Steel Cylindrical Shells Research Articles

Buckling Analysis for Wind Turbine Tower Design: Thrust Load versus Compression Load Based on Energy Method

Tubular steel towers are the most common design solution for supporting medium-to-high-rise wind turbines. Notwithstanding, historical failure incidence records reveal buckling modes as a common type of failure of shell structures. It is thus necessary to revisit the towers’ performance against bending-compression interactions that could unchain buckling modes. The present investigation scrutinises buckling performances of a cylindrical steel shell under combined load, by means of the energy method. Within the proposed framework, the differential equations to obtain dimensionless expressions showed the energy-displacement relations taking place along the shell surface. Furthermore, shell models integrated with initial imperfection have been embedded into finite element algorithms based on the Riks method. The results show buckling evolution paths largely affected by bending moments lead to section distortions (oval-shaped) that in turn change the strain energy dissipation routine and section curvature. The shell geometrical parameters also show a strong influence on buckling effects seemingly linked to a noticeable reduction of the shell bearing capacity during the combined loading scenarios.

A design approach for the ring girder in elevated steel silos

Silos in the form of the thin-walled cylindrical steel shells are commonly supported on a ring girder, which rests on a limited number of columns to discharge the content by gravity flow into transportation systems. Local supports in the elevated steel silos produce a significant circumferential non-uniformity in the axial membrane stresses in the silo shell. One way of reducing the non-uniformity of these stresses is to use a very stiff ring girder which partially or fully redistributes the stresses from the local support into uniform stresses in the shell. Previous works that attempt to produce design expressions only address isolated ring girders and ignore the key role of the interaction between the cylindrical shell and the supporting ring girder. The aim of this study is to achieve a more efficient and realistic design of ring girders resting either on four supports, or on four supports with secondary beams, or on eight supports. Pursuant to this goal, variations of the stress resultants and displacements in the ring girder which rests on different support conditions are derived for the first time using Vlasov's curved beam theory. These expressions have been evaluated with finite element analyses for an isolated ring girder. Subsequently, a complementary finite element parametric study was conducted to investigate the variation of the stress resultants and displacements caused by the connection of the shell and ring girder resting on different supporting conditions. These variations were plotted as a function of the shell-ring girder stiffness ratio (ψ) for each support condition. Finally, considering lower bound limits for the stress resultants and displacements, design equations were proposed for ring girders which rest on different support conditions. These expressions may easily be placed in a practical spreadsheet, which could be used with different data to give realistic predictions.

Research on the intermediate phase of 40CrMnSiB steel shell under different heat treatments

In this study, 40CrMnSiB steel cylindrical shells were tempered at 350, 500 and 600 °C to study the effect of tempering temperature on the dynamic process of expansion and fracture of the metal shell. A mid-explosion recovery experiment for the metal cylinder under internal explosive loading was designed, and the wreckage of the casings at the intermediate phase was obtained. The effects of different tempering temperatures on the macroscopic and microscopic fracture characteristics of 40CrMnSiB steel were studied. The influence of tempering temperatures on the fracture characteristic parameters of the recovered wreckage were measured and analyzed, including the circumferential divide size, the thickness and the number of the circumferential divisions. The results show that as the tempering temperature was increased from 350 to 600 °C, at first, the degree of fragmentation and the fracture characteristic parameters of the recovered wreckage changed significantly and then became essentially consistent. Scanning electron microscopy analysis revealed flow-like structure characteristics caused by adiabatic shear on different fracture surfaces. At the detonation initiation end of the casing, fracturing was formed by tearing along the crack, which existed a distance from the initiation end and propagated along the axis direction. In contrast, the fracturing near the middle position consists of a plurality of radial shear fracture units. The amount of alloy carbide that was precipitated during the tempering process increased continuously with tempering temperature, leading to an increasing number of spherical carbide particles scattered around the fracture surface.

An Experimental and Modeling Study on Vibro-Acoustic Response of Double-Walled Steel Cylindrical Shells

Based on precise transfer matrix method (PTMM), the analytical model of the double-walled steel cylindrical shell was setup by taking into account of the annular plate and interlayer water. Under the linear sweep frequency excitation or the fixed frequency excitation, an experimental model of the double-walled steel cylindrical shell has been designed, which is performed to gain the natural frequencies, forced vibration in air and water, underwater acoustic radiation. The analytical model was established to calculate natural frequencies, vibration acceleration level and sound pressure level and compare with the relevant experimental results. The compared results show that analytical results coincide with the experimental value and prove that the analytical model established by PTMM is reliable and credible. Meanwhile, the forced vibration behaviour of measuring positions at inner and outer shells was investigated both theoretically and experimentally. Effects of different types of external excitations on the vibration and sound radiation of the double-walled cylindrical shell are discussed. As to acoustic radiation, the acoustic excitation plays a leading role in the low-frequency range. The force excitation is a major contributor in middle-high frequency range conversely.

Acoustic Scattering from Bi-Layered Cylindrical Shells: Influence of the Layers Thicknesses on the Guided Waves

The current work focuses on the study of acoustic scattering from bi-layered stainless steel-copper and copper-stainless steel cylindrical shells filled with air and immersed in water. This paper is interested in revealing the effects of physical and geometrical characteristics of the layers constituting the shells on the scattering phenomenon. The object of this work, is to study the influence of the layers thicknesses on guided waves, the overall thickness of the shells is fixed. The plane of modal identification was chosen to analyze the scattering phenomenon. We investigate the resonance trajectories of the guided waves, especially the curves change. The investigation and comparison made on resonance trajectories, show a shape change, a gradual deviation, or both, appear on the resonance trajectories of different guided waves, for the reduced cutoff frequencies of guided waves a sliding to higher and lower value are noticed. The interaction between guided waves is also manifested in the scattering phenomenon. The findings for the bi-layered cylindrical shells are then compared with those obtained for the mono-layered stainless steel and copper cylindrical shells. Then, this work is completed by an investigation on the reduced cut-off frequencies of the A1 wave, that have been extracted for different possible values of the intermediary radius. In this part, to understand the observed phenomena, other examples of bi-layered cylindrical shells are introduced. The obtained results are analyzed and investigated.

Seismic performance of single layer steel cylindrical lattice shells

This paper examines the elastic and inelastic seismic behaviour of single layer steel cylindrical lattice shells. The main dynamic characteristics for this form of structure are firstly examined through a parametric assessment, which also leads to proposed expressions for estimating the fundamental period and mode of vibration. The seismic response of five typical shell configurations, representing a wide range of rise to span ratios, is then assessed within the linear elastic range under selected earthquake excitations. Particular focus is given to the relative influence of the horizontal and vertical seismic components on the internal actions. In order to provide a means for evaluating the underlying inelastic behaviour, a simple pushover approach, which is suitable for this structural form, is suggested using the forces obtained from the fundamental mode shape. The peak angle change is proposed as a damage parameter within the nonlinear analysis for characterising the inelastic global and local demands in shells of different geometries. Incremental dynamic analysis is subsequently carried out in order to evaluate the detailed nonlinear time history response. The results provide detailed insights into the influence of the horizontal and vertical excitations on the nonlinear seismic response, and illustrate the suitability of the peak angle change as an inelastic deformation measure for shells of different geometric configurations. The main findings from the linear and nonlinear assessments are highlighted within the discussions, with a view to providing guidance for performance based assessment procedures as well as simplified design approaches.

GBT-based buckling analysis of steel cylindrical shells under combinations of compression and external pressure

Abstract This paper reports the results of an investigation on the use of Generalised Beam Theory (GBT) to assess the buckling behaviour of steel cylindrical shells (pipes, tubes and pressure vessels) acted by combinations of axial compression and external lateral pressure. Initially, the derivation of an adequate GBT formulation is addressed − it (i) incorporates all the effects stemming from the presence of longitudinal and/or hoop stresses (the latter act in the circumferential direction), and (ii) takes into account the destabilising influence associated with the follower nature of the external pressure, which remains normal to the shell wall along the deformation process. Then, after numerically implementing the above formulation, by means of GBT-based beam finite elements, its application and capabilities are illustrated through the presentation and discussion of numerical results concerning the buckling behaviour of (i) pressure vessels and pipes acted by external pressure and (ii) tubes subjected to combinations of compression and external pressure. For validation purposes, most GBT results are compared with values either available in the literature or yielded by A nsys shell finite element analyses .

Nonlinear Buckling Analysis of Steel Cylindrical Shell with Elliptical Cut-out Subjected to Longitudinal Compressive Load

The current paper investigates the effect of cut-out design parameters on load-bearing capacity and buckling behaviour of steel cylindrical shell using a nonlinear finite element analysis in modelling cylinder buckling under longitudinal compressive load. The effect of four geometry design parameters: shell diameter to thickness ratio, cut-out location, orientation, and size were investigated in this study. To enhance the prediction of buckling behaviour, both geometrical and material nonlinearities were considered. An ANSYS APDL code was written and tested by verifying its validity through comparison with former buckling study. The results showed that changing the cut-out location from mid-height of the cylindrical shell towards a fixed edge caused an increase in the buckling load value. Moreover, the study showed that increasing parameters such as shell thickness and cut-out orientation have a positive influence in which the buckling load value increased too. For fast design purposes, an empirical numerical based regression formula was presented for the calculation of the critical buckling load of a cylindrical shell having an elliptical cut-out.

Deformation Phenomena in the Collapse of Metallic Cylindrical Shells. Buckling

The structural mechanisms of buckling and the deformation behavior of copper and steel cylindrical shells (pipes) during collapse under the action of an explosion are studied. The dependence of deformation behavior on the transverse dimensions of the shell and properties of the loaded material is described. It is established that the stability of radial collapse depends on absolute dimensions of the shell rather than relative dimensions, with the collapse of large-diameter shells occurring more stably. It is demonstrated that the collapse stability is violated due to the formation of a characteristic pattern of localized strain in the sample, consisting of homogeneous, orderly arranged structural elements whose dimension depends little on the material properties and experimental conditions. A criterion for stable radial collapse that relates the characteristic dimensions of the structural element of localized strain and the shell radius is proposed.

Buckling strength of thin-walled steel cylindrical shells with stiffened plates

Thin-walled steel shell members are structurally superior as structural members. However, the thin-walled steel shell with stiffeners has been only studied in a part by reason of excelling dynamically on ordinary thin-walled shell without stiffeners. In this paper an investigation in regard of the increase of the buckling capacity on steel cylindrical shells with out- and inside stiffened plates is generated under pure axial compression. Then, so as to clarify the effect of the buckling capacity on thin-walled steel cylindrical shells with out- and inside stiffened plates, exact buckling strength and buckling mode shapes are generated by using the extended transfer matrix method. The buckling strength of cylindrical shell with out- and inside stiffened plates are obtained during the combination of half wave number (n) for perpendicular direction to axis and half wave number (m) for axis direction. Depending on circumstances, the local buckling strength of thin-walled shells with stiffened plates is sometimes failing by local buckling of stiffened plate to differ from local buckling of shell-panel in comparison with that of ordinary thin-walled shells without stiffener. Therefore, this study aims to plan increase of the local buckling capacity on the thin-walled steel cylindrical shells with out- and inside stiffened plates due to pure axial compression.

Instability of thin steel cylindrical shells under bending

Bending of steel cylindrical shells is generally characterized by the interaction among ovalization, bifurcation, and material plasticity when the slenderness of the shell is relatively low. It is a nonlinear phenomenon, which is dictated by buckling-sensitivity of the shells to imperfections. The behavior of cylindrical shells under bending and its imperfection sensitivity have not been yet fully understood for all the range of dimensions. This study investigates the buckling behavior and imperfection sensitivity of thin steel cylindrical shells under pure bending, focusing on a specific range of slendernesses, which are commonly found in energy structures such as tall wind turbine towers (60<R/t<120). The inelastic localized buckling instability is studied using computational methods to assess the critical load of the thin steel cylindrical shells. One of the main goals is to predictively describe the buckling sensitivity of the shells and to the provide relationships between the knockdown factor and geometric imperfections. In addition, an extensive study has been done to investigate the impact of steel strain-hardening models on the bending behavior. Four types of plasticity models are utilized to observe the effect of strain-hardening models on the bending behavior and imperfection sensitivity of the thin steel cylindrical shells: a bilinear and three versions of the Ramberg-Osgood plasticity model.

Fibre reinforced polymer for strengthening cylindrical metal shells against elephant’s foot buckling: An elasto-plastic analysis

This article describes the use of fibre reinforced polymer composites to increase the strength of an isotropic metallic cylindrical shell against elephant’s foot buckling. This form of buckling occurs when a cylindrical shell structure is subjected to high internal pressure together with an axial force, such as those that may occur in tanks and silos. It is particularly relevant to tanks under seismic action. Although fibre reinforced polymer composites have been widely applied to different types of structures under several loading conditions, its use to strengthen thin steel cylindrical shells has been very limited. Here, a non-linear elasto-plastic finite element idealisation is used to explore the strengthening effect of a fibre reinforced polymer strip on a thin cylinder. The optimum size and position of the fibre reinforced polymer sheet were obtained and empirically formulated. This study has shown that the strength after repair is sensitive to minor changes in the fibre reinforced polymer parameters so that a close adherence to the optimum parameter values is very desirable.

Bearing Capacity and Deformability of Three-Component Steel Reinforced Concrete Constructions Made of Lightweight Concrete

The article contains the study of strength and deformability of three-component steel-reinforced concrete structures made of a thin-walled steel shell, light concrete and rigid reinforcement in the form of a light steel thin-walled profile. The results of calculation, simulation and experimental researches of more than 40 steel-concrete elements are presented. The diagrams of the work of these constructions are compared with the comparison of experimental data and numerical modeling, which confirm the correctness of the introduction of the calculation model into the software complex, where special attention was paid to the boundary conditions of the work of the structure. The model with the indication of the concentration of internal stresses and the nature of the deformation of the structure in general, which fully corresponded to the experimental research, was analyzed. An adapted calculation algorithm for three-component steel-concrete constructions is presented, where the coefficients of working conditions for each of the constituent constructions are indicated. The relationship between relative flexibility and the lowering coefficient of operation of a thin-walled cylindrical steel shell is shown. Appropriate conclusions are formulated.  Â

Design of axially loaded isotropic cylindrical shells using multiple perturbation load approach – Simulation and validation

Thin-walled cylindrical shells subjected to axial load are prone to buckling and very sensitive to the geometric imperfections. In order to determine a rational design load for axially loaded cylindrical shells, different analytical and numerical design methods have been developed. As an extension of single perturbation load approach (SPLA), multiple perturbation load approach (MPLA) is a promising method but has not been thoroughly studied. In this paper, the buckling tests of three steel cylindrical shell specimens are conducted. Combined with experimental and numerical results, the advantages and limitations of several commonly used design methods are discussed in detail, including NASA SP-8007, the measured imperfection approach, SPLA and MPLA. The results validate that SPLA is indeed risky to be adopted as a design method for isotropic metallic cylindrical shells. Meanwhile, it indicates that MPLA can not only improve the knock-down factor but also give a more safe design load than SPLA. The comprehensive numerical investigations are performed to study the effects of each perturbation load parameter on MPLA, including the number of perturbation loads, their relative position and magnitude. It is found that the symmetry of perturbation loads plays an important role in the global buckling load of cylindrical shell. Moreover, some guidance for the future application of MPLA is provided and the four perturbation load approach (4PLA) is proposed as an improved method for the preliminary design of isotropic metallic cylindrical shells.

Indentation of the cylindrical shell in the elastoplastic half-space

The article deals with the problem of pressing the steel cylindrical shell into the elastoplastic half-space having a cylindrical concavity. The calculation and analysis of the stress-strain state of the steel shell and elastoplastic half-space. Given the dependence of the shear half-space, the safety factor and stress state in steel shell from the force pushing the shell in the half-space. The calculations were carried out for three radii of concavities and two types of half-space materials. It was assumed that the elastoplastic half-space obeys the Mohr-Coulomb fracture criterion.

Ultimate Strength of 10 MW Wind Turbine Tower Considering Opening, Stiffener, and Initial Imperfection

This paper evaluates the effects of door opening, collar stiffener, and initial imperfection on the ultimate strength of a 10 MW wind tower. The lower segment of the tower was modeled to investigate the ultimate strength using steel cylindrical shell elements of finite element program ABAQUS. The wind tower was classified into three categories; without opening nor stiffener (C1), with opening but no stiffener (C2), and with opening and stiffener (C3). The C2 and C3 were further divided into long axis and short axis categories depending on the position of the opening. Result from linear and nonlinear analyses shows that the bigger the opening the bigger the reduction in strength and the same thing goes for the initial imperfection ratio or ovality of the shell. Also, there is a significant decreased in strength as the initial imperfection ratio increases by as high as 18.08%.

Determining the crack acceptability in the welded joints of a wind loaded cylindrical steel shell structure

Abstract Engineering critical assessment can be considered as a mandatory request in the civil engineering designing and manufacturing process. The paper is presenting the procedure for determination of crack acceptability based on fracture toughness with failure assessment methods (FAD-1 and FAD-2) which is applied to a cylindrical steel shell structure with welded joints which is having the wind as the main load [7]. The stresses in the structure were determined based on a structural analysis. According to [3] an in depth finite element analysis was applied to the segment joint of the steel shell element (pillar), thus revealing the stresses in the joint (as well in the welded joints). There were assessed common types of flaws met at steel shell cylindrical structure elements using failure assessment diagrams – level 1 – FAD-1. The results are presenting the acceptability level for each type of flaw with comparative graphs, determining also the critical dimension of the flaw. For each flaw was calculated the failure assessment diagram level 2 (FAD-2). Comparisons between groups of flaws were done, revealing the critical crack like flaw. Also the critical values of flaw dimensions were calculated for each flaw type [7]. The methodology establishes clear rules for assessment of structural elements with cracks, determining the initial flaws, assessed flaws and critical values of the cracks. The conclusion of the research reveals the fracture resistance failure susceptibility of different parts of the segment joint given an existing discovered flaw. Based on the detailed procedures described in the paper, on conclusions to the assessment done on each type of flaw, the method can be applied from the design phase on these types of structure elements.

Buckling of externally pressurized cylindrical shell: A comparison of theoretical and experimental data

This study examined the buckling of unstiffened cylindrical shells under external pressure. Six stainless steel cylindrical shell specimens were tested, with a length-to-radius ratio, L/R, ranging from 1 to 7. The wall thickness, diameter, axial length, and geometry of each specimen and the material properties of the corresponding sheets were measured. All cylindrical specimens were subjected to external pressure in a pressure chamber; the buckling load and final collapsed mode were recorded. This paper presents a comparison among theoretical calculations, finite element (FE) results, and experimental data for externally pressurized cylindrical shells. In the numerical calculations, true geometry, average wall thicknesses, and elastic–perfectly plastic modeling were considered. Deviation between theoretical and FE results was 0%to − 22%, and it increased with the length-to-radius ratio. Experimental results are consistent with FE results, with deviation of 2–9%, and final collapsed modes of all shells are consistent.

Experimental studies on the deformation and damage of steel cylindrical shells subjected to double-explosion loadings

Metal cylindrical shells with different wall thicknesses were subjected to double explosion detonated at varying stand-off distances. For comparison, single-explosion tests were conducted under the same conditions as those in the second explosion of the double- explosion tests. Five different types of failure modes were observed. Here, the energy distribution of the different failure modes is discussed. The effects of the double-explosion impact, the stand-off distance, and the wall thickness of the cylindrical shell on the deformation and damage of the metal cylindrical shells were investigated. The results indicated that the deformed cylindrical shells which were impacted by the first blast absorbed more energy under a given explosion load than the undamaged shells under the same explosion load according to the energy absorption theory. Vickers hardness tests presented a noticeable increase in the hardness of the cylindrical shell at the plastic hinge region and the central region with the number of witnessed blast loads increased. The stand-off distance and the wall thickness significantly influenced the failure mode and the energy absorption and distribution of the cylindrical shells under double-explosion loadings. The severity of the damage observed in the cylindrical shell increased with a decreasing stand-off distance. Moreover, when the cylindrical shell further deformed from local plastic deformation to crack, the local plastic deformation zone was decreased abruptly. The ability of the cylindrical shell to resist double explosions was enhanced by increasing the wall thickness because thicker shells have more energy absorption capacity and higher threshold for damage than thinner shells. Under the same explosive load, of which the energy has not reached the damage threshold of the cylindrical shell, the energy absorption of the cylindrical shell and the magnitude of the energy reduction both decreased when the wall thickness of the cylindrical shell increased in equal increments. Under the presented experimental conditions, the cylindrical shell first cracked along the radial direction.

Mid-Explosion Recovery of an Intermediate Phase of a Cylindrical Metal Shell

To understand the complex dynamic response of cylindrical metal shells under highstrain-rate loading, a mid-explosion recovery device is designed to recover cylindrical shells at an intermediary phase, chosen in this study to be the phase wherein cracks penetrate through the entire casing wall thickness. The surface dynamic processes of the expansion, fracture propagation, and rupture of a 40CrMnSiB steel cylindrical shell are measured with a high-speed framing camera for determining the appropriate inner diameter of the mid-explosion recovery device. The numerical simulation software Autodyn-3D is used to predict the influence of the device wall thickness and the maximum radial deformation of the device inner wall upon the outer fracture diameter of the casing. The casing at the desired phase is recovered by the device, and the outer diameter of the shell is found to increase by 1.77 times, while the radial deformation of the device is 5 mm. The crack distributions, the distance between the adjacent penetrating shear cracks, and the number of circumferential divisions are found to vary along the axis of the cylindrical casing.