced layer is an important parameter that affects the mechanical properties of the RTPs when the ply number of the reinforced layer and materials used have been determined. To examine the influence of multiple winding angles, the angle of each reinforced layer was taken as the design variable in the optimization model. When the ply number of the reinforced layer is, the number of design variables is.

3) Constraint

Considering the limitation of the winding process, the winding angle is limited to ±15?–±80?. Every two layers of the reinforced layer are wound at the same angle in opposite directions,, the winding scheme is [, ?,, ?].

4) Optimization model

The mathematical model for this optimization can be expressed as follows:

_( ) is the progressive failure model established above. By entering values of the winding angle of each layer of the reinforced layer, the maximum internal and external pressure loads in this scheme can be obtained, where (1, ?1, ···,theta, ?theta) is the simplified lay-up scheme of the RTPs with 2winding layers.

In the iterative process of the multi-angle optimization model, the MIGA method is used to introduce migration between populations to increase the diversity of optimal solutions in the evolution of the model to prevent the optimization from falling into a local optimum. The relevant parameter settings of MIGA are shown in Table 3.

Table 3 Parameter settings for MIGA

3 Experiments

The RTPs were subjected to a burst capacity test to prove the accuracy of the proposed theory and an experimental basis for the theoretical analysis. The geometric parameters and experimental data of the sample pipes are shown in Tables 4 and 5, respectively. The structurally reinforced layer of the pipes consisted of several angle-ply layers formed from fiber reinforcements and PE with a winding angle of ±55?. The matrix materials of the inner layer, outer protection layer, and reinforced layer of the RTPs studied in this paper were all high-density PE that has high crystallinity and is a non-polar thermoplastic resin. Adjacent angle-ply layers were wound at opposite angles.

Table 4 Material parameters of the sample pipes

Table 5 Geometric parameters of the sample pipes

Figs.5 and 6 show the experimental apparatus, which featured a 120MPa bursting test machine, pipe fixing device, bursting protection device, data acquisition instrument, monitor, joint treatment device, and three sample tubes used in the test at 6-, 8-, 10-, and 12-layered fiber-wound RTPs.

The sample pipe after burst failure is shown in Fig.7. A large amount of fluid leaked into the pipe and failure occurred in the middle, far from the joint at both ends, which indicates that the experimental results were reasonable.

To intuitively analyze the forms of the bursting failure, the sections of 4-, 6-, 8-, and 12-layered pipes were compared and analyzed, as shown in Fig.8. The fracture angle at failure was 55?. In terms of failure form, fiber fracture and matrix cracking of the reinforced layer occurred. With 12 wound layers, the reinforced layer exhibited prominent interlayer separation inside the pipeline.

Table 6 shows the results of the bursting pressure test. With an increase in the number of wound layers, the bursting pressure did not increase linearly and the growth rate gradually slowed. When the number of reinforced layers was small, such as increasing from four to six layers, the bursting pressure increased by 10.10MPa. With an increase in the number of reinforced layers from 10 to 12 layers, the bursting pressure increased by 7.46MPa.

Fig.5 Experimental apparatus.

Fig.6 Sample pipe and fixture.

Fig.7 Sample pipe after failure.

Fig.8 Cross section comparison under different winding layers.

Table 6 Bursting pressure test value

4 Numerical Analysis

4.1 Comparison of the Theoretical Model and Experimental Results

Calculations for the mechanical analysis of the progressive failure of RTPs were performed according to the established model and the results were then compared with the experimental results. The parameters of the RTPs used in the numerical simulation were consistent with the experimental parameters, and the parameters of the ultimate strength of the reinforced layer are shown in Table 7.

Table 7 Ultimate strength parameters of fiberglass tape

The stress-strain relationships of the materials used in the thermoplastic flexible pipes were determined experimentally, as shown in Fig.9. The secant modulus was usedto characterize the properties of the elastoplastic materials.

Fig.9 Strain curve of HDPE.

The burst pressure of 4-, 6-, 8-, 10-, and 12-layered fiber-wound RTPs were analyzed by a progressive failure model. The failure scenario of the reinforced layer was characterized by the 3D Hashin failure coefficient, and failure of the lining layer and outer protective layer was represented by the strain. Failure occurred when the failure coefficient was greater than one and the strain was greater than 0.077. To verify the model accuracy, the predicted burstingpressureandexperimentalvalueofthemodelwere summarized, and their relative errors analyzed, as shown in Fig.10 and Table 8. The predicted value of the model coincided with the experimental value and the maximum relative error was controlled to within 8%.

Fig.10 Comparison between numerical results and experimental results.

Table 8 Relative error of experimental and theoretical models

4.2 Optimization Results

4.2.1 Internal pressure conditions

Fig.11 shows the relationship between the genetic algebra and optimal solution in the optimization of RTPs under internal pressure. The optimal solution for each layer was stable when the genetic algebra was 300. At this point, the burst pressure of the RTPs can be considered a maximum burst pressure under the corresponding number of reinforced layers.

Table 9 shows the scheme of the optimal winding angle for each layer of the RTPs with 4?12 reinforced layers under internal pressure. Therefore, the winding angle decreased from the innermost to the outermost reinforced layer.

Table 10 shows a comparison of the burst pressures before and after the winding angles of the RTPs were optimized for different ply numbers of the reinforced layer. The results show that increasing the ply number of the reinforced layer improved the burst pressure of the RTPs; however, it did not increase linearly. Compared with the RTPs at a single angle of ±55? before optimization, the burst pressure of the RTPs optimized with multiple winding angles significantly increased, with a rate greater than 10%, up to a maximum of 14.01%. The rate of increase of the burst pressure with different ply numbers of the reinforced layer differed slightly. Overall, the overlay scheme for multiple winding angles can improve the burst pressure of the RTPs more than the single-winding angle scheme.

Table 9 Optimal winding angle (?) for 4?12-layered RTPs under the action of internal pressure

Table 10 Burst pressures before and after optimization of 4?12-layer RTPs

Fig.11 Optimization results of RTPs under internal pressure.

4.2.2 External pressure conditions

Fig.12 shows the relationship between the genetic algebra and optimal solution in the optimization of the RTPs under external pressure. The optimal solution of each layer was stable when the genetic algebra was 200. The external pressure load obtained can be considered a maximum external pressure on the RTPs under the corresponding number of reinforced layers.

Table 11 shows the optimal scheme of the winding angle for each layer of the RTPs with 4?12 reinforced layers under external pressure.

Table 12 shows a comparison of the maximum external pressures before and after the winding angles of the RTPs were optimized for different ply numbers of the reinforced layer. Increasing the ply number of the reinforced layer improved the maximum external pressure of the RTPs but not linearly. Compared with RTPs with a single angle of ±55? before optimization, the maximum external pressure of the RTPs optimized with multiple winding angles was significantly higher, for up to a maximum of 73.78%. The rate of increase of the external pressure of the RTPs with different ply numbers of the reinforced layer differed slightly. Therefore, the overlay scheme for multiplewindinganglescanimprovethemaximumexternalpressure of RTPs more than the single-winding-angle scheme.

Fig.12 Optimization results of RTPs under external pressure.

Table 11 Optimal winding angle (?) for each layer with 4?12 layers under external pressure

Table 12 External pressure before and after optimization of 4?12-layer RTPs

5 Conclusions

To consider the nonlinear mechanical behavior of a material when the winding angle changes by deformation, a 3D thick-walled cylinder theory was used with the 3D Hashin failure criterion and the theory of the evolution of damage to composite materials to formulate a model to analyze the progressive failure of RTPs. The MIGA was then introduced to establish a model to optimize the multiple winding angles of the RTPs, and to obtain the optimal scheme for the winding angles under maximum internal and external pressures.

The burst pressure and maximum external pressure of the RTPs for different ply numbers of reinforced layers were analyzed according to the numerical analysis. The results show that the internal burst pressure and maximum external pressure of the RTPs increased significantly with the ply number of the reinforced layer, but not linearly. The MIGA was introduced to improve the internal and ex- ternal pressure capacities of the RTPs. The overlay scheme for multiple winding angles based on the proposed model can improve the internal and external pressure capacities of RTPs compared with RTPs with a single angle of ±55?.

Acknowledgements

This research was funded by the National Key Research and Development Program of China (No. 2016YFC0303800), and the National Natural Science Foundation of China (No. 51579245).

Ansari, R., Alisafaei, F., and Ghaedi, P., 2010. Dynamic analysis of multi-layered filament-wound composite pipes subjected to cyclic internal pressure and cyclic temperature., 92 (5): 1100-1109.

Antoniou, A. E., Kensche, C., and Philippidis, T. P., 2009.Mechanical behavior of glass/epoxy tubes under combined static loading.Part I: Experimental., 69 (13): 2241-2247.

Antoniou, A. E., Kensche, C., and Philippidis, T. P., 2009. Mechanical behavior of glass/epoxy tubes under combined static loading. Part II: Validation of FEA progressive damage model., 69 (13): 2248-2255.

Bai, Y., Tang, J. D., Xu, W. P., Cao, Y., and Wang, R. S., 2015. Collapse of reinforced thermoplastic pipe (RTP) under combined external pressure and bending moment., 94: 10-18.

Bai, Y., Xu, F., and Cheng, P., 2012. Investigation on the mechanical properties of the reinforced thermoplastic pipe (RTP) under internal pressure.. Rhodes, 109-116.

Bai, Y., Xu, F., Cheng, P., Badaruddin, M. F., and Ashri, M., 2011. Burst capacity of reinforced thermoplastic pipe (RTP) under internal pressure. In:. Rotterdam,281-288.

Bakaiyan, H., Hosseini, H., and Ameri, E., 2009. Analysis of multi-layered filament-wound composite pipes under combined internal pressure and thermomechanical loading with thermal variations., 88 (4): 532-541.

Camanho, P. P., and Matthews, F. L., 1999. A progressive damage model for mechanically fastened joints in composite laminates., 23: 2248-2280.

Chang, F. K., and Larry, B. L., 1991. Damage tolerance of laminated composites containing an open hole and subjected to compressive loadings: Part I–Analysis, 25 (1): 2-43.

Chang, K. Y., and Liu, S., 1991. Damage tolerance of laminated composites containing an open hole and subjected to tensile loadings., 25 (3): 274-301.

Conley, J., Weller, B.,and Sakr, A., 2010. Recent innovations in reinforced thermoplastic pipe.. Canada, 1-13.

Ellyin, F., Carroll, M., Kujawski, D., and Chiu, A. S., 1997.The behavior of multidirectional filament wound fibre glass/epoxy tubulars under biaxial loading., 28A: 781-790.

Herakovich, C. T., 1984. Composite laminates with negative through-the-thickness Poisson’s ratios., 18 (5): 447-455.

Hsu, P. W., and Herakovich, C. T., 1977. Edge effects in angle-ply composite laminates., 11 (4): 422-428.

Kaddour, A. S., Hinton, M. J., and Soden, P. D., 2003. Behaviour of±45? glass/epoxy filament wound composite tubes under quasi-static equal biaxial tension-compression loading: Experimental results., 34(8):689-704.

Kruijer, M., Warnet, L., and Akkerman, R., 2005. Analysis of the mechanical properties of a reinforced thermoplastic pipe (RTP)., 36 (2): 291-300.

Kuang, Y., Morozov, E.V., Ashraf, M.A., and Shankar, K., 2015. Analysis of flexural behaviour of reinforced thermoplastic pipes considering material nonlinearity., 119: 385-393.

Kuang, Y., Morozov, E.V., Ashraf, M.A.,and Shankar, K., 2015. Numerical analysis of the mechanical behaviour of reinforced thermoplastic pipes under combined external pressure and bending., 131: 453-461.

Kuang, Y., Morozov, E.V., Ashraf, M.A.,and Shankar, K., 2017. A review of the design and analysis of reinforced thermoplastic pipes for offshore applications., 0 (0):1-17.

Lou, M., Wang, Y. Y., Tong, B.,and Wang, S., 2020. Effect of temperature on tensile properties of reinforced thermoplastic pipes., 241: 1-12.

Melo, J. D. D., Neto, F. L., Barros, G. A. B., and Mesquita, F. N. A. M., 2011. Mechanical behavior of GRP pressure pipes with addition of quartz sand filler., 45 (6): 717-726.

Onder, A., Sayman, O., Dogan, T., and Tarakcioglu, N., 2009. Burst failure load of composite pressure vessels., 89: 159-66.

Pindera, M. J., and Herakovich, C. T., 1986. Shear characterization of unidirectional composites with the off-axis tension test., 26 (1): 103-112.

Rafiee, R., 2013. Experimental and theoretical investigations on the failure of filament wound GRP pipes., 45: 257-267.

Rafiee, R., 2016. On the mechanical performance of glass fibre reinforcedthermosettingresinpipes:Areview., 143: 151-164.

Rafiee, R., 2017. Stochastic fatigue analysis of glass fiber reinforced polymer pipes., 167: 96-102.

Rafiee, R., and Abbasi, F., 2020. Numerical and experimental analyses of the hoop tensile strength of filament wound composite tubes., 56 (4): 423-436.

Rafiee, R., and Ghorbanhosseini, A., 2020. Developing a micro-macromechanical approach for evaluating long-term creep in composite cylinders., 151: 106714.

Rafiee, R., and Habibagahi, M. R., 2018a. On the stiffness prediction of GFRP pipes subjected to transverse loading., 22 (11): 4564-4572.

Rafiee, R., and Habibagahi, M. R., 2018b. Evaluating mechanical performance of GFRP pipes subjected to transverse loading., 131: 347-359.

Rafiee, R., and Sharifi, P., 2019. Stochastic failure analysis of composite pipes subjected to random excitation., 224: 950-961.

Rafiee, R., Faramarz, A., and Sattar, M., 2020. Fatigue analysis of a composite ring: Experimental and theoretical investigations., 54 (26): 4011-4024.

Rafiee, R., Ghorbanhosseini, A., and Rezaee, S., 2019. Theoretical and numerical analyses of composite cylinders subjected to the low velocity impact., 226: 111230.1-111230.12.

Rafiee, R., Mohammad, A. T., and Sattar, M., 2018. Investigating structural failure of a filament-wound composite tube subjected to internal pressure: Experimental and theoretical evalua- tion., 67: 322-330.

Skinner, M. L., 2006. Trends, advances and innovations in filament winding.,50 (2): 28-33.

Soden, P. D., Kitching, R., and Tse, T. C., 1989.Experimental failure stresses for±55? filament wound glass fiber reinforced plastic tubes under biaxial loads., 20: 125-135.

Soden, P. D., Leadbetter, D., Griggs, P. R., and Eckold, G. C., 1978.The strength of a filament wound composite under biaxial loading.,9: 247-250.

Spencer, B., and Hull, D., 1978. Effect of winding angle on the failure of filament wound pipe.,9: 263-271.

Tamer, A. S., 2019. Design of oil and gas composite pipes for energy production., 162: 146-155.

Xing, J., Geng, P., and Yang, T., 2015. Stress and deformation of multiple winding angle hybrid filament-wound thick cylinder under axial loading and internal and external pressure., 131: 868-877.

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