Thin-walled cylindrical shells in engineering designs and critical infrastructures: A systematic review based on the loading response

: Cylindrical shell structures are ubiquitous and essential supporting structures in various engineering applications. The aim of this research work is to provide a comprehensive overview of the behavior of cylindrical shell structures under di ﬀ erent loading conditions, including external pressure, axial compression, and bending moment. The study found that the behavior of cylindrical shells was a ﬀ ected by their geometry, including diameter, length, thickness, and imperfections. These factors should be care-fully considered in the design and analysis of cylindrical shells. Additionally, sti ﬀ eners and sandwich structures can be applied to improve the structural performance of cylindrical shells under di ﬀ erent loading conditions. The work also highlighted the latest research trends in the ﬁ eld, such as the use of advanced materials, and numerical simulations to improve the understanding and design of cylindrical shell structures. Overall, this study has provided a valuable resource for engineers and researchers working on cylindrical shell structures, helping them to design and analyze the cylindrical shell structures more e ﬃ ciently and e ﬀ ectively.


Introduction
The global demand for energy is linked to activities that require a lot of energy, such as industry and transportation [1].Various energy sources such as fossil fuels, nuclear energy, and renewables have been exploited to satisfy the global demand for energy.Among these energy sources, fossil fuels, especially oils and natural gases, have the largest portion in supporting world energy consumption, reaching 55.4% in 2021 [2,3].Despite its high economic value, the use of fossil fuels must be reduced immediately due to their harmful CO 2 emission which causes raise in global temperature.Global temperature has risen by around 1.1°C since the beginning of the twentieth century, and with no reduction in reliance on fossil fuels, the temperature rise is anticipated to be 1.5°C within 15-20 years [4,5].Various attempts to limit the global greenhouse gas emissions had been discussed in numerous international conventions, for example, Intergovernmental Panel on Climate Change in 1988 and United Nations Framework Convention on Climate Change in 1992, which later proposed the first regulation limiting the greenhouse gas emissions, the Kyoto Protocol, in 1997 [6].In 2016, through Paris Agreement, more than 170 countries agreed to limit the global temperature rise to 2°C by 2050.However, considering the fact that catastrophic consequences will occur when the global temperature rise exceeds 1.5℃, in 2018, a new target was set up to reach net zero emission by 2050.This task will be challenging since it involves not only transforming from a fossil-fuel-based system to an alternative energy system, but also maintaining global economic stability.According to this consideration, developing renewable energy is preferable even though the results cannot be seen instantly [4].
Rapid transition to alternative energy cannot be made since the world is still highly dependent on fossil fuels.Moreover, large scale energy transition is still struggling with several factors such as immature technology readiness and insufficient resource [6].Currently, the highest portion of renewable energy source is dominated by hydropower energy (6.86%), followed by wind and solar energy with 2.90 and 1.54%, respectively.Although wind and solar energy account for only a small proportion of renewable energy sources, they have the greatest potential for large-scale expansion, particularly wind energy [4].Three main objectives strived during energy transition process are producing more energy from renewable sources, reducing the greenhouse gas emissions, and enhancing the efficiency of energy use.The main target of the transition to alternative energy is the electricity sector due to its considerable contribution to greenhouse gas emissions [7][8][9].However, this decision affects other vital fields, such as transportation and industries, that support human life.Despite being the largest energy source worldwide, fossil fuels need to be minimized due to the harmful CO 2 emissions causing a global rise in temperature [10,11].
A cylinder shell is a type of structure that is commonly used for fuel storage.These shells have a high load carrying capacity and are structurally efficient [12,13].They are particularly useful for storing liquids like oil, chemicals, and liquefied natural gas [14].However, these shells are also subject to damage and failure due to hydrostatic pressure and other factors.Engineers must be aware of these risks and take appropriate measures to ensure the safety and reliability of these structures.Despite these challenges, cylindrical shells remain a popular choice for fuel storage due to their specific strength and stiffness, lightweight design, and cost-effectiveness.However, their load carrying capacity is often determined by buckling, which can occur at loads much lower than the material's failure loads [15].The post-buckling behavior of shell structures is usually unstable.Many optimization strategies use the linear buckling load as the design's objective function, but the buckling mode interaction phenomenon can cause different post-critical behavior and high sensitivity to imperfections, resulting in a decrease in load bearing capacity due to geometric, load, and material deviations [16].The consequences of large tanks' behavior during internal and external pressure events extend beyond their economic value and the value of their contents.
Engineering structures are designed to meet the needs of people, safety must be the top priority in their construction and maintenance [17][18][19].Any structural failure can have catastrophic consequences, potentially endangering the lives of those who rely on these structures [20][21][22].The cylindrical shell is one of the oldest structures in human history.It was first introduced to create the most iconic Roman dome concrete constructions, and nowadays, it is also used in various engineering fields: in civil engineering: water tanks, largespan roofs, nuclear reactor containments, and wind turbine towers; in mechanical engineering: automobile, piping systems, and pressure vessel; and aeronautical and marine engineering: aircrafts, ships, and submarines.Recently, a numerical method such as finite element analysis has gained popularity in the field of engineering for evaluating structural behavior [23][24][25][26][27]. Studies showed that numerical analysis can be used to analyze the free vibrations of laminated composite conical and cylindrical shells [28].Furthermore, free vibration analysis of laminated anisotropic doubly-curved shells of arbitrary geometry with general boundary conditions using MATLAB code called DiQuMASPAB [29] can also be performed.Additionally, the discrete singular convolution technique [30] can be used to analyze the free vibration analysis of rotating cylindrical shells.In real life, cylindrical shell structures are not only used in such safe circumstances, but can also be installed in hostile environments such as offshore and undersea.Regardless of how safe or dangerous the environment where cylindrical shell is installed, they will face various types of loadings, i.e., axial load, external pressure, bending moment, and twisting moments.In several cases, these loads could occur simultaneously [12,31].These loadings have been a challenge to all engineers all over the world as loads have a great potential to damage the structure.Nevertheless, when using the cylindrical shell, the material selection and geometry are important aspects that should be considered [16,29,32].
Calculation and prediction of the structural strength play an important role to prevent any failure to occur in the structure which lead to cost loss, accident, environmental issue, or even endangering involved parties' lives.This process of evaluating structural strength encompasses scenarios such as analyzing cylindrical shells subjected to different loading conditions within relevant application domains.This study presents a review of numerous literature which observe the behavior of cylindrical shell structures, and several loading conditions are selected to be the main criteria, i.e., axial compression, external pressure, and bending moment.Remarkable accomplishments since before millennium is considered to be the first period of research, which is followed by two decades, i.e., 2001-2010 and 2011-2020 as the recent works after millennium.The achievements during these time spans provide the foundation for predicting future trends in cylindrical shell structures.Additionally, the papers from 2021 onward are also included in the discussion.Based on this concept, it is projected that the overall reviews on the conventional approaches, modern techniques, and prediction of future methodology and application in terms of the cylindrical shell structures can be comprehensively assessed and studied.

Shell behaviors under external pressure cases
Cylindrical shell is a structure that can be found in many forms such as pipes for transporting fluids or pressure hull of submarine construction.In daily life, large scale of pipe installations on land are nowhere to be seen but in factories or power plants because the pipes are buried beneath the ground for safety reason considering that these pipes may carry fluids potentially harmful for the surroundings and living matter [33].
Even though the pipe is protected by being buried in the ground, it will experience pressure due to the weight of the concealing material and activities above it [34].Furthermore, when the pipe installation is made underwater, the pipe is susceptible to hydrostatic pressure.The internal pressure caused by the flowing fluids will help the pipe encounter the hydrostatic pressure acting along its surface.However, if there is no fluid or the pipe is not internally pressurized, hydrostatic pressure will increase the compressive hoop stress on the pipe which will lead to the failure of the pipeline [35].Through the years, researchers have conducted numerous types of research to enhance the performance of pipe enabling it to withstand higher external pressure and making it possible to be used under various extraordinary circumstances even placed on seabed.This section of the article will review several methods commonly employed to enhance the pipe strength based on the failure.
In 2010, Moon et al. [36] investigated the buckling and post buckling behavior of composite cylinders for deep underwater vehicle.The filament winding method was used to manufacture the cylinders due to its ability to reduce the material and geometric imperfections.The cylinders consisted of two different windings.The helical winding was used to form the inner side of the cylinder and the hoop winding is the contrary.Variations were implied to the winding angle of the helical winding: ± ± ± 30°, 45°, 60°a nd the hoop winding was 90°.The specimens were built with average R/t ratio = 18.8, which can be categorized as relatively thick-walled cylindrical shell.The nominal inner radius, axial length, and thickness of the cylinder are 150, 695, and 8 mm, respectively (Table 1).In order to examine the optimum buckling pressure of the pipe, the hoop ratio must be lower than 50% of the total thickness.Exceeding this number, the static strength of the cylinder will be weakened.To replicate the hydrostatic pressure, the cylinders were tested inside hydrostatic chamber, which was equipped with high pressure pump capable of generating hydrostatic pressure up to 10 MPa similar to the pressure at a depth of 1,000 m underwater.The cylinders were attached to the steel flange by using adhesive at one end and the other end of the cylinders were closed with steel bungs.
According to the experiment and finite element method (FEM) analysis, it can be deduced that the cylinder with stacking sequence [±60°/90°] showed the best performance with respect to buckling pressure.Furthermore, all the cylinders cannot reach the initial buckling pressure after buckling which causes the cylinder to collapse.Thin-walled cylindrical shells in engineering designs and critical infrastructures  3 Similar research had been carried out by Moreno et al. [37], where filament-wound cylinders were divided into two different categories i.e., thin-walled and thick-walled cylinders with the thickness of 4.4 and 12.6 mm, respectively.The cylinders were 350 mm long with 125 mm inner diameter, and 250 mm long at the central parallel section with a winding angle of ±55°.After winding process was done the specimens were cured at 50°C for 15 h before the two ends were machined flat to fit the dimension.Two winding patterns of 1-and 5-unit cells were used to manufacture the cylinders.The influence of the winding pattern on the mechanical response of the cylinders was investigated through experiment where the cylinders were tested in hyperbaric chamber.The experimental results showed that the average implosion pressure of the thin-walled cylinders with 5-and 1-unit cells winding pattern are 65.9 and 64.7 bar, respectively.In comparison, the thick-walled cylinders were 483.9 bar for 5-unit cells pattern and 520.6 bar for 1-unit cell pattern.According to the data, it can be inferred that winding pattern had no significant effect on the implosion pressure of the filament-wound cylinders.
Failure of filament-wound composite cylinders was also investigated by Almeida et al. [38].In this research, the cylinders were varied in D/t ratio by varying the amount of non-geodesic layers between the hoop layers.Three stacking sequences were used to manufacture the cylinders, i.e., [90°/±55 4 °/90°], [90°/±55 8 °/90°], and [90°/±55 12 °/90°].The manufacturing process was then completed by curing the cylinders in an oven at a temperature of 105°C for 24 h.The finished specimens were then coupled in a flange before being tested in a hyperbaric chamber with a constant rate of pressure of 5 bar/min.The results from the experiment showed that the cylinders with stacking sequence of [90°/ ±55 4 °/90°] and [90°/±55 8 °/90°] underwent buckling followed by collapse, while the cylinder with stacking sequence of [90°/±55 12 °/90°] failed without buckling but showed evidence of delamination.
Buckling performance of cylinders can be enhanced by applying ring stiffener as done by Cho et al. [39].The ring stiffener were welded on the inside or outside surface of the steel cylinders.Both the cylinders and the ring stiffeners were built with variation in dimension as given in Table 2.It can be seen from Figure 1 that the ring stiffeners had distinct spacing towards the ends of the cylinders so that failure merely occurs in the middle of the cylinders.In this study, the failure of cylinders under uniform external pressure is defined as either shell yielding, local buckling, or overall buckling of the cylinder and stiffeners.However, the failure of ring-stiffened cylinders may occur in a combination of local and overall buckling which are mostly caused by shell imperfection and stiffener tripping.
Once the flange, ring stiffeners, and the cylinders were welded together, the model was painted and grid lines were drawn with a spacing of 5°on the outer surface and 10°on the inner surface, then the initial shape imperfection of the cylinders was measured.Afterwards, the cylinders were tested in hyperbaric chamber capable of replicating the hydrostatic pressure at 800 m below sea level.One end of the cylinder was attached to the open flange of the chamber and the free end of the cylinder was supported using a rubber block to avoid bending moment.The test was initiated by pressurizing the chamber at approximately 2 bar and the pressure was held momentarily to estimate the chamber stabilization then carried out by increasing the pressure in three phases of increment.The first increment was 0.5 bar, which used within 15% of the predicted collapse pressure, the second increment was 1 bar, which used 12-80% of the predicted collapse pressure, and the third increment was 0.5 bar, which was used until the cylinder collapsed.The predicted collapse pressure was obtained from finite element analysis using ABAQUS software which was also used to predict the failure mode of the cylinders.The experiment showed that four models, i.e., RS-4, RS-5, RS-6, and RS-7 were collapsed by local buckling, RS-9 was collapsed by overall buckling, RS-8 and RS-10 were failed by shell yielding, and RS-I and RS-II were collapsed by combined local and overall buckling.
Stiffener tripping also occurred on the cylinder after testing which caused several cylinders to collapse by overall buckling.Strengthening cylinders by using stiffener without adding auxiliary material can be done by denting the surface of the cylindrical shells.This method had been used by Aydin et al. [40] when investigating the effect of using carbon fiber reinforced polymer (CFRP) strips on dented cylindrical shell buckling behavior.In this research, the cylinders were created with the dimension: 500 mm of height (h), radius (R) of 500 mm, and thickness ( ) t c of 1 mm.The cylinders were divided into two groups, the first group are the cylinders without CFRP including the intact model and the second group are the cylinders with CFRP strips bonded on the dents using adhesive including the intact specimen wrapped in CFRP.The detailed geometry of the specimens is presented in Table 3.
A vacuum pump was utilized to generate hydrostatic pressure up to 600 kPa.The result obtained from the experiment can be seen in Figure 2.Even though there were three parameters, i.e., initial buckling, overall buckling, and collapse buckling, initial buckling was considered as the most important parameter for thin cylindrical shell structures.As described in Figure 2, both groups had similar behavior, when there was only one dent line, increasing the dent depth would decrease the initial buckling pressure.However, when the dent line was two, increasing the dent depth will increase the initial buckling pressure.Dent depth is responsible for the weakening effect of the dented cylinder and dent lines are able to transform dents into stiffeners.Thus, it can be concluded that increasing both dent line and dent depth will generate stiffening effect out of the dents.
Similar research with the same method was conducted by Korucuk et al. [41].However, in this research, the specimens were more intensely dented (Table 4).The cylinders were built with the dimension: 1,250 mm in height (h), radius (R) of 500 mm, and 1 mm of thickness (t).The specimens were divided into two groups, i.e., with CFRP and without CFRP, each group including the intact models.With the same testing method, the result of the experiment can be seen in Table 5 and Figure 3.According to the graph shown in Figure 3, it can be seen that increasing the dent number and dent intensity were not followed by improvement of the initial buckling pressure.Instead, the initial buckling pressure of the dented cylinder dropped significantly from 161.4 to 76.02 kPa and 168.92 to 98.36 kPa as the dent intensity and dent number increased for the models without CFRP and with CFRP, respectively.However, Thin-walled cylindrical shells in engineering designs and critical infrastructures  5 improvement was found in the initial-overall buckling and initial-collapse buckling range corresponding to the increase in the dent number and dent intensity.
Even though the method used in the research conducted by Aydin et al. [40] and Korucuk et al. [41] was similar to each other, the results showed different behaviors as described in Figures 2 and 3. From the data given in Figure 2, it can be concluded that initial buckling pressure of the cylinders can be improved by denting the cylinder wall and attaching CFRP strips to the dented area.On the other hand, the graph shown in Figure 3 proved that dents cannot improve the initial buckling pressure of the cylinder, but are able to improve the initial-overall buckling and initial-collapse buckling range of the cylinders.This difference may be caused by variance in the geometry of the specimens, i.e., the dimensions of the specimens used by Aydin et al. [40] is 500 mm in height (h), radius (R) of 500 mm, and thickness ( ) t c of 1 mm, while that used by Korucuk et al. [41] is 1,250 mm in height (h), radius (R) of 500 mm, and 1 mm of thickness (t).In summary, the stiffening effect of the dents on the cylinders occurs when the length to diameter ratio of the cylinders is approximately ±0.5 and when the cylinders have l/d ratio of approximately 1.25 the dents will enhance the buckling capacity of the cylinders.
In certain circumstances, denting the surface of a cylindrical shell will create stiffening effect which is very beneficial because the strength of the cylinder can be enhanced without additional stiffener.The research carried out by Aydin et al. [40] and Korucuk et al. [41] were done by denting the cylinder wall in vertical direction which is very similar to the corrugation method.In 2015, Ghazijahani et al. [42] conducted research investigating the effect of corrugation on the buckling performance of cylindrical shell.Tin cans made of mild steel with D/t ratio of 758.85, l/d ratio of 1.44, and thickness of 0.2 mm were used in the experiment.The corrugation was done with variation in three parameters: length, orientation, and number of corrugation lines (Table 6).
The testing was done using material testing system machine equipped with LVDT sensor and pressure gauge.Specimens were placed between grooved plates of the testing machine to avoid the rotational movement during the test.Table 7 shows the critical buckling pressure of the specimens under uniform external pressure.Compared to the intact model, SDF-5 and SDF-4 can reach much higher initial buckling pressure up to 18.56 and 17.8 kPa, respectively.SDF-7 and SDF-6 were the specimens with the highest number of stiffeners.However, the initial and overall buckling pressure of these two specimens were lower than those of the SDF-5 and SDF-4 which were built with 16 and 12 stiffeners, respectively.Stiffeners with diagonal orientation also performed poorly in enhancing the buckling performance of the cylinders.From this result, it can be concluded that there was a limit to increase the number of stiffeners and within this limit the buckling pressure of the cylinder can be improved.From Figure 4, it can be concluded that the buckling pressure can be enhanced efficiently by using 8 or 10 stiffeners.
In the previous study, Ghazijahani et al. [42] had conducted research on stiffening thin-walled cylindrical shell by corrugation method in which two specimens were corrugated diagonally with the angle of = α 75°.However, the diagonally corrugated cylinders were not presenting better performance than longitudinally corrugated cylinders.In another research, Ghazijahani et al. [43] also investigated the buckling performance of horizontally corrugated cylinders.The corrugation profile used in the experiment was two-half-sine-wave.
The specimens were divided into three categories: intact model, partially corrugated, and fully corrugated.CSC1 is the intact model.CSC2 was corrugated right in the middle of the height, CSC3 had two corrugation lines and divided into three unstiffened sections, and CSC4 had 3 corrugation lines.Figure 5 shows that the plain specimen CSC1 had an initial buckling strength, overall buckling strength, and ultimate failure capacity which were all increased by 56, 73,and 78%, respectively, when compared to the same properties of the specimen CSC2 which had a single circumferential corrugation.Similarly, specimen CSC3 with two circumferential corrugations had respective increase of 114, 114, and 129%, while specimen CSC4 with three circumferential corrugations had an increase of 188, 188, and 150%.These results demonstrated the effectiveness of corrugations in enhancing the buckling and ultimate failure capacity of a plain and unstiffened thin cylindrical shell structure.To generate uniform external pressure a vacuum pump capable of creating 78 kPa of pressure was employed in this experiment.
The experimental result reported that increasing the number of corrugation lines will increase the buckling performance of the cylinder, with respect to initial buckling pressure.It was also proven in the test result of specimen CSC5, the fully corrugated cylinder, which showed no evidence of buckling or failure when reaching the maximum pressure of 78 kPa.All the equations had overestimated the buckling pressure of the cylinders.These discrepancies can be affected by several factors of nonlinearities: material and geometrical imperfections, material inelasticity, boundary conditions, and assumptions.
Further study to investigate the buckling performance of circumferentially corrugated cylinders were carried out by Zhang et al. [44] by using numerical method consisting of two types of analysis.The first one was linear buckling analysis and the second one was non-linear buckling analysis which include the non-linear parameter: material  Thin-walled cylindrical shells in engineering designs and critical infrastructures  9 inelasticity, geometrical inelasticity, and initial geometrical imperfections.FEM software, ABAQUS, was used to perform the linear and non-linear buckling behavior of the cylinders.The material properties of mild steel are as reported by Ghazijahani et al. [43].The cylinders were set with dimension: 370 mm in length (H) for intact cylinder and 310 mm for corrugated cylinder, 285 mm in diameter (D), and 0.4 mm in thickness (t).The imperfection size was assumed to be 2.5, 5, 10, 20, 25, 50, 75, and 100% of the shell thickness.For the first analysis, the corrugation of the cylinder was set using sine profile with amplitude s = 5 mm and base length S = 11 mm, and the number of corrugation lines n = 18.Compared to the experimental data obtained by Ghazijahani et al. [43], the linear analysis estimated that the buckling value of the cylinder is 36.6 kPa, this value is much higher than the actual buckling pressure of the cylinder 25.5 kPa, while the corrugated cylinder can reach the value of 431.8 kPa.On the other hand, the nonlinear analysis was able to predict the buckling pressure of the intact cylinder more accurately, 25.6 kPa at 100% imperfection, while the predicted buckling pressure of the corrugated cylinder was varying from 86.3 to 86.1 kPa based on the imperfections.
The second analysis was aimed to investigate the buckling performance of a cylinder with different corrugation forms (Figure 6).The cylinder was set with dimensions: 370 mm in length (H), 285 mm in diameter (D), and 0.4 mm in thickness (t).The corrugation was set with amplitude s = 5.5 mm, base length S = 11 mm, and the number of corrugation line n = 30.The initial imperfection size used in nonlinear analysis varied from 0.1 to 0.4.The results of the analysis are described in Table 8.In conclusion, corrugation with sine profile was the most effective in increasing the buckling performance of the cylinder and all the corrugated specimens can be considered insensitive to initial geometrical imperfections due to relatively stable buckling pressure under varying imperfection size.Recently, several research have been focused on investigating the buckling performance of composite reinforced cylinder.The research carried out by Taraghi et al. [45] evaluated the buckling performance of CFRP strips strengthened steel cylinder under numerous parameters: slenderness ratio, CFRP configuration, number of layers, fiber orientation, and CFRP thickness.All cylinders were 500 mm in diameter, 250 mm in length, and were divided into three groups based on the slenderness ratio of 312.50, 416.67, and 625.In Figure 7, two CFRP strengthening strategies are depicted: circumferential and meridional.Within the circumferential strengthening approach (Figure 7a), reinforcement was applied to three regions: the middle section, the top and bottom sections, and the top, middle, and bottom sections.This involved 50mm-wide layers (equivalent to 1/10 of the cylinder height) and CFRP layers with thicknesses of 0.334 mm and 0.668 mm.Regarding the meridional reinforcement technique (Figure 7b), symmetrical strengthening of four and eight sections of the cylinder was achieved using CFRP strips.These strips were 500 mm in length, 50 mm in width, and had thicknesses of 0.334 mm and 0.668 mm.The CFRP layers consisted of one or multiple strips with diverse fiber angles, encompassing , 45°, 90°, 0°/45°, 0°/90°, 45°/90°, and 0°/45°/90°.In total, there were 1 plain cylinder without any reinforcement and 70 CFRP strips strengthened cylinders in each group.ABAQUS was used to perform the numerical simulation.The result reported that circumferential strengthening was more effective to enhance the buckling performance of the cylinder under uniform external pressure compared to the meridional strengthening.It is also found that fiber angle, CFRP strip thickness, and slenderness ratio were the parameters that significantly affected the buckling performance of the cylinder.CFRP strips with 0°fiber angle showed the best performance in enhancing the buckling performance.Furthermore, doubling the CFRP strip thickness will result in further increase in the buckling pressure of the cylinder.
Conversely, in 2022, Zuo et al. [46] investigated the buckling performance of CFRP wrapped steel cylinder.The CFRP layer was wrapped on the outer surface of the cylinder with variation in the stacking sequence [ ] − 55°/ 55°4 [ ] and 90°/90°/0°/90°/90°/0°/90°/90°.The cylinders were all equal in outer radius of 79.5 mm and thickness 1.5 mm except the length, i.e., 320 mm for cylinder with stacking sequence [ ] − 55°/ 55°4 and 280 mm for cylinder with stacking sequence [ ] 90°/90°/0°/90°/90°/0°/90°/90°.Two solid steel bungs were attached to both the ends of the cylinder, which will act as rigid boundary condition.The testing was carried out in a pressure vessel capable of pressurizing the cylinder up to 8 MPa.Since the testing would be performed underwater, the specimens were coated using polyurea to avoid water absorption.As reported from the experiment, local dent collapse mode appeared in all specimens with the average collapse pressure from the cylinder with stacking sequence [ ] − 55°/ 55°4 and [ ] 90°/90°/0°/90°/90°/0°/90°/90°being 2.853 and 3.098 MPa, respectively.According to the data, it can be concluded that the cylinder wrapped with CFRP layer with stacking sequence [ ] − 55°/ 55°4 was considered to be the most  Thin-walled cylindrical shells in engineering designs and critical infrastructures  11 efficient in enhancing the buckling performance of cylinder since it required less amount of CFRP layers to obtain just about the same collapse pressure of the cylinder with stacking sequence [ ] 90°/90°/0°/90°/90°/0°/90°/90°.The col- lapse behavior of the cylinder wrapped with CFRP layer was further investigated using numerical simulation.Specimens with wrap angle [ ] 90°/90°/0°/90°/90°/0°/90°/90°w ere chosen to be investigated.In order to obtain the actual geometric shape, the finite element model was determined from scanning data.As a result, the predicted collapse pressure obtained from the nonlinear RIKS analysis was 3.024 MPa, which was slightly lower compared to the experimental data.The equilibrium curve obtained from the numerical analysis confirmed that local dent collapse mode was related to the initial geometric imperfection and the plastic behavior of the steel cylinder.
Alternately, research on enhancing the performance of cylindrical pipe by employing sandwich structure with various core materials have been gradually developed.Such research had been performed by Maali et al. [14].The research was aimed to investigate the buckling and postbuckling behavior of steel cylindrical shell filled with four core materials, i.e., polypropylene (PP), waste polymer (W-PP), silicon (S), and steel adhesive glue (S-A).In addition, two other specimens were built by wrapping the steel cylinder with single and double CFRP layer noted with CFRP and T-CFRP, respectively.In total, there were seven models including the plain model.The steel cylinders were manufactured with dimensions: inner diameter of 400 mm, outer diameter of 410 mm, 800 mm in height, and thickness of 0.45 mm, while the CFRP wrapped cylinders were created with singular steel pipe with dimensions: 500 mm in height, 250 mm in radius, and thickness of 1 mm.The models were later tested under uniform external pressure generated by a vacuum pump with a maximum pressure of 600 kPa.As described in Table 9, the sandwich pipe showed much better buckling performance compared to the plain specimen.Sandwich pipe with PP core material yielded the highest buckling performance compared to other core materials.
However, the CFRP wrapped cylinder showed even better buckling performance compared to the sandwich pipe with PP core material.
Sandwich and hybrid composite pipes are very promising method in enhancing the buckling performance of cylindrical structure under external pressure as it is increasingly discussed in the recent research works.However, future works are still highly required to discover the influence of parameters on the buckling behavior of cylindrical structure.All mentioned studies can be seen in Table 10.

Axial compression on cylindrical shells
Through the years, fossil fuels such as oil, coal, and natural gas have supported the world's demand for primary energy that is constantly rising until today.Based on the data provided by Ritchie et al. [47], it is known that the world's demand for coal is the highest among the three types of fossil fuels.Recently, the demand for coal has started to descent slightly regardless of the use of oil and natural gas, which was still an increase by the end of 2021.International Energy Agency forecasted that worldwide demand for primary energy will still be on the rise until 2035 [48].Oils and natural gases are distributed in liquid phase.Ships are used to transport fossil fuels over long distances whereas cylindrical shells in the form of pipelines are used in relatively short distance fuel transport [49].Cylindrical shells such as tanks and pipelines can be installed in various circumstances: in land, onshore, and offshore.If the pipeline installation is made in land with the pipe buried in the ground, the pipe is susceptible to ground movement [50].7% of total incidents in pipelines are caused by ground movement [51].It is also found that pipes with smaller diameter are more vulnerable to ground movement than those with the larger diameter.In some cases, pipelines are buried in sloped ground [52].The slope instability may cause the ground to move which can be classified as shallow or deep-seated ground movement.Transverse ground movement will create lateral forces which cause the pipe to bend.On the other hand, when the ground movement is parallel to the pipe axis, axial force will be induced and the pipe will be subjected to either tension or compressive stresses.In the transportation of oil and gas, subsea pipeline is highly affected by temperature.Inside the pipe, oil and gas are transported with a temperature difference of approximately 100℃ above the surrounding water to prevent solidification of the fluid inside the pipeline.This high temperature will cause thermal expansion on the pipe which induces axial compression [53,54].Subsea pipeline used to transport oil and gas should be modeled as long pipe subjected to constant temperature and pressure.The heat from the fluid flowing inside the pipe will cause the pipe to expand.The force induced by the expanding pipe are resisted by the frictional force of the seafloor resulting in effective compressive force which increases linearly from both ends of the pipe.In a relatively flat seabed, subsea pipelines tend to buckle laterally rather than vertically (upheaval) due to low friction coefficient of the seabed which makes the pipe to tend to move sideways [55].
As described above, the cylindrical shell in the form of pipelines has very high contribution to human life in terms of energy distribution.However, cylindrical shells are developed in many other forms and in many other fields as well, such as wind turbine towers, automobile, marine, building structures, etc.In accordance with Section 3, it is known that axial compression may cause the cylindrical shell to fail.Thus, in this section, numerous research investigating the cylindrical shells behavior under axial compression from various fields will be discussed.
In a car body design, aluminum is such a novel material which is very promising to be used in car body structure due to its lightweight characteristic.It offers weight reduction of up to 25% compared to conventional steel body structure [56].However, as a new material in car body design, research must be conducted to assess the energy absorption capabilities of aluminum to make sure the structure integrity and safety of the passengers.Assessment of material energy absorption capability can be done by using circular tube model.Such research had been carried out by Al Galib and Limam [56].The main objective of the research is to observe the static and dynamic axial crushing behavior, i.e., peak load and energy absorption of aluminum allow A6060 temper T5 circular tube comprising weight and velocity parameter.Cylinders with dimensions of 58 mm in diameter, 2 mm thick, 200 mm in height were used in the experiment.Quasi-static tests were conducted by using Universal Tension-Compression Testing Machine with load capability of 200 kN, while the dynamic tests or impact tests were carried out by using impacting truck with maximum speed of 7.2 m/s and the impact mass varied from 87 to 117 kg.
The quasi-static experiment reported that under the same load and boundary conditions, the models showed different deformation modes as described in Table 11.In general, there were two modes of deformation that occurred during the test, i.e., axisymmetric and mixed deformation.Pure axisymmetric deformation can be seen in models SR002 and SR003, while the rest were mixed deformations.The average first peak load of the cylinder deformed in axisymmetric mode was 72 kN, which then decreased to around 60 kN on the next peaks.The next peak loads were lower than the first peak because the deformation occurred after the first peak produced local bending which triggered the formation of the next folds.
When the two modes of deformation were compared, it is found that mixed mode deformation can absorb energy up to 7% higher compared to axisymmetric deformation with the same displacement.However, axisymmetric deformation is preferable instead of mixed deformation because mixed deformation tend to induce global bending which will reduce the energy absorption capacity.The result of dynamic test showed that there was no significant effect of increasing the mass on the force-displacement curve of the tubes.Compared to the static test result, the dynamic test result showed significant higher value of energy absorption, around 40-60%; the mean crushing load of dynamic test was 10% higher than the static test.However, the deformation mode occurred in both tests were relatively same.
Steel cylindrical shell have been widely used in the field of civil engineering.Based on the cross-section measurement, steel cylindrical shell structure is categorized as structural steel tube, pipe, and fabricated steel column.At first, fabricated steel column is used in offshore structures.Later, the structure was developed by using high-strength steel (HSS) material to create the steel column which is now widely used in numerous engineering application.However, further observation is required to study the structure buckling response and residual stress distribution.Such research was conducted by Shi et al. [57] to investigate the flexural buckling behavior of welded steel column.The buckling behavior of the steel column was assessed by experiment and finite element analysis.In total, there were 24 models used in the experiment.The specimens were divided into 8 groups based on the slenderness ratios with groups 1-5 having slenderness ratio λ of 20, 30, 40, 50, 60, respectively and groups 6-8 having slenderness ratio of 20, 40, and 60.Groups 1-5 were built with un-galvanized HSS material and the other groups were built with galvanized HSS material.The nominal yield strength of the HSS material was 420 MPa.The axial compression test was carried out under hydraulic actuator capable of generating 5,000 kN of load.
The experimental result reported that the relatively short models (λ = 20) underwent overall buckling with interactive local buckling and bulging occurred at both ends of the column.The medium length model (λ = 30 and 40) tended to buckle in overall buckling mode and bulging at both ends of the column.Overall buckling also occurred on the relatively long models (λ = 50 and 60) and the models were fractured at the middle or at one-third of the model height.
Numerous similar studies focused on investigating the behavior of circular hollow section (CHS) under axial compression with different materials have been carried out [58][59][60][61][62]. The research carried out by Young and Hartono [58] investigated the buckling behavior comprising local buckling and overall flexural buckling on various column length.The models were made with cold-rolled annealed 304 stainless-steel.The models were divided into three groups based on the thickness and average outer diameter.The specimens denoted by C1, C2, and C3 corresponded to D/t ratios of 32, 50.5, and 74.7, respectively.Geometric imperfections were measured at the mid-length of the models.According to the experimental result shown in Figure 8, it can be seen that as the length of the model increased within the same D/t ratio, the ultimate strength of the model will be decreased and the failure mode occurring at ultimate strength are local buckling, overall buckling, and combined local and overall buckling.
The buckling behavior of axially compressed coldrolled steel column was also investigated in the research carried out by Hu et al. [61].The material used in this research was S690 HSS.Two types of tests were performed in the experiment, i.e., stub column and slender column test.The models were grouped based on the experiment type.The geometry of the specimens can be seen in Tables 12  and 13.From the stub column test, it was known that the typical failure of stub column was material yielding and local buckling.Buckling typically occurred near the end of the column.However, the model CHS04-S1 showed different buckling pattern than other columns, in which the buckling occurred near the mid-length of the column.The difference in buckling pattern can be affected by the difference in initial imperfections.On the other hand, the long column test reported that all columns failed in overall buckling and local buckling modes.
Zhu and Young [59] investigated the effect of welding on the load carrying capacity of CHS with material 6063-T5 and 6061-T6 heat-treated aluminum alloy.In total, there were 29 models involved in the test, with the models divided into 4 groups based on the type of aluminum and cross-section geometry.Each group included five specimens with both ends welded to aluminum plates and two un-welded specimens.In general, three failure modes occurred in the test, i.e., shell yielding, overall buckling, and material yielding in the heat-affected zone.According to the experimental result, it was revealed that the non- Thin-walled cylindrical shells in engineering designs and critical infrastructures  17 welded specimens had higher ultimate strength compared to the welded specimens with the same slenderness ratio and both welded and non-welded specimens will become weaker with the increase in the slenderness ratio.Furthermore, the models with low slenderness ratio tended to be in heat affected zone which is located at both ends of the column where the welding was made, while the models with relatively high slenderness ratio tended to fail in flexural buckling mode.CHS can be produced by cold-drawing and cold-rolling process.However, cold-drawing process is preferable to produce sections with large diameter without welding.The flexural behavior of cold-drawn duplex stainless-steel CHS under axial compression was observed by Shu et al. [60].The specimens were built with 3 mm thick S22053 grade stainless-steel.Stub column and long column tests were carried out to obtain the ultimate loads and failure modes of the steel columns.In total, there were six specimens used in the stub column test with variation in D/t ratio and length (Table 14).A 200T hydraulic testing machine was utilized for the stub column test.In order to observe post-buckling behavior, the loading was performed at very low rate.Long column test was carried out using circular tube with a diameter of 102 mm and 3 mm of thickness with a length variation of 700, 1,000, 1,500, 2,000, 2,500, 3,000, and 3500 mm.To accommodate the length of the column, 500T hydraulic testing machine was utilized in long column test.However, the loading was done by using 100T screw jack placed at the bottom of the testing machine to provide better loading control.
The stub column test reported that clear buckling wave occurred when the load reached about 90% of the ultimate strength.However, when the loading was continued at very low rate, the end-shortening of the column rapidly raised.Circumferential drum deformation suddenly occurred at both ends when the load nearly reached the ultimate strength which followed by gradual decrease in the load.It is also reported that all specimens failed in elephant foot buckling mode.On the other hand, all specimens in the long column test failed in overall buckling mode.The 700 mm long column (named CHS-700) which is the column with lowest slenderness ratio showed different behavior than other columns with higher slenderness ratio.The displacement at the mid-height of CHS-700 column was increased significantly after the peak load, which led to second order bending moment or combined axial compression and bending resulted in local buckling at the mid-height.
Another material that can be used to create tubular column is copper.With the help of the modern smelting technology copper can be produced with high level of purity.Oxygen-free copper (OFC) is a product of high purity copper which offers much better mechanical properties compared to ordinary copper products.Zhang et al. [62] investigated the buckling behavior of cold-drawn TU1 OFC tubular column.In this research, the columns were expected to fail in overall buckling mode instead of local buckling.Thus, both ends of the columns were reinforced with steel buckling-restrained devices and steel hoops instead of welded rib stiffeners to prevent weakening effect due to the heat in welding process.Prior to the test, the load eccentricity was calculated and the result can be seen in Table 15 alongside the geometry of the models.The experimental result is plotted into a graph as shown in Figure 9.According to the graph, it can be seen that the buckling capacity of the column with the lowest slenderness ratio (TU1-1) was below model TU1-2 which had higher slenderness.This happened because model TU1-1 had much higher load eccentricity (4.33%) compared to model TU1-2 (0.39%).It was also reported that not a single model failed due to local buckling.The columns with relatively low slenderness ratio tend to experience large residual horizontal deformation which means slender columns tend to experience elastic buckling, while the less slender column tend to fail due to elastic-plastic buckling.
High strength aluminum alloys have gained its popularity in many engineering practices such as tower structures, bridge structures, and space structures.Compared to conventional aluminum alloys, high strength aluminum alloys offer more efficiency in terms of dimensions, weight, and cost.Recently, numerous research have been carried out to investigate the behavior of CHS made of high strength aluminum alloys.Such research was carried out by Li et al. [63] and Rong et al. [64].In the research carried out by Li et al. [63], the buckling behavior of circular tubes made of 7A04-T6 high strength aluminum alloys were investigated.The geometry of the models is given in Table 16.In accordance with the experiment, after the load was released, the residual deformation of the slender column was relatively small.All tubes failed due to global buckling and no local buckling occurred in the test.After the occurrence of global buckling, the load started to descent.However, it should be noted that the descent of the load was more significant on the less slender tube.
Rong et al. [64] conducted similar research investigating the behavior of axially compressed CHSs with the same type of aluminum alloy used in the experiment conducted by Li et al. [63].In total, there were 16 specimens used in the experiment with the model geometry given in Table 17.The test result was identical to that of the experiment conducted by Li et al. [63].All specimens failed due to the overall flexural buckling and after the unloading process, the tube can recover from the deformation.Less slender tube can recover approximately 50% of deformation, while highly slender tube can recover up to 80% of deformation.Furthermore, parametric analysis was also undertaken in this research.Cross-section size, eccentricity ratio, and slenderness ratio were taken into account.From the parametric analysis, it was known that the ultimate strength of the column will decrease significantly when λ ≤ 30 and λ ≥ 70.
Composite structures offer great mechanical properties, such as high strength, high stiffness, lightweight, and corrosion resistance.Several studies investigating the behavior of composite cylindrical shells under axial compression were carried out [65][66][67][68].Kepple et al. [65] investigated the influence of imperfections on the buckling performance of composite cylindrical shell.In total, there were four imperfections taken into consideration: UlƟmate load (kN) Figure 9: Load carrying capacity of the OFC columns.
Thin-walled cylindrical shells in engineering designs and critical infrastructures  19 initial geometric, loading, thickness, and material imperfections.Finite element analysis was utilized to generate 50 identical models of cylindrical shells with variations in imperfection magnitude.From the research, it was found that thickness imperfections played the most significant role in the load reduction of the unstiffened cylindrical shells.It is proved by the fact that any slight change in its value would affect the buckling load considerably.Loading imperfections, in terms of unevenness in the end plates, were ranked second in affecting the buckling load of cylindrical shells.Geometric imperfections also play an important role in affecting the axial buckling load as it is responsible for causing large knockdown factors.Material imperfections including longitudinal compression modulus, shear modulus, and Poisson ratio can barely affect the axial buckling load.Some of its components that are perpendicular to fiber direction such as transverse Young's modulus and shear modulus have negligible effect on axial buckling load.However, one of its components, i.e., transverse compression modulus turns out to play an important role in affecting the axial buckling load.In the research carried out by Ma et al. [66], the energy absorption properties of the filamentwound composite cylindrical shell was assessed.The models were made of aramid and carbon fibers with variation in fiber distribution (Table 18).Once the winding process was finished, the models were heat treated at 100℃ for 100, 200, and 400 h.The experiment reported that the heat-treated carbon/aramid models had higher energy absorption compared to the untreated-models.Heating time plays an important role in increasing the energy absorption capacity of the models.Models with longer heating time obtain higher energy absorption capability.However, heat treatment process did not show distinct effect on the energy absorption of carbon/carbon CFRP models.The experiment also revealed that in terms of energy absorption, models with three layers showed better performance compared to five layers models.Furthermore, there were three failure modes occurring in the models after testing, i.e., bending, splaying, and buckling mode.Splaying and bending mode occurred on the tube with high energy absorption capacity, while buckling failure mode indicates that the tube has low energy absorption capacity.Almeida et al. [67] investigated the buckling and postbuckling behavior of composite cylindrical structure.The models were made of T700-12K-50C carbon fiber with filament wound method.The manufacturing process was finished by curing the models at 105℃ for 24 h.In total, six models were created for the experiment with variations in stacking sequence: ±55 showed the best buckling performance among other stacking sequences in single-layered laminates.For multi-layered composite shells, the best buckling performance was achieved when the hoop layer was placed at the outermost, instead of middle or innermost.This was proven by the fact that the shell with stacking sequence [ ] ± ± ± 75/ 55/ 89.6 obtained the highest buckling load in multi-layered laminates.Furthermore, it was also revealed that all single-layered composite tubes failed due to buckling followed by a post-buckling field.On the other hand, thicker tubes failed due to material failure, i.e., transverse compression and in-plane shear stresses.The buckling behavior of axially compressed GFRP composite tube was performed by Ghalghachi et al. [68].Six models of cylindrical shells with dimension: 300 mm of internal diameter, 1.1 mm of thickness, and height varying from 150, 225, to 270 mm.Only one layer was used to build the model with fiber orientation of 0°and 90°.It was reported from the experiment that the major failure that occurred in almost every model was shear.In this experiment, the failure was classified into four phases: pre-buckling, full buckling, failure, and unloading.After the load was released, the models were able to return to its initial shape which means they showed elastic behavior.Furthermore, the stiffness was sensitive to the height of the cylinder.As the height of the cylinder is increased, the stiffness will be decreased.This result is in agreement with that of the previous experiment carried out by Qian et al. [69], where it was found that GFRP tubes with relatively low slenderness ratio have the failure characteristic of linear elastic and brittle under axial compression, while in terms of long tube, if the slenderness ratio of the long tube was relatively small (approximately 35) the tube will fracture when reaching the ultimate strain due to lateral deformation after buckling.On the other hand, the long tube with high slenderness ratio will experience elastic buckling and fail in oversize deformation.In the research carried out by Ma et al. [66] and Almeida et al. [67], it was revealed that heat would affect the energy absorption of CFRP composite cylindrical shell.However, in both research works, the specimens were not subjected to any moisture as they were tested under dry condition.Thus, the effect of moisture on the load carrying capacity of the heat-treated filament-wound composite cylinder was still a big secret.The research carried out by Azevedo et al. [70] was aimed to investigate the hygrothermal effect on the behavior of axially compressed composite tube.The models used in the experiment had 136 mm internal diameter and 300 mm length, with variation in pattern number: 1/1, 3/1, and 5/1.The models were then heated at 130℃ for 4 h.To create hygrothermal effect, the manufactured cylinders were immersed in liquid.Two different liquids were utilized in the experiment, i.e., distilled water and saltwater (salinity of ≈3.5% and pH 8.2).Prior to immersion, the cylinders were ensured to be dried out thoroughly to prevent initial moisture from affecting water absorption.It should be noted that every pattern includes one un-immersed model as control.The immersion process was done at room temperature and took approximately 400 h.
The experiment reported that highest water absorption was obtained by the model with winding pattern 1/1 followed by 5/1 and 3/1.In comparison to saltwater, the absorption of distilled water was generally higher except for 1/1 winding pattern with maximum water saturation achieved was 3.15%.The axial compression test result is shown in Figure 10.In accordance with the experimental result, the highest axial compressive strength was achieved by the un-immersed model.The specimen with winding pattern 1/1 yielded the lowest load carrying capacity, while the 5/1 winding pattern obtained the highest load carrying capacity.It was also known from the experiment that distilled water gave more significant effect on the reduction of load carrying capacity with the highest load reduction of 14.61% with respect to the reference model.
Such research was also conducted by Fitriah et al. [71].In this research, the hydrothermal aging affecting the behavior of axially compressed GFRP tube was investigated.The models were built by filament winding with stacking sequence variation: 45°, 55°, and 63°.The dimen- sion of the tubes was 100 mm in length, 100 mm in internal diameter, and 2.5 mm in thickness.Once completely manufactured, the models were cured at 160℃ for 2 h.The accelerated aging was simulated by immersing the models in tap water maintained at 80℃ for 500, 1,000, and 1,500 h.Once the immersion process was complete, the models were compressed under various temperatures: 65, 45, and 25℃ (room temperature).The experimental result reported that in terms of winding angle, 45°winding angle yielded the highest load carrying capacity.In accordance with the experimental result in Figure 11, the GFRP tubes showed identical behavior with the tubes in the hygrothermal experiment carried out by Azevedo et al. [70].The load carrying capacity of the GFRP tubes was highly sensitive to water saturation.Longer aging time at high temperature will cause more water absorption which caused degradation in the fiber-matrix bonding resulting in significant decrease in load carrying capacity of the tube as shown in Figure 11.Furthermore, it was found that the glass transition temperature of the GFRP tube was around 66.39°C.At this temperature, the properties of the composite will start to change from rigid to more flexible state.Thus, the models that compressed near the transition temperature will experience significant drop in load carrying capacity.
In the research carried out by Han et al. and Escobar et al. [72,73], sandwich structure was to enhance the strength of tubular columns.Han et al. [72] investigated the strength of sandwich column with stainless-steel outer tube, carbon steel inner tube, and concrete as filler material.Stub column models were created according to the dimensions given in Table 19.As can be seen from Table 19, the inner tube diameter of model C2 had been reduced to 106 mm and the specimens labelled with CH were the Thin-walled cylindrical shells in engineering designs and critical infrastructures  23 control models with no concrete filling.The experiment reported that the C2 model yielded the highest average ultimate load of 3,471 kN compared to model C1 and CH1.Typical failure mode occurred when the test was buckling.However, the outer and inner tubes showed different buckling behavior.The outer tube failed in elephant foot like buckling, while the inner tube showed inward buckling.
Further study based on this experiment was later carried out by Wang et al. [74] by utilizing the finite element analysis to investigate the effect of tube strength, concrete strength, and hollow ratio on the axial compressive strength of the column.In accordance with the simulation result, it was found that higher tubes and concrete strength will result in higher column ultimate strength.Moreover, as the hollow ratio was decreased, the cross-sectional area of concrete will be larger resulting in higher load carrying capacity.Escobar et al. [73] investigated the efficiency of sandwich columns in terms of weight and cost.Four models with identical dimensions of 900 mm in length, 60 mm internal diameter, 80 mm outer diameter, and 2 mm thick steel tube were filled with different core materials: polyurethane foam, Elastopack ® polyurethane grout, Multitek thixotropic epoxy, and SikaGrout ® -295 high strength cement.The test result is shown in Table 20.Three columns withstood two load cycles except the column filled with polyurethane foam and the highest peak load was reached in second peak load of Multitek filled column followed by cement-filled column.Both epoxy and cement-filled columns could yield the highest peak load due to high elastic moduli which enabled them to absorb large amount of energy.Among all models, cement-filled column was considered as the most efficient column configuration in terms of cost and weight (Figure 12).Several studies proposed stiffeners to enhance the axial compressive strength of cylindrical shell.Tao et al. [75] investigated the load carrying capacity of sandwich composite tubular column reinforced by longitudinal stiffeners.The inner face, outer face, and stiffeners were made of GFRP composite and the core was made of PVC material.There were two types of models used in the experiment: the stiffened and non-stiffened sandwich column.In each stiffened column, there were 32 6 × 6 mm stiffeners placed inside the core (Figure 13).All columns were identical with dimensions of 700 mm in height, 400 mm inside diameter, and 40 mm in core thickness, with variations of 2.4 and 1.2 mm in the thickness of the face.The test result reported that in terms of face thickness, models with 2.4 mm of thickness obtained higher load carrying capacity compared to the model with 1.2 mm face thickness and in terms of effect of the stiffeners, the stiffened models yielded higher load carrying capacity.According to Figure 14, it can be seen that increasing the face thickness of the stiffened model can enhance the ultimate load of the column significantly, which means that this method is pretty efficient considering its relatively high load/mass ratio.Such unique sandwich column design was proposed by Hou et al. [76].The distinctive part of the model was the core structure which was made of thin corrugated metal shell instead of solid filler material (Figure 15).AA6061-O aluminum alloy was used to build the model.The experimental model was built with dimensions of 160 mm of height, 80 mm of outer tube diameter, and equal thickness of inner tube t 1 , core column t 2 , and outer tube t 3 .Parameter peak height A and number of corrugations of the core column N are illustrated in Figure 15, the parameters used in the experimental model were A = 4 mm and, N = 6.The result from the quasi-static test reported that the column could achieve 101.3 kN of peak load and absorbed 5.6 kJ of energy by plastic deformation.Numerical models were also built to compare the energy absorption capacity of the sandwich column with double circular column and core column.The result reported that the energy absorbed by sandwich column was much greater than the energy absorbed by other models and the three models showed different collapse modes.The sandwich column showed progressive collapse, core column showed translational collapse, and double cylinder column showed progressive-translational collapse.Parametric study was also carried out to investigate the effect of parameter corrugation height A and number of corrugations N on the crashworthiness of the sandwich column.The parametric study reported that both A and N may affect the energy absorption of the sandwich column.The value of both parameters must be matched to obtain high energy absorption capacity.The model with highest energy absorption capacity was the model with A = 4 mm and N = 14.The model was collapsed in progressive collapse mode.Thus, it can be concluded that the progressive collapse is very favorable because it enables higher energy absorption than other collapse modes.
Realizing the fact that global demand in infrastructures, buildings, transportations, etc., will continuously rise, improved structures become very favorable solution to support the demand.In the previous paragraphs, numerous methods of improving the compressive performance of cylindrical shell have been discussed.Among many proposed methods, there are two methods that   Thin-walled cylindrical shells in engineering designs and critical infrastructures  25 have great chance to be further developed in the future.The first method is the utilization of alloy metals and high strength materials.In general, high strength materials and alloy metals offer much better mechanical properties which can be adjusted according to circumstances.Another advantage of using alloy and high strength materials is the cost efficiency as they require smaller cross-sectional area and are relatively less heavy than conventional materials.The second method is the development of sandwich structures in cylindrical shells especially load carrying columns.Currently, the best and most common material used as the core of sandwich column is cement-based materials.
Even though this method is quite effective to enhance the crushing strength of the column, the weight of the structure is still considerably high.Thus, novel sandwich structure such as stiffened core and corrugated core are great solution to obtain high load/mass ratio.The assessment regarding previous studies in axial compression is summarized in Table 21.

Performances under bending moment
In many cases, cylindrical shell structures are used as compression members where the load is applied parallel to the axis of the shell.However, in real life, it is possible for more than one load acting on the structure.In case of compression members, such as columns, bending moments   usually occur on the structure beside the primary load [77].This case is very similar to what happened in wind turbine towers where a heavy turbine is placed on top of the tower which is responsible for high axial force due to gravity combined with lateral load due to wind.In the case of ideal compression members, the only force acting on the structure is the gravitational force.This force is responsible for considerable axial force working on the structure.Actually, the gravitational force will produce bending moment as well, but the magnitude is negligibly small.On the other hand, when the lateral load is taken into account, it is responsible for the addition of bending moment in the structure even though the amount of bending moment produced by lateral force is less significant compared to axial force due to gravity [78].Bending moment also occurred on underground pipelines.In most cases, bending moment on buried pipelines is caused by landslides and earthquakes which lead to permanent ground deformations.Bending moments occurred when the ground movement is normal to the axis of the pipelines [79].Bending moment is such an important issue that has to be carefully considered in designing cylindrical shell structures.It is responsible for structural failures such as the collapse of wind turbine towers or leaking in underground pipelines especially oil and gas pipelines which may lead to economic loss and environmental hazards.In this section, numerous research investigating the behavior of cylindrical shell structures with various materials and configurations in various applications subjected to bending moment is discussed.
The world attempts to transition away from fossil fuels has been the driving factor to accelerate the development of renewable energy sources.Among many energy sources, wind energy is considered to be the most feasible energy source to be developed.The challenge now is that to increase the efficiency of wind turbines they must be built with higher capacity to increase the energy density and taller towers to achieve stronger and more stable wind profile [80,81].Steel cylindrical shell structures are very suitable for wind turbine towers since they offer high structural efficiency.In 2019, Yadav and Gerasimidis [81] investigated the effect of imperfections on the behavior of cylindrical shells for super tall wind turbine towers under pure bending.20 m long and 4 m wide steel pipes with slenderness and R/t variations from 60 to 120 with an interval of 20 were investigated using finite element method by utilizing ABAQUS software validated with experiment from previous studies.Four types of geometric imperfections, namely, modal shape, dimple like, unbiased, and biased were analyzed.The result showed that all models from all ranges of R/t ratios were sensitive to imperfections under inelastic bending which showed by the change in moment-curvature diagram and significant decrease in collapse curvature and peak moment.However, due to the appearance of nonlinear region before buckling, the reduction in collapse curvature was more obvious than that in the peak moment.Similar pattern behavior occurred in all R/t ratios of 60, 80, 100, and 120.Shells with R/t ratio of 60 experienced maximum reduction in load carrying capacity (peak moment) and collapse curvature of approximately 18 and 51%, respectively, under biased imperfection.On the other hand, the reduction in peak moment and collapse curvature was less significant under dimple-like imperfection, which reached only 6 and 30%, respectively.Guo et al. [82] experimented on four-point bending and cantilever test to study the bending behavior of CHS.Each test included 8 models with D/t ratio ranging from 75 to 150 for four-point bending test and 100-300 for cantilever test (Table 22).The models used in four-point bending test were stiffened by two stiffeners plate welded on each model to support the vertical load and avoid the local buckling between two loading points (Figure 16), while in the cantilever test, only two beams were stiffened by the stiffeners welded inside the tube, denoted by "R" (Figure 17).
The experimental results were plotted in force vs displacement graph as presented in the study (ref.[82]).As can be seen in the study, models with smaller D/t ratio reached lower peak load.Highest peak load was achieved by models with D/t ratio of 150 and the lowest peak load was achieved by models with the lowest D/t ratio of 75.The test was repeated for each model within the same D/t ratio and the result showed that discrepancy occurred between the force-displacement curve of the first and the second test.This discrepancy was more pronounced as the D/t ratio increased.Similar behavior was shown in the cantilever test where higher D/t ratio yielded higher peak load and the discrepancy got more pronounced with the increase in D/t ratio.Larger discrepancy occurring in cantilever test on models with higher D/t ratio was caused by initial imperfections.Stiffeners significantly increased the peak load of the CHS and the peak load is higher on the models with larger diameter.
The experiment also reported that extensive plastification failure mode occurred around the central part of the tube on the models with relatively low D/t ratios without visible local buckling.As the D/t ratio increased, ranging from 100 to 150, wave-buckling failure mode occurred.Local buckling appeared in the form of inward deformation on the top side, the compression part of the tube.Local buckling also occurred on the models with D/t ratio of 200 and 300.However, the local buckling on the D/t ratio of 200 and 300 were more severe indicated by the number of buckling ripples in the CHS.The stiffened models showed different buckling behaviors.The stiffeners increased the shells' strength at the compression part which resulted in local buckling that occurred near the stiffeners and the inward buckling deformation is smaller compared to the unstiffened models.
The flexural strength and failure mode of full scale 65-kW wind turbine tower had been investigated by Sim et al. [83] through experimental method.The tower consisted of three CHSs with equal thickness of 6 mm connected to each other by double flanges with pre-tensioned bolts stiffened with 8 mm thick triangular vertical plates.The tower was built with a door located at the base, and positioned upwards during the test.Due to the failure at the base plate connection, the test was conducted twice utilizing the same specimen.The experiment reported that the first test had already created less visible local buckling on the compression side which became more pronounced when the loading was continued in the second test.When the loading was continued in the second, the failure load was lower than that in the first test.A parametric study was also carried out to investigate the effect of base boundary condition and initial geometric imperfections on the flexural behavior of the tower.By utilizing finite element analysis, it was revealed that boundary condition influenced the ultimate strength and failure mode of the tower.Local dent that appeared in the first test was also investigated by numerical simulation and the result showed that the dent influenced the location and type of local buckling.The dent is also responsible for the decrease in failure load, even though the decrease is not significant.
Research focusing on the effect of geometries (diameter, thickness, and length) and openings on the structural behavior of steel CHS was carried out by Khalaf et al. [84].The models were divided into four groups with each group varying in one geometrical parameter.The details of the specimen geometry can be seen in Table 23.The result from the experiment showed that for the models without openings, increasing the wall thickness by 200% will result in significant increase in bearing strength (81.75%), stiffness (22.66%), and ductility (58.04%).However, decreasing the wall thickness by 33.33% will decrease the bearing strength, stiffness, and ductility by 38.87, 49.21, and 64.86%, respectively.Considerable increase in bearing strength and stiffness of 237.59 and 221.56%, respectively, was shown by increasing the diameter of the section by 115.55%; on the contrary, the increase in diameter will result in significant decrease in ductility by 76.67% and affects the failure mode of the section.On the other hand, decreasing the diameter of the section by 25% will decrease the bearing strength and stiffness of the section by 56.75 and 76.61%, respectively.In terms of section length, increasing the length by 33.33% will decrease the bearing strength, stiffness, and ductility by 3.28, 58.34, and 37.13%, respectively; however, reducing the length of the section will increase the strength and stiffness by 89.78 and 58.59%, respectively.In contrary, the ductility was decreased by 50.21%.Deformation mode is also affected by the decrease in section length.Creating openings in the section were responsible for the decrease in bearing capacity, ductility, and stiffness.Among these three structural parameters, ductility was the parameter which experienced the highest reduction, followed by stiffness and bearing capacity.The experiment was later numerically analyzed by finite element method with the geometry of the models described in Table 23.The numerical simulation reported that the general behavior of the section is not sensitive to the change in opening location; however, it affected the ultimate strength and deflection of the section which in turn affected the location of failure.If the opening is located at the loading point or the region where bending occurs, it will reduce the strength capacity and ultimate deflection of the section, making it less resistant to collapse [85].
The effect of dent on the flexural capacity of steel CHS had been investigated in the previous research carried out by Ghazijahani et al. [86].Mild steel material was used to manufacture the CHS models with the dimensions of   24).From the cantilever beam test, it was known that the failure mode occurred on the intact model was yielding on the compression side.The section also showed symmetric bulge-shaped deformation at around 30 mm from the welded end.The typical failure mode occurred on the dented models located on the compression side was deepening in dented region, while on the model TS7, where the dent was located on the tension side, the dented section gradually recovered its initial shape as the load increased and as the loading continued, the section yielded at both compression and tension sides, accompanied by the appearance of bulge-shaped deformation on the compression side.The failure mode for the section with dent located parallel to the loading direction was inward deformation on the compression side between the end plate and the initial dent.The bending capacity of the sections are shown in Figure 18.Based on the graph, it is revealed that the load carrying capacity of CHS is highly dependent on magnitude and position of the dent.Dent located at the mid-length barely affects the load carrying capacity and failure mode of the section; however, dent can significantly reduce the ultimate strength if it is located near the end plate.Zeinoddini et al. [87] conducted research to investigate the behavior of API-5L X808 high-strength steel cylindrical tubes.The models were built with a total length of 1,100 mm and nominal diameter of 50 mm.Both ends of the tubes had thickness of 5 mm, while the central part was machined to a thickness of 2 mm.The interconnection between thicker ends and gauge length was machined to taper to avoid local elastic buckling in the gauge length.In this research, there were two kinds of models: the perfect models and the defected models.The defected models were built to replicate the corrosion effect due to transportation of oil, gas, and water.The experiment was done using four-point bending  testing rig designed for monotonic bending test.During the test, the models were gripped by dumbbell-shaped rollers resting on free-sliding supports so that the models would experience uniform pure bending.Under bending, the defective models showed abrupt collapse, while the perfect models showed diffuse local collapse.The load carrying capacity of the tubes was also reduced by increasing the magnitude of the defect.The collapse of defective model indicated by the appearance of short wrinkling on the defective side later became sharp local inward kinks at final collapse stage.
In the research performed by Maduliat et al. [88], the energy absorption of steel CHS under pure bending moment was investigated analytically based on the existing experimental result.The bending moment-rotation curve obtained from the experiment was used to generate an empirical equation to estimate the rotational capacity of the section.Later, the simplified equation was used to calculate the total energy absorption of the sections varying in geometries.Based on the calculation using the proposed equation, it is revealed that within the same cross-section area, sections with lower slenderness ratio have lower bending capacity; however, the energy absorption turned out to be higher than those with higher slenderness ratio which is very favorable for industrial use.The high energy absorption capacity of the less slender sections was due to its potential to reach inelastic range before reaching ultimate moment so that they will not collapse suddenly and are able to distribute the stress along the section length.
Hilditch et al. [89] had investigated the load carrying capacity, energy absorption, and failure modes of aluminum and magnesium cylindrical shells.Several alloys were utilized in the research: magnesium alloy AZ31, and aluminum alloys 6063 and 7075.These materials were extruded to equal the thickness of 1.0 mm and diameter of 15 mm except for one AZ31 tube extruded to 1.5 mm to achieve equal mass as the aluminum tubes.Three-point bending test was utilized to replicate the deformation mode occurring in the automobile bumper during collision.The test result reported that within the same mass, AZ31 tubes absorbed much greater energy and yielded much higher ultimate load than aluminum 6060.In comparison to the AZ31 1.0 mm thick tubes, the energy absorption of thicker AZ31 tubes increased significantly, based on which it can be concluded that the ultimate load of the tubes was highly dependent on the wall thickness.Extrusion temperature and speed were also important to determine the ultimate load of magnesium alloy tubes since they highly affected the grain size.However, the effect of extrusion temperature and speed were not significant for aluminum alloys.Similar experiment was carried out by Hu et al. [90] to specifically investigate the energy absorption and ultimate load of magnesium alloy tubes subjected to bending moment.There were three types of magnesium alloys investigated: ZM20E, ZM20EX, and AZ31.The loading speed was varied from 1, 10, 60, to 240 mm/min.As described in Figures 19 and 20, the test result reported that ZM20EX tubes had the best stability in terms of energy absorption among all tubes in all range of loading speed, even though the highest energy absorption was achieved by ZM20E tube at low loading rate.In terms of peak load, AZ31 tubes achieved the highest ultimate load of 3.14 kN.However, among other tubes, the energy absorbed by AZ31 tubes in all range of loading speed was the lowest.This was due to the fact that the energy absorption is related to the displacement at peak load; tubes which are able to reach high displacement at peak load tend to have high energy absorption capacity.Thin-walled cylindrical shells in engineering designs and critical infrastructures  35 Functionally graded materials (FGMs) are the combination of ceramic and metallic constituents.These materials have the ability to withstand high temperature due to low thermal conductivity of ceramic and ductility of metallic constituents.The properties of the FGMs can be varied by changing the volume fraction of the constituents.Huang et al. [91] investigated the buckling behavior of cylindrical shells made of FGM material.The shells were divided into two types: type A with ceramic constituent on the inner wall and type B with ceramic constituent on the outside of the shell.The effect of shell geometry, radius, thickness, and length, on the buckling behavior of the shell was also investigated in this research.Based on the numerical buckling simulation, the shell with high volume fraction of ceramic will have greater buckling critical moment.The geometry parameters also played an important role in determining the buckling critical moment of the shell; increasing the shell diameter and thickness will result in higher buckling critical moment.However, varying the length of the shell from 50 to 300 mm showed less pronounced effect on the buckling critical moment of the shell.Another parameter investigated in this research was temperature.The effect of temperature was quite significant on the critical buckling moment of the shell; as the temperature increased, the shell will be weakened because heat reduced the structural stiffness.
Hu et al. [92] carried out research to enhance the bending performance of cylindrical shell used in wind turbine towers by using stiffeners.In this research, the structural performance of cylindrical shells with longitudinal and circumferential stiffeners with parameters, number of stiffeners and central angle β (in longitudinal stiffener), were investigated and compared.Each type of stiffener was applied to 50, 150, and 250 m long wind turbine towers with both types of stiffeners being equal in mass.The structural response of the model was analyzed using finite element method, and based on the analysis, it was revealed that in low-height towers, the use of ring stiffeners was more effective to enhance the structural performance of the towers compared to longitudinal stiffeners.However, longitudinal stiffeners turned out to be efficient in intermediate and high towers.The parameters number of stiffeners and central angle β are the important keys to enhance the structural strength of the towers; if these parameters increased, the strength of the towers will be enhanced, which will be indicated by lower von Misses stress and maximum horizontal sway.
Beside single wall, in several cases, sandwich structure is implied in cylindrical shells which have been gaining popularity for its high strength, stiffness, ductility, and cost efficiency.The behavior of various sandwich cylindrical shells subjected to bending moment were investigated previously [93][94][95].In the research carried out by Cheng et al. [93], the behavior of sandwich pipe consisted of steel inner and outer shells filled with strain-hardening cementitious composite (SHCC) was investigated through full-scale bending test on a rigid surface.The interlayer behavior effect on the bending capacity of the sandwich pipe was observed in the experiment, while the effect of geometric parameters and initial ovality on bending capacity of sandwich pipe was investigated through finite element analysis.Based on the experiment and numerical simulation, it was found that the bending capacity of sandwich pipe was related to the friction coefficient.Therefore, pipes with rough surface tend to have greater bending capacity.Bending capacity was also affected by the thickness of the steel tubes and core where the ultimate bending was decreased exponentially as these parameters increased.Another important factor responsible for the decrease in the bending capacity was the initial ovality, which on increasing will result in lower ultimate bending.Similar research was carried out by Ali et al. [94] with different materials, where 6082-T6 aluminum alloy tubes were utilized instead of steel tubes.In total, five models varying in geometry were utilized in the experiment.The experiment was later investigated through numerical simulation to examine the effect of cross-section slenderness of the aluminum inner and outer shells, hollow ratio, and concrete compressive strength on the flexural strength of the models.During bending test, the typical failure modes that occurred on the specimen was small outward local buckling at the top surface of the outer shell and fracture on the tension side as they reached the ultimate bending capacity.In general, the bending capacity of sandwich pipes was enhanced by increasing the inner tube dimension and concrete compressive strength, though the strengthening effect was less significant compared to increasing the cross-sectional dimension of the outer tube.Combination of composite and metallic materials was proposed by Idris and Ozbakkaloglu [95] to build sandwich pipes in which FRP was used as outer tube and steel was used as inner tube.There were three circular hollow column models built for the experiment (Figure 21).The models were then tested under four-point bending test.According to the experiment, it was reported that all models showed high inelastic flexural deformations and low rate of strength degradation.The slip occurring between the concrete and steel inner tube can be relatively high which can reduce the ultimate strength; however, it can be reduced by using mechanical connectors so that the concrete can have better grip.The bending capacity of sandwich pipes was sensitive to the diameter and thickness of the inner steel tube, and the strength of the filler concrete will result in higher ultimate strength with the increase in these dimensions.
The flexural performance of double layer composite tubes was investigated in the research carried out by Chen et al. [96].Scaled high performance centrifugal concrete wrapped with GFRP tubes were tested in four-point bending test, whereas the full-scale model was tested using cantilever bending test.According to the bending test, it was revealed that concrete-filled models had average ultimate strength of 128% greater than that without concretefilled models.Increasing the thickness of the FRP tube significantly increased the ultimate strength of the tubes.The increase in concrete thickness actually increased the ultimate strength as well; however, the strengthening effect was less significant compared to the increase in the thickness of the FRP tube.Slip occurred between concrete and FRP tube; however, the effect of the slip can be neglected.
Composites were well known for their high strength and stiffness, corrosion resistance, and design flexibility which make them highly favorable in many recent engineering applications such as pipelines, infrastructures, and aerial vehicles.Numerous research aimed to investigate the flexural behavior of composite thin-walled cylindrical shells have been carried out [97][98][99][100].Thermoplastic tubular composites reinforced by carbon fiber were proposed in the research carried out by Bhudolia et al. [98].The models used in this experiment were built using special manufacturing method, the Bladder-assisted resin transfer, to achieve fully impregnated composite tube models.The experiment was carried out to make a comparison between thermoplastic composite shell created with Ellium® resin and thermoset composite shell created with conventional epoxy resin.Based on the flexural test, the thermoplastic tube performed better than the thermoset one, indicated with higher strain to failure and the failure modes that were dominated with deformation.Even though the manufacturing method proposed by Bhudolia et al. [98] have a great potential to be utilized for mass production, the most common method used to create composite tubes is filament winding process which was utilized in previous studies [97,99,100].Stefanovska et al. [100] studied the bending behavior of composite tubes of different winding angle and number of layers (Table 25).Once the manufacturing process was done, the models were cured at 100℃ for 6 h.Simply supported beam flexural test with 400 kN servohydraulic testing machine at 5 mm/min loading rate and 80 mm support span was utilized to test the flexural performance of the models.According to the test result described in Figure 22, the model number 4 yielded the highest bending strength of 129.3 MPa.From the experiment, it was also revealed that all models showed matrix cracking and fiber failure due to tension and compression on the outer and inner layers which led to delamination.
The flexural behavior of filament-wound composite cylindrical shells with 55°winding angle was investigated by Betts et al. [97].In total, there were 15 models tested  Thin-walled cylindrical shells in engineering designs and critical infrastructures  37 under four-point bending test to observe the effect of diameter to thickness ratio which is varied from 20 to 75.The stacking sequence of the models was also varied as described in Table 26.The test results showed that all the models experienced similar behavior: post-peak gradual decrease in load, indicated with visible and audible damage on the tubes, followed by abrupt compression failure caused by either local buckling or material failure.The ultimate bending moment of each model can be seen in Figure 23.From this figure, it can be seen that reducing the D/t ratio will result in the increase in flexural capacity of the tubes.Zhu et al. [99] investigated the flexural behavior CFRP cylindrical shell using three-point bending test.The model was built using mold with dimensions of 21.1 mm in radius, 1.2 mm in thickness, length of 320 mm, and stacking sequence of [0/45/-45/90] 3 .The test was repeated three times to observe the energy absorption capacity of the tubes which finally yielded average energy absorption capacity of 18.78 J.The typical failure process of the tubes was crushing cracks at the edges of the compression zones which later spread laterally.This spreading crack later developed into secondary malposed crack (corresponding figures are provided in Figure 6c of ref. [99]).
The superiority of steels in terms of strength and ductility among many other materials make them very preferable to be used in conventional cylindrical shells.As seen in the discussion, studies before 2015 generally still developed or investigated steel thin-walled cylindrical shells, even though alloy metals had been introduced.In the following years, numerous researchers proposed various methods to increase the bending capacity of both steel and alloy metal cylindrical shells by applying sandwich structure.The effect of various core materials and outer and inner tubes on the flexural behavior of the shells has been the focus of the recent research.Furthermore, composite materials are also quite popular topic discussed in recent research.Thus, it can be inferred that in the future sandwich structure and composite cylindrical shells are great issues to be discussed.The summarized works in this section is presented in Table 27.The slips between the concrete and GFRP tubes had negligible effect on ultimate strength To build long-lasting infrastructures, high-quality structures are obligatory.The cylindrical shell structure is one of the most common structures used in human history due to its high structural efficiency.However, as cylindrical structures have a wide range of applications, they may be subjected to various loads that can lead to failure.Furthermore, external pressure simulation methods include hyperbaric chamber and vacuum tests.Filament-wound cylindrical shell strength is mainly determined by thickness and stacking sequence rather than winding pattern.Additional stiffeners can prevent implosion but may be vulnerable to tripping.Sine corrugation profile is the most effective corrugated stiffening method.The horizontal direction and number of stiffeners affect stiffening effectiveness.Sandwich structures and composite material wrapping are also effective methods to improve implosion pressure, with thicker composite wrapping resulting in greater implosion pressure.Also, cylindrical shell behavior under axial compression is influenced by geometry and imperfections.Cylindrical shells are classified as stub or slender columns based on length, with stub columns failing due to local buckling and slender columns failing in flexural buckling.Increasing D/t ratio improves column strength, but increasing column length reduces load capacity.Aramid or glass fiber cylindrical shells are sensitive to heat treatment and high humidity.

Load carrying capacity
Heat-treated aramid/carbon composite shells have higher energy absorption capacity, while GFRP composite shells lose strength with longer aging time.Increasing the thickness of inner and outer tubes of sandwich shells improves load capacity.And, bending moment on structural members is caused by lateral force from natural disasters or wind.Thin-walled cylindrical shells' behavior under lateral load depends on geometry and imperfections.Greater diameter and thickness increase load capacity, while high slenderness shells have higher energy absorption.Longitudinal stiffeners are more effective than ring stiffeners at increasing flexural performance.Applying a sandwich structure improves flexural performance by optimizing flexural strength through increasing the thickness of the inner and outer layers and eliminating interlayer slippage.

Figure 4 :
Figure 4: Optimal number of stiffeners to enhance the buckling pressure.

Figure 10 :
Figure 10: Compressive test result of CFRP tubes based on variation in pattern number.

Figure 12 :
Figure 12: Efficiency of the core material in terms of weight and cost.

Figure 13 :
Figure 13: Schematic diagram of the stiffened sandwich column.

Figure 14 :
Figure 14: Summarized results: (a) ultimate load and (b) load/mass ratio of the columns.

Figure 21 :
Figure 21: Cross-section of the models.

Figure 22 :
Figure 22: Bending strength of the tubes.

Figure 23 :
Figure 23: Ultimate moment of the models.
Theoretical and experimental bending properties of composite pipes General All models showed matrix cracking and fiber failure due to tension and compression on the outer and inner layers Bending responses of CFRP thin-walled tubes with different sectional shapes: experimental, analytical, and numerical investigation General (transportation) The typical failure process of the tubes was crushing cracks at the edges of the compression zones cylindrical shells in engineering designs and critical infrastructures  41

Table 1 :
Thicknesses of cylinders

Table 2 :
Dimensions of ring-stiffened cylinders

Table 3 :
Detailed dimension of the cylinders

Table 4 :
Detailed dimension of the models

Table 5 :
Initial buckling, overall buckling, and collapse buckling of the tested models

Table 6 :
Specimens geometry details

Table 7 :
Critical buckling pressure of the specimens

Table 8 :
Experimental test result

Table 9 :
Sandwich pipe experimental test result

Table 10 :
Studies related to pipe subjected to external pressure Thin-walled cylindrical shells in engineering designs and critical infrastructures  13

Table 11 :
Quasi-static test result

Table 12 :
Initial geometry of stub column models

Table 13 :
Initial geometry of slender column models

Table 14 :
Initial geometry of the models

Table 15 :
Initial geometric and load eccentricity of the models

Table 16 :
Initial geometry of the models

Table 17 :
Initial geometry of the models

Table 18 :
Structural design of the CFRP model

Table 19 :
Initial geometry of the models

Table 20 :
Compressive test result of the columns with different core materials

Table 21 :
Summary of the pioneer works in axial compression

Table 21 :
Thin-walled cylindrical shells in engineering designs and critical infrastructures  29

Table 22 :
Initial geometry of the models

Table 23 :
Initial geometry of the modelsThin-walled cylindrical shells in engineering designs and critical infrastructures  33 620 mm in length, 76.2 mm in diameter, and D/t ratio of 47.6.In total, there were 8 models of CHS used in the experiment, including intact model, with each model having distinct geometry of the dented area (Table

Table 24 :
Geometry of dent on the shells

Table 27 :
Studies related to pipe subjected to bending moment Parameter 1 Parameter 2 Material Thin-walled cylindrical shells in engineering designs and critical infrastructures  39