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The collapsible tubular mast (CTM) can be compactly folded for transport and deployed in orbit to serve as a key structural element. Once deployed, the CTM is vulnerable to buckling under axial load and bending moments, compromising its load-bearing capacity. The intricate relationship between the CTM's cross-section and its buckling behavior poses a significant challenge for designers. This is due to the ultra-thin nature of the CTM, which gives rise to highly localized buckling modes rather than global ones. To overcome this challenge, we developed surrogate models using a neural network (NN) trained with data from finite element analysis (FEA). These NN-based surrogate models provide high computational accuracy in predicting nonlinear buckling loads under axial force and bending moments around the two principal axes of the CTM's cross-section, achieving R 2 values of 0.9906 , 0.9987 , and 0.9628 , respectively. These models also significantly improve computational efficiency, reducing prediction time to a fraction of a second compared to several minutes with FEA. Furthermore, the NN-based surrogate models enable the usage of the non-dominated sorting genetic algorithm (NSGA-II) for multi-objective optimization (MOO) of the CTMs. These models can be integrated in the NSGA-II algorithm to evaluate the objective function of existing and new individuals until a set of 1000 non-dominated solutions, i.e., cross-sectional configurations optimizing buckling performance, is identified. The proposed approach enables the design of ultra-thin CTMs with optimized stability and structural integrity by promoting design decisions based on the quantitative information provided by the NN-based surrogate models. [ABSTRACT FROM AUTHOR]

This paper conducts the analytical investigation on the buckling of cylindrical shells with axially variable elastic modulus subjected to axial compressive load for the first time. First, it proves that the axially distributed elastic modulus can be expressed as the combination of constant and variable component. Then, governing differential equations for buckling analysis are derived and exactly solved by the combined perturbation method and Fourier analysis. Accordingly, the closed analytical solutions for the cylinder with arbitrarily variable elastic modulus are obtained, which reveal the explicit relations among buckling load, shell sizes and elastic modulus functions. Based on the presented analytical formulas, four types of elastic modulus variations for shell material which are uniform, periodic, linear and combined are studied in detail, and the results are also well verified. The derived analytical solutions in this paper can serve as benchmarks for buckling analyses of thin-walled cylinders with elastic modulus variations resulted from design, material manufacturing process, material imperfections and so on. [ABSTRACT FROM AUTHOR]

In practical engineering, a thin-walled cylindrical shell structure is more easily subjected to localized axial compression loads caused by external adjacent structures or devices. However, until now there are few studies to reveal the buckling behavior of cylindrical shells under such nonuniform loading conditions based on initial imperfection sensitivity. Therefore, buckling analysis of cylindrical shell under localized axial compression loads is investigated in this paper. Based on the buckling test, the influence of the morphology and amplitude of measured initial geometric imperfection are studied using the finite element method. Meanwhile, the inherent reason for initial geometric imperfection affecting the buckling load is elaborated. The influence of amplitude, distribution range, and different combinations of local dent imperfections are also elucidated. In addition, the effects of inclined loading imperfection and uneven shell thickness distribution imperfection are analyzed in the form of deterministic numerical simulation. Finally, a new buckling load knockdown factor that can reasonably consider the influence of loading imperfection and shell thickness variation imperfection is proposed. This work elucidates the initial imperfection sensitivity of the thin-walled cylindrical shell structures under localized axial compression load and can provide useful guidance for the buckling design and preventing buckling failure of these structures. [ABSTRACT FROM AUTHOR]

This paper aims to evaluate the seismic response of multitiered buckling-restrained braced frames (MT-BRBFs), assess the design provisions specified by the 2022 AISC Seismic Provisions for multitiered BRBFs, and propose improvements to these provisions. A set of 17 frames is first selected by varying bracing configuration, frame height, number of tiers, and tier height ratio. The frames are then designed in accordance with the 2010 and 2022 AISC Seismic Provisions. A numerical parametric study is performed under scaled ground motion accelerations. The results of the parametric study show that when the frames are designed to the 2010 provisions, the frame inelastic deformation tends to concentrate in the tier(s) undergoing tensile yielding due to their lower postyield stiffness, compared to BRBs yielding in compression, which creates unequal story shear, contributed by braces, in adjacent tiers with BRBs in tension and compression and engages column flexure to compensate for unbalanced brace story shears between tiers. Columns experience yielding and even buckling in several cases due to combined flexural and axial load demands. MT-BRBFs designed to the 2022 AISC Seismic Provisions exhibit a more uniform deformation response between tiers and relatively lower flexural demands in their columns. However, these provisions may overestimate column in-plane flexural demands (on the order of 3), resulting in potentially uneconomical design solutions. On the basis of the numerical simulations, modifications are proposed to compression BRBs' adjusted strength to better estimate column in-plane flexure and tier deformation while achieving an economical column design. The proposed improvements are validated using dynamic analyses. [ABSTRACT FROM AUTHOR]

A simplified column-buckling model is developed to understand the buckling mechanism of thin-walled strips restrained by uniform lateral pressure in the milling process. The strip is simplified as two rigid columns connected by a rotation spring, resting on a smooth surface, restrained by a uniform pressure and loaded by an axial force. Two loading cases are considered, i.e., the dead load and the follower load. Analytical solutions for the post-buckling responses of the two cases are derived based on the energy method. The minimum buckling force, Maxwell force and stability conditions for the two cases are established. It is demonstrated that the application of higher uniform pressure increases the minimum buckling force for the column and thus makes the column less likely to buckle. For the same pressure level, the dead load is found to be more effective than the follower load in suppressing the buckling of the system. The effect of initial geometric imperfection is also investigated, and the imperfection amplitude and critical restraining pressure that prevent buckling are found to be linearly related. The analytical results are validated by finite element simulations. This analytical model reveals the buckling mechanism of strips under lateral pressure restraint, which cannot be explained by the conventional bifurcation buckling theory, and provides a theoretical foundation for buckling-prevention strategies during the milling process of thin-walled strips, plates and shells commonly encountered in aerospace or automotive industries. [ABSTRACT FROM AUTHOR]

By experimental methods, 26 specimens were designed to conduct elastic and elastic–plastic buckling tests on cylindrical shells containing cracks. This study discusses the influence of factors such as the length–diameter ratio, the diameter–thickness ratio, the crack length, the inclination of the crack, etc., on the buckling load. Additionally, finite element models were established to compare with experimental results. For the PMMA cylindrical shell, the results showed that as the length–diameter ratio of the cylindrical shell increased, the buckling load first decreased and then increased. For the 6063 aluminum alloy cylindrical shell, with increasing length–diameter ratio, diameter–thickness ratio, and crack length of the cylindrical shell, the buckling load decreased accordingly. However, concerning the crack inclination, as the crack inclination increased, the buckling load increased accordingly. This indicates that the larger the crack inclination, the higher the load capacity of the cylindrical shell containing cracks. Through finite element simulations of cylindrical shells with cracks, it was found that through compressive mechanical properties, both elastic and elastic–plastic buckling loads yielded results that are closer to the experimental results. Additionally, the inclusion of contact effects in numerical simulations further improved the agreement with the experimental results, and the variation trend of the buckling load in the finite element simulation was consistent with the experimental results. The research findings provide valuable references for the assessment of load capacity in structures containing cracks. [ABSTRACT FROM AUTHOR]

The nonlinear buckling and postbuckling of functionally graded carbon nanotube reinforcement composite (FG-CNTRC) plates resting on the nonlinear effect of elastic foundation under combined load including external pressure and axial compression loads with uniformly distributed temperature rises are fully investigated in this paper. The FG-CNTRC plates are reinforced by FG-CNTRC stiffeners and the plate-foundation interaction is modeled using a nonlinear model. The higher-order shear deformation plate theory with the geometrical nonlinearities of von Kármán is applied to establish the basic formulations. Additionally, by using the anisotropic higher-order shear deformation beam theory, a new smeared stiffener technique is successfully developed for FG-CNTRC stiffeners. Galerkin's method is used to achieve the equilibrium equation system in the nonlinear algebraic forms, and the critical load and postbuckling load–deflection curve expression are explicitly determined. The numerical investigations discuss the influences of FG-CNTRC stiffeners, hardening/softening nonlinear elastic foundation, uniformly distributed temperature rises, geometrical and material features on nonlinear stability of stiffened FG-CNTRC plates. [ABSTRACT FROM AUTHOR]

In the process of horizontal well construction, the working environment in the well is very complicated. It is difficult to determine the actual deformation and force of the coiled tubing in the wellbore from the load change at the wellhead along. In addition, the coiled tubing wrapped around the reel and entering the wellbore through the injection head may cause an initial residual bending. In this paper, the mathematical model of the coiled tubing under axial load during buckling deformation is established, and the analytical solution with the time term is derived by reasonable simplification of the model. The effect of residual bending on the post-sinusoidal buckling of the coiled tubing in the horizontal well was investigated using the separation variable method. The effect of residual bending variations on the well wall contact forces is analyzed. The research shows that the initial parameter Г is the main factor influencing the post-sinusoidal buckling of the coiled tubing with residual bending. The larger the parameter value Г, the greater the effect of the residual bending on the post-sinusoidal buckling deformation of the coiled tubing, and the earlier the critical point of the mixed sinusoidal-helical buckling of the coiled tubing appears. The compression velocity of the coiled tubing has a significant effect on the well wall contact force. The faster the compression, the greater the contact force. By introducing the time term and the separation variable, this paper provides a new method and theoretical basis for further study of the process of entering sinusoidal-helical buckling of the coiled tubing with initial residual bending. [ABSTRACT FROM AUTHOR]

The present investigation has analyzed the buckling of bi-directional functionally graded conical micro-shells bearing axial loading. The dominant equations serve on the basis of the theory of first-order shear deformation in the modified couple stress theory (MCST). The Ritz technique is used so as to solve the governing equations. Bi-directional functionally graded material is the material used to construct the shell, and in a predefined composition profile, the volume fractions pertaining to the constituent materials constantly vary through the conical edge directions and thickness. The model predictions are compared and successfully validated using the ones available in the literature. According to the results, in comparison with the classical theory, the micro-shell buckling load is higher in the MCST. In addition, the contribution of a number of geometrical and mechanical parameters, for example, radius-to-thickness ratio, thickness-to-length scale ratio, length-to-radius ratio, semi-vertex angle, homogenization schemes, and material gradient indexes, to the buckling performance of conical micro-shells has been investigated. It is noteworthy that this investigation is the first effort to present a buckling analysis for the purpose of bi-directional functionally graded truncated conical micro-shells in accordance with the MCST. [ABSTRACT FROM AUTHOR]

This article analyses static buckling of the so-called Gao beam nonlinear model. It considers pure buckling problems in which the vertical loads are omitted. The analysis, using minimisation of energy and the concept of a modified Rayleigh quotient, leads to new results regarding the critical load necessary for buckling, and the existence and number of post-buckling solutions. Computational results are provided for cases with fixed axial loading. Furthermore, the authors explore the impact of the system parameters on the solutions, which are summarised in a table. The new findings in this research are unique and help to better understand the behaviour of the static and dynamic Gao beam. [ABSTRACT FROM AUTHOR]

Geometric imperfections are understood to play an essential part in the buckling of a thin shell, but how multiple defects interact to control the onset of failure remains unclear. Here, we examine the failure of real cylindrical shells by experimentally poking soda cans with a large imparted dimple. By high-speed imaging of the can's surface, the initiation of buckling from axial loading is directly observed, revealing that larger dimples tend to set the initial buckling location. However, the influence of the shell's background geometric imperfections can still occasionally dominate, causing initiation to occur far from the dimple. In this situation, probing at the dimple leads to an over-prediction of the axial capacity. Using finite-element simulations, we understand our experimental results as a competition between the large dimple and the shell's inherent defect structure. In our simulations, we empirically observe a deformation-based criterion that connects the ideal poking location to the initiation site. This article is part of the theme issue 'Probing and dynamics of shock sensitive shells'. [ABSTRACT FROM AUTHOR]

Buckling analysis of functionally graded piezoelectric nanoshell is studied in this paper based on the higher-order shear and normal deformation theory and accounting thickness stretching effect. The nanoshell is subjected to axial load, applied electric potential and thermal loads. Thickness stretching effect is accounted in the analysis based on higher-order shear and normal deformation theory. Small scale effects are accounted based on the Eringen nonlocal elasticity theory. The Navier solution is used for the buckling analysis of the cylindrical nanoshell with simply-supported boundary conditions. The accuracy and trueness of the present paper is justified using comparison with literature. The importance of the present analysis and corresponding results is justified using presentation of results with and without thickness stretching effect. A large parametric analysis is presented to investigate the influence of significant parameters such as dimensionless small scale parameter, length to radius ratio, thickness to radius ratio, temperature rising and applied electric voltage on critical buckling axial loads. One can conclude that the critical buckling axial loads are decreased with increase of small scale parameters and applied electric potential. [ABSTRACT FROM AUTHOR]

Buckling of slender members due to gravity loading or thermal effects is influenced by the member's geometric imperfections, boundary conditions, and intermediate lateral supports. When assessing the capacity of such members, these parameters are often unknown (e.g., the rotational stiffness of end connections in a truss or the lateral support provided by the ties to a rail track), and conservative assumptions must be made resulting in conservative assessments. Distributed fiber optic sensors (DFOS) can potentially be used to determine these parameters with greater accuracy using strain measurements along the length of a member. A series of buckling experiments was conducted on a slender member instrumented with DFOS subjected to axial load with varying levels of lateral restraint or to increasing temperature. The distributed strain data were then used to evaluate the geometric imperfections, boundary conditions, and lateral support stiffness. These inputs were used to create a finite-element model to estimate the ultimate load response of the member using data acquired at service loads. [ABSTRACT FROM AUTHOR]

A thin-walled steel cylindrical shell is a common engineering structure that has an efficient load-carrying capacity. This structure is more easily subjected to partial axial compression loads in application, and buckling is the main failure mode. However, there are few available design methods for partial axially compressed steel cylindrical shells. Motivated by this, a design method called the localized perturbation load approach (LPLA) is proposed in this paper. The finite element framework for the application of LPLA is established. The location and number of perturbation loads are determined by considering the imperfection sensitivity and the buckling failure mode of partial axial compressed cylinders. A series of buckling experiments are carried out to validate the LPLA method. In addition, the reliability of LPLA for the design of cylindrical shells with different imperfection locations and dimensions is also verified. The results show that LPLA can give conservative and reliable lower-bound buckling loads. Therefore, LPLA can be used as a design method for thin-walled steel cylindrical shell structures under partial axial compression in actual engineering. [ABSTRACT FROM AUTHOR]

Thin-walled cylindrical shells under axial compression load are prone to buckling. The influencing factors leading to a reduction of the buckling load are a major design challenge. The sensitivity to imperfection increases with rising slenderness. In literature, cylinders with the same parameters and different slenderness are rarely tested in a larger number of samples. In this contribution, seven cylindrical shells, six of them nominally identical, are tested on two different test rigs and compared with twelve specimens with a smaller radius and same wall thickness from a previous series of tests. It is shown how the imperfection sensitivity is dependent on the R/t-ratio. Additionally, it is demonstrated how the quality of the test set ups corresponds with the achieved buckling load. Finally, the suitability of selected design approaches is determined based on the test results. Based on that, recommendations for the choice of a suitable approach are given. [ABSTRACT FROM AUTHOR]

In high-pressure and high-temperature gas wells, tubing string buckling behavior is a significant engineering problem to be addressed. To solve this problem, a finite element model of tubing string buckling with geometric nonlinearity and contact nonlinearity is established, and the buckling behavior of tubing string in the whole wellbore section is simulated. The effects of axial compression, connector and wellbore diameter on tubing string buckling are studied. It is found that a variety of complex buckling forms may co-exist in the same wellbore and that with the increase of axial compression load, the lateral displacement of tubing string increases gradually, and the buckling state of tubing string gradually intensifies. Under the same axial compression load, buckling is relieved when the effect of the connector is considered, indicating that the connector has the effect of delaying the buckling and promoting the transfer of axial force. Wellbore diameter has a great influence on the buckling critical load and the buckling behavior of tubing string. The work presented in this paper can provide a technological basis for tubing string buckling behavior analysis in high pressure and high temperature gas wells. [ABSTRACT FROM AUTHOR]

Double-beam systems have found many applications in civil and mechanical engineering. Extensive works of research have been conducted on the investigation of double-beam systems in which some have studied the vibration characteristics of general double-beam systems without considering the effect of axial load, whereas others investigated the vibration and buckling of axially loaded double-beam systems with classical boundary conditions. A few previous studies have considered a general axially loaded double-beam system, but none of them have provided a general solution to calculate the critical buckling load of the system with arbitrary boundary conditions. In the present study, free vibration and buckling of an axially loaded double-beam system, which was composed of two nonidentical beams with generalized boundary conditions, were analytically studied by using the Euler–Bernoulli beam theory. A semianalytical method was proposed to calculate the natural frequencies and mode shapes of the system, and an explicit formula was derived to determine the critical buckling load of the system. Parametric investigations were performed to study the influences of the connecting stiffness of the interlayer and axial loads on the dynamic characteristics and critical buckling load of the system. Results show that the proposed method can be used for free vibration and buckling analyses of generalized double-beam systems subjected to axial loads. [ABSTRACT FROM AUTHOR]

The buckling of new three‐phase composite shells, which include the base material combined with macro fiber composite and reinforced with graphene (MFC‐GP), is investigated in this article. The bifurcation condition of the buckling is obtained by implementing the first‐order shell theory and wave propagation theory in conjunction with the principle of minimum potential energy. The buckling analysis is transformed into a bifurcation problem of equations. Parametric study is conducted to investigate the effects of the GP volume fraction, length, neutral surface radius, and thickness on the critical buckling loads and critical buckling modes. Furthermore, the influences of voltage and temperature change on the critical buckling displacements are explored. Reliable theoretical support for the design and manufacture of the MFC‐GP structures is provided in the results. [ABSTRACT FROM AUTHOR]

Rectangular concrete-filled steel tubular (RCFST) columns can be designed to have unequal wall thickness to maximize their resistance to combined axial and uniaxial bending loads. However, there is very little published research on their local–global interaction buckling behavior. This paper presents an efficient fiber-based simulation model for analyzing the inelastic interaction buckling of eccentrically loaded RCFST slender columns with unequal wall thickness. The model considers the progressive local–global interaction buckling, distributed plasticity, concrete cracking and crushing, second-order effects, and geometric imperfections. The mathematical model is programmed to compute not only the axial load–displacement responses but also the interaction curves of axial load and moment of slender RCFST columns. The simulation modeling is validated by experimentally measured data. The validated computer model is used to parametrically study the interaction local–global buckling responses of RCFST columns while the range analysis is conducted to identify the relative significance of key parameters. It is demonstrated that the proposed computer model accurately simulates experimentally measured responses. Hence, it can be used with confidence in practice to analyze and design RCFST slender columns fabricated with steel plates of unequal thickness. The existing design standard AS/NZS 2327:2017 provides acceptable strength predictions of RCFST slender columns and beam-columns while the procedure specified in Eurocode 4 overestimates their capacities. [ABSTRACT FROM AUTHOR]

Concrete encasements are usually utilized to protect bridge above-ground piles from corrosion. These concrete encasements are usually square or round shapes reinforced by longitudinal rebars. However, the contributions of concrete encasements are not considered in traditional pile design procedures. On the other hand, rating engineers need to have realistic evaluations of the piles to estimate the capacity of the foundation for scour-critical bridges. Underestimation and overestimation of pile capacity can result in either potential bridge failure or uneconomical assessment. The objective of this paper is to investigate the effect of concrete encasement on pile buckling behavior subject to concentric load. To achieve this objective, four full-scale concrete encased pile specimens with various pile and concrete encasement lengths were fabricated and tested with concentric axial loading to measure the specimen ultimate capacity. In addition, the finite-element (FE) approach was utilized to simulate the buckling behavior and predict the ultimate capacities of the lab-tested specimens. The developed FE models were validated against the laboratory test data. Finally, the validated FE models were utilized in the parametric study to investigate the effect of the length and shape of the concrete encasement on the ultimate capacities of the steel H-piles. The results indicated that the concrete encasement could increase the buckling load of the pile, and ignoring the effect of the concrete encasement, as with the use of the equations suggested by the AISC, could result in a significantly underestimated prediction. It was also found that the concrete encasement increases the initial axial stiffness of the pile before the buckling load is achieved. [ABSTRACT FROM AUTHOR]

The mechanical post-buckling behaviour of variable stiffness layered composite beams reinforced by curvilinear fibres subjected to compressive loads is investigated here using a sine function-based shear flexible beam model. The neutral axis stretching force stemming from the axial movement restraints is accounted for through von Karman's assumption based geometrical nonlinearity. Furthermore, the modified beam constitutive equation arising from the consideration of the Poisson's effect is introduced in the formulation for the laminated beam analysis with general lay-up or ply sequences. The governing equations incorporating the incremental stiffness matrices are formed through the minimization of total potential energy principle and are solved by numerical method. The solutions for the developed governing equations are evaluated iteratively based on eigenvalue analysis and the characteristics of post-buckling of laminated beams can be inferred through the relationship between the beam deflection level and post-buckling axial load. An in-depth analysis selecting many design parameters for instance lamina's curvilinear fibre angles, beam slenderness ratio, lay-up and edge conditions, load type and so on is dealt with in bringing out the behaviour of variable stiffness laminated beam in linear and post-buckling regions. Also, the influence of flexible end supports by restraining elastically against ends rotation is studied on the beam elastic stability behaviour. [ABSTRACT FROM AUTHOR]

The buckling behaviors of drill string may cause serious down-hole problems, such as high friction during drilling, loss of weight on bit (WOB), and even drill string failure. This paper analyzes the dynamic buckling characteristics of drill string, considering the friction between drill string and wellbore. In the theoretical research, the key parameter expressions are determined, especially the contact behaviors of drill string and mathematical models are proposed, which include axial displacement, angular displacement and contact force. The numerical calculation results show that the influence of friction on the drill string buckling is mainly reflected in angular displacement. The influences of friction effect on the dynamic characteristics of drill string become greater with the increase of inclination angle, while become lower with the increase of drill string length. The friction effect appears to have insignificant influence on drill string condition with the accumulation of time. The comparison results indicate that the friction affects the action of axial load on drill string and delays the onset of buckling. On the other hand, the angular displacements decrease with drill string length increasing, while the axial displacements have an opposite effect. The research results provide theoretical references for studying dynamic buckling characteristics; furthermore, we can determine the methods and solutions to prevent drill string buckling based on this, and improve the safety of downhole drilling. [ABSTRACT FROM AUTHOR]

In this paper, a new buckling-controlled member (BCM) is introduced for use in space structures. This member is composed of four components; namely: the encasing, joints, core, and adjustable nuts. The core is intended to act as a structural element to resist the axial loads by its yielding under compression loading. The steel encasing is supposed to confine the steel core. Adjustable steel nuts on the steel core act as lateral bracings and are responsible for lateral load transmission between the encasing and core. The joints at the two ends of the supports of the member. Six experimental tests have been performed under compression load to show the efficiency of the new member. The test results reveal that the proposed member can provide the needed ductility and can delay the brittle buckling of the members. Also, the BCM is capable of considering buckling modes and controlling the plastic range. The experimental and numerical results have also been compared. Additional numerical evaluations have been carried out using finite element models, in which the effects of different parameters of the member have been investigated. The obtained results showed that the arrangement of inner elements is the main factor affecting ductility and postponing the buckling of the members. In the end, the effects of the BCMs on the overall behavior of four double-layer space structures have been studied. The obtained results of analyses indicated that the BCMs can enhance the strength and ductility of space structures, thereby reducing the risk of collapse. Also, the seismic collapse of the space structure was postponed. [ABSTRACT FROM AUTHOR]

Defects/imperfections can occur during manufacturing, assembly, welding, and other processes, which can reduce the critical buckling load. However, the axial buckling load is beyond the scope of this work, and there are many studies on the stiffening effect of longitudinal dents. This concept combined the idea of the dent-to-stiffener evaluation concept for thin-walled steel cylinders. This study aims to transform the dents into artificial dents for a stiffening effect on the buckling phenomena. For this purpose, 37 thin-walled steel cylinder models, including the perfect model, were designed for varying dent shapes, dent widths, dent depths, dent lengths, and dent angles. The study also contributed to the effect of dent parameters on the critical buckling load of thin-walled steel cylinders. In particular, increasing the initial buckling will motivate the industry to convert dents into stiffeners with small artificial touches to enhance the longevity of the structure. The results showed that the introduction of certain artificial dents can significantly increase the critical buckling load of cylinders, thus improving their resistance against buckling, which has significant implications for various industries that use thin-walled steel cylinders in their structures. The proposed simulations for transforming dents into artificial stiffeners can be a valuable tool for enhancing the longevity and safety of thin-walled steel cylinders and other structures. [ABSTRACT FROM AUTHOR]

The purpose of this research was the analysis of the stability of compressed thin-walled composite columns with closed rectangular cross-sections, subjected to axial load. The test specimens (made of carbon–epoxy composite) were characterized by different lay-ups of the composite material. Experimental tests were carried out using a universal testing machine and other interdisciplinary testing techniques, such as an optical strain measurement system. Simultaneously with the experimental studies, numerical simulations were carried out using the finite element method. In the case of FEA simulations, original numerical models were derived. In the case of both experimental research and FEM simulations, an in-depth investigation of buckling states was carried out. The measurable effect of the research was to determine both the influence of the cross-sectional shape and the lay-up of the composite layers on the stability of the structure. The novelty of the present paper is the use of interdisciplinary research techniques in order to determine the critical state of compressed thin-walled composite structures with closed sections. An additional novelty is the object of study itself—that is, thin-walled composite columns with closed sections. [ABSTRACT FROM AUTHOR]

Composite cylindrical shells play a crucial role in aerospace and marine structures. This study investigates the optimal structure for cylindrical multilayer composite shells under the effect of axial pressure using the finite element method and NSGA-II genetic algorithm to determine the maximum buckling load capacity. The critical buckling load of multilayer composite shells depends on various parameters, such as fiber angle, the number of layers, the material of the layers, and their thickness. The objective functions are used to increase the structure load capacity and reduce its weight. ABAQUS software was used to perform finite element analysis on the composite cylindrical shell for determining the buckling load. Using the response surface model, the relationship between variables and objective functions has been determined. Results of the proposed response surface model for the training stages are evaluated using various statistical indices and the root mean square error for buckling load and shell weight variables is 0.065 and 0.140, respectively. In the next step, the NSGA-II genetic optimization algorithm was used to modify the layout and thickness of the composite layers to optimize the buckling strength and weight of the structure. A genetic algorithm based on NSGA-II was used to optimize the geometric characteristics. [ABSTRACT FROM AUTHOR]

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Considering the practical conditions, it has been observed that the support structures of wind turbines inevitably experience bending and axial compression, both during the installation phase and throughout their operational lifespan. The monopile is the most commonly utilized support structure for offshore applications and a reliable method for creating a detachable section within these structures is using a Pile-in-Pile (PIP) slip joint. Consequently, the behavior of PIP slip joints, under combined axial compression and bending, has been meticulously investigated. To facilitate a thorough analysis, overlapping lengths proportional to the pile diameters have been used, encompassing three distinct variations. This approach allows for a comprehensive understanding of structural integrity and performance under varying stress conditions, which are comprehensively understood and accounted for in design considerations. The current study builds upon assessing the pure bending characteristics of slip joints in cylindrical hollow section (CHS) structures. Additionally, two ring stoppers have been strategically employed inside the piles to withstand the axial load. Furthermore, the complexity of the pressure acting in the overlapping length, attributed to the frictional coefficient in that region, has been carefully addressed. The current research also encompasses a comprehensive overview of the P-M envelopes for the existing arrangements, with a particular focus on non-linear buckling, which is known to significantly influence the performance of tubular structures. Finally, a design equation was introduced to concisely describe the behavior of the components and compare it with other design equations provided by an established code. [ABSTRACT FROM AUTHOR]

This paper analytically studies the buckling of a cylindrical shell having varying thickness under non-uniform axial compressive loads for the first time, which widely exists in engineering practice. A novel quadratic perturbation technique is developed to establish general buckling load formulas for the shell. This method overcomes the difficulties of traditional energy methods in solving high order determinants and deriving direct expressions for buckling loads when shell thickness and axial load are unknown. Applying presented formulas, various shell thicknesses and axial loads are analyzed, and a series of new results for buckling loads are obtained and validated. Even for classical cosine thickness variation under uniform axial compression, we also give general conclusions compared with Koiter's results by the energy method. The effects of thickness variations and load distribution parameters on buckling loads are analyzed in detail. The presented study in this paper fills the gap and establishes a foundation of buckling analysis for non-uniformly loading cylindrical shells with variable thickness. Certainly, the established formulas are general and available for buckling resistance capacity evaluation for the shells under all circumstances involving thickness variations or/and non-uniform axial compressive loads. [ABSTRACT FROM AUTHOR]

In this paper, a set of partial differential equations considering the dynamic effects of the coiled tubing (CT) is established based on the bending theory of slender beams considering the axial loads. The analytical solution of sinusoidal deformation with the time term is obtained. The critical load of coiled tubing during sinusoidal buckling and the change of half-wave number during sinusoidal post-buckling are studied through the introduction of the necessary conditions, solution and the separation constant. The contact force of coiled tubing with sinusoidal post-buckling on the horizontal well wall is analyzed. The results show that the critical load for sinusoidal buckling of fixed-size CT is related to the section angular acceleration coefficient. The half-wave number produced by the sinusoidal post-buckling bending of the CT gradually decreases during compression. The contact force of the deformed CT to the borehole wall is related to the compression speed of the CT. By introducing the dynamic term and the separation constant, this research model can provide a theoretical basis for studying the transformation of the CT from sinusoidal buckling to helical buckling. [ABSTRACT FROM AUTHOR]

This paper presents an improved design approach based on the direct strength method (DSM) in American Iron and Steel Institute (AISI) design specification S100 for cold-formed steel (CFS) built-up closed cross-section columns subjected to local, global, and local–global interaction buckling modes. Initially, the failure mode and load data corresponding to various design parameters such as intermediate fastener connection spacing, boundary conditions, material properties, slenderness, and cross sections from various researchers are collected, including the authors' test results. The design predictions using the current DSM design provisions are compared with the collected test results. The results show that the current DSM approach requires improvisation to adequately predict the axial compression load. The data are then analyzed to understand the behavioral features of the built-up closed cross-section column such as limit for interaction buckling, erosion of strength due to arrant interaction buckling, and increase in strength due to flange or web overlapping effect. The interpretation methods used to improve the current design approach are presented. The original DSM design procedure is improved by failure mode classification and modified slenderness to account for increase and erosion in strength. Finally, the safety (accuracy and reliability) of the design predictions from the improved DSM-based approach is assessed using the large amount of data collected. Since the introduction of the direct strength method to the North American Specification for the Design of Cold-Formed Steel Structural Members (AISI S100) in 2001, it has gained traction among design engineers due to its simplicity, advantages over other design methods, and specific design curves for individual buckling modes. To implement the DSM for CFS built-up members, several researchers have proposed different design approaches, and research is still happening. This study is also aimed toward the same objective but is specific to the local–global interaction in built-up members. It is demonstrated why the DSM prediction is unsafe for CFS built-up members with larger intermediate fastener connection spacing and excessively safe for CFS built-up members with closer intermediate fastener connection spacing. An intermediate fastener connection spacing limit that separates the local–global interaction buckling and element overlapping effect is determined. A design proposal for limiting the interaction buckling mode and considering the overlapping effect of elements in the DSM design method is suggested. More specifically, the proposed design method is in line with the current AISI approach so the designer need not confuse how to use this new design approach in practice. Therefore, for further ease of understanding, two design examples for built-up closed cross-section columns—(1) subjected to local–global interaction buckling; and (2) subjected to element overlapping effect—are included in this paper. It is also recommended that future research may focus on further classifying the AISI main specification sections, E2 and F2 (simple classifications based on the global failure modes), based on the interaction buckling modes in built-up cross-section members. [ABSTRACT FROM AUTHOR]

A mini basket type mapping catheter consists of thin film flexible sensors and is applied in the medical field to measure the electrocardiography (ECG) signals in order to localize and quantize the physiological condition/status of heart. The flexible nature of the thin film changes the configuration with respect to the contact boundary conditions when it contacts a target surface. Therefore, to accurately localize the flexible sensor, the thin film flexible sensor's configuration must be determined accurately in an on-line fashion. As a study of localizing the thin film flexible sensor, this study proposes an on-line thin film buckling configuration determination method using parametric optimization and interpolation technique. With the specific modulus of elasticity and dimensions of the thin film flexible sensor of the mapping catheter prototype, the buckling configuration with two point boundary condition under axial load can be calculated in desktop environment. The proposed calculation method is validated by mapping catheter sensor prototype test. The calculation/test results showed that the maximum overall length L, x a , and y a value error between the calculation and experiment are approximately 0.16 mm, − 0.12 mm. − 0.10 mm in 50 ms calculation time. The calculation result of the proposed method is also compared with that of the numerical simulation by FEM, which has approximately 0.44 mm y a value error compared with that of the experiment. [ABSTRACT FROM AUTHOR]

The elastoplastic buckling behaviors of functionally graded material (FGM) beams under axial compression loading are studied in consideration of temperature dependence of material properties. Firstly, elastoplastic material properties are obtained on the basis of bilinear hardening model and temperature dependence, meanwhile the elastoplastic constitutive equations of the FGM are established as well. Then introducing the Hamilton principle, the elastoplastic buckling behaviors of FGM beams are transformed into solving the eigenvalues in symplectic space. At the same time, the buckling critical loads corresponding to the generalized eigenvalues of the canonical equations can be calculated by the bifurcation conditions. Finally, the elastoplastic buckling characteristics and solution process of them are revealed by the symplectic method and effects of material gradient, geometrical parameters of structure and ambient temperature on the critical loads of elastoplastic buckling are discussed in detail. [ABSTRACT FROM AUTHOR]

The axial buckling load of single carbon fiber or composite strands is typically predicted using Euler's formula, developed for isotropic materials. This study introduces anisotropy in a mechanical carbon/epoxy Z‐pin model under axial pressure. It examines the influence of compressive modulus, shear modulus, off‐axis angle, and aspect ratio on its buckling behavior. Results show that the axial instability performance of the Z‐pin decreases with lower compression, shear modulus, and aspect ratio while keeping the tensile modulus fixed. Anisotropy decreases buckling load by up to 14% compared with Euler's formula, which only considers tensile modulus. Additionally, the impact of the deflection Angle between the pressure and pin‐axis can be ignored when it is less than 3°. Highlights: Euler formula overestimates composite Z‐pin buckling force under axial pressure.Anisotropy decreases buckling load by up to 14% for carbon/epoxy.Shear modulus is more influential on Z‐pin with a small aspect ratio.For off‐axial compression angles <3°, influence can be ignored. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to investigate the postbuckling and buckling of functionally graded graphene-reinforced composite (FG-GRC) laminated cylindrical shells strengthened by stiffeners under axial compression with the uniform temperature change effect. The stiffener design option for FG-GRC cylindrical shells under axial compression is presented and a suitably smeared stiffener technique for GRC laminated stiffener system is developed. Basing on the von Kármán Donnell shell theory, the Galerkin's procedure, and the three-term solution of deflection, the explicit forms of critical buckling and expression of load-deflection postbuckling curves relation are obtained. Effects of the GRC laminated stiffeners, the environment temperature, the graphene-reinforced parameters on the compressed buckling behavior are validated. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive analysis of a nonlinear buckling of a cylinder with a crack with the new regression equation. For this purpose, the effective material properties and geometry parameters are considered. For geometry properties, the length, thickness and diameter for cylinder, the length, location and angle of crack are considered. For material properties, the modulus of elasticity, yield stress and plastic properties are considered. Then using the response surface method, a regression equation for predicting the cylinder's critical buckling load is proposed. To validate the results, some experimental tests are presented and the results show that there is good agreement between the proposed equation and experimental tests. Then the effects of considering parameters on the critical buckling load of the cylinder are investigated. The results show that in low values for thickness the yield stress has a more negligible effect, but for large thickness values, the yield stress has more effect on critical buckling load. Furthermore, the critical crack occurs when the crack locates perpendicular to the direction of the loading. Also, the crack's location and the cylinder's boundary condition are effective parameters on critical buckling load. Because of the interaction effect of material and geometry properties, the material and geometry parameters should be considered simultaneously to predict the critical buckling load. [ABSTRACT FROM AUTHOR]

In structural engineering, buckling is usually associated with compressive stress and/or shortening deformation states. Recently, several works came to light alerting to the propensity of some structural systems to buckle under tension. Within this context, the present work examines the buckling and post-buckling behaviours of repetitive rods systems under tensile axial loading, and comprises three distinct parts. At first, the tensile stability behaviour of a single rigid rod with an edge section supported by a slider that is forced to follow a pre-established path, developed in the literature that lays behind us, is revisited and related to the buckling behaviour of an alternative two rods system whose buckling propensity arises from a secondary compressed bar overlapping the tensioned one. In the second part of the paper, overlapping is used to create innovative repetitive frames that buckle under tension, in the present case a sequence of lined up rigid rods connected by rotational joints. The tensile critical load shows little change as new modules are added to the system, in clear contrast with the compressive case. The tensile post-buckling behaviour is also assessed, in some cases showing original shapes, and overlapping is used to create repetitive frames with negative thermal expansion coefficient as well. In the third part of the paper, the effects of applying global gradients to the relevant mechanical properties, in the form of smooth variations of the joints rigidities and rods lengths as the module is repeated, on the stability behaviour under tension are assessed. Although these variations are smooth and kept within small values, they provoke significant changes on the tensile buckling load, on the buckling type and on the type of buckling as well. The findings pave the way to the development of innovative repetitive frames, cellular materials, polymer chains and origami structures showing original constitutive behaviours under tension. [ABSTRACT FROM AUTHOR]

This study investigated the effect of an auxetic structure, positioned as the central layer in a three-layered cylindrical shell, on its buckling behaviour. The material for all three layers is aluminium. The covers are assumed isotropic. Axial and static loads are modelled as pressure on the shell's surface. In this study, modified shear deformation theory and Galerkin's numerical solution method were used, and the effect of the presence of an auxetic core on the buckling behaviour of a three-layered cylindrical shell was investigated. The assumed structure for the auxetic cell was a 2D Re-entrant honeycomb. Finally, we explore how the length-to-radius ratio, core thickness-to-total thickness ratio, and cell angle of the auxetic structure impact the system's stability, presenting the results. The distinguishing feature of the current work compared to previous studies lies in its mathematical approach. We present the system's equations as comprehensively as possible. Finally, the effect of the length-to-radius ratio, the auxetic layer's thickness relative to the whole shell's thickness, and the cell angle's size on the buckling load were investigated. In short, with the increase of both ratios, the amount of load required for buckling decreases, or in other words, system stability is reduced. Also, the size of the cell angle has little effect on the system's stability. [ABSTRACT FROM AUTHOR]

The stability of structures is an important aspect that the designer must pay particular attention to in order to ensure safety against collapse. This investigation is concerned with analytical and numerical analyses of the dynamic buckling of plane structures. A rigorous mechanical model is proposed, consisting of a beam-column element with nodal ends possessing two rotational springs of rigidities acting in parallel with the bending stiffness of the beam-column. The model is first analyzed with respect to the dynamic behavior by investigating the influence of the variation in the stiffness of the nodal springs on the fundamental frequency of the proposed mechanical model. Compression axial loading is applied to the beam-column in order to study the nonlinear dynamic behavior by introducing buckling. This novel approach is used to highlight the interaction between the fundamental frequency and the critical buckling load. Simple examples are treated using the approach and the results are compared with those obtained from a global analysis. The results revealed that it is possible to reproduce the stability analysis of a global structure by simply analyzing a target element, taking into account all elements adjacent to it with less than 1% error on the results. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to study the static buckling and free vibration of continuously graded ceramic-metal beams by employing a refined higher-order shear deformation, which is also the primary goal of this paper. Design/methodology/approach: The proposed model is able to catch both the microstructural and shear deformation impacts without employing any shear correction factors, due to the realistic distribution of transverse shear stresses. The material properties are supposed to vary across the thickness direction in a graded form and are estimated by a power-law model. The equations of motion and related boundary conditions are extracted using Hamilton's principle and then resolved by analytical solutions for calculating the critical buckling loads and natural frequencies. Findings: The obtained results are checked and compared with those of other theories that exist in the literature. At last, a parametric study is provided to exhibit the influence of different parameters such as the power-law index, beam geometrical parameters, modulus ratio and axial load on the dynamic and buckling characteristics of FG beams. Originality/value: Searching in the literature and to the best of the authors' knowledge, there are limited works that consider the coupled effect between the vibration and the axial load of FG beams based on new four-variable refined beam theory. In comparison with a beam model, the number of unknown variables resulting is only four in the general cases, as against five in the case of other shear deformation theories. The actual model represents a real distribution of transverse shear effects besides a parabolic arrangement of the transverse shear strains over the thickness of the beam, so it is needless to use of any shear correction factors. [ABSTRACT FROM AUTHOR]

In this study, buckling and vibrational characteristics of a nanoshell reinforced with graphene nanoplatelets under uniform axial load are investigated. The material properties of the piece-wise graphene-reinforced composites (GPLRCs) are assumed to be graded in the thickness direction of a nanoshell and are estimated using a nanomechanical model. The effects of the small scale are analyzed based on nonlocal stress–strain gradient theory (NSGT). The governing equations and boundary conditions (BCs) are developed using Hamilton's principle and are solved with assistance of the generalized differential quadrature method. The novelty of the current study is the consideration of GPLRC and size effect as well as satisfying various boundary conditions implemented on the proposed model using NSGT. The results show that, nonlocal parameter, graphene platelet (GPL) distribution pattern, length scale parameter, number of layers, and GPL weight function have significant influence on the buckling and natural frequency of the GPLRC nanoshell. Another significant result is that nonlocal parameter does not have any effect on the buckling load for each BC. The results of the current study are useful for design of the nanoactuators and nanosensors. [ABSTRACT FROM AUTHOR]

This paper argues that in the understandable enthusiasm to use the now readily available high- fidelity numerical software allowing the analysis of the complexities of shell buckling, and especially the notorious case of the axially loaded cylinder, there has been insufficient consideration of classical shell buckling theory and its more recent reduced stiffness extension. If future design is to be able to effectively exploit the potential benefits of the use of advanced composite materials and/or the use of rib reinforcement, it is suggested that these numerically driven research programmes would benefit from more explicit integration within the framework of classically extended buckling theory. This suggestion is reinforced in what follows by highlighting the results from a longstanding research programme in which classically extended buckling theory has been demonstrably enhanced through its integration with reliable numerical experimentation. This enhancement has helped to resolve a number of important issues including: identification of the most critical forms of imperfection affecting the buckling loads; how the most critical knockdown factors are influenced by changes in the shells' geometric and material characteristics and how safe design might be more explicitly related to the prescribed levels of geometric tolerances. Recommendations are made as to how such integrated research programmes could in the future further enhance our ability to design materially efficient shells against buckling. [ABSTRACT FROM AUTHOR]

This paper presents an experimental and numerical study on the global buckling behavior of welded thick H-section columns of Q460GJ steel under axial load. The thickness of the flange and web is 42 and 25 mm, respectively, and the slenderness ratios of the columns vary between 49.8 and 85.0. Six specimens with different section sizes were tested, and their overall buckling results showed significant lateral displacement. Test results and design values calculated in accordance with several national design codes were compared. Finite-element models that considered the initial inflexion and residual stress were established. The comparison between the finite-element calculation and test results confirmed the reliability and accuracy of the model. A parametric study of the bearing capacity of thick H-section columns was conducted on the basis of their slenderness ratio and section size. Design recommendations were provided on the basis of the comparative analysis of the finite-element calculation results and design curves obtained using different codes. Recommendations for selecting column curve types in national codes is given when designing global buckling of welded thick H-section columns of Q460GJ steel under axial loading. [ABSTRACT FROM AUTHOR]

Hybrid fibre reinforced polymer (FRP)-timber (HFT) thin-walled structural members are a novel technology developed recently as a sustainable alternative to thin-walled steel and aluminium structures. HFT structures are made by forming thin timber veneers and FRP laminates into efficient cross-sectional geometries. While existing studies have demonstrated the potential of HFT thin-walled members to be used as structural elements, a systematic study to investigate the behaviour of HFT thin-walled structures is yet to be carried out. This paper presents a study aimed at investigating the behaviour of HFT C-section columns under concentric axial loading. In total five HFT C-section specimens each from 700 mm to 2000 mm lengths were fabricated and tested. It was found that shorter HFT C-section columns failed due to local buckling while increase in length changed the failure mode to global buckling. Effect of GF orientation and density on load carrying capacity of the HFT C-section columns was investigated numerically. It was found that it’s necessary to provide adequate GF volume in transverse to axis direction, but further increase in GF volume in transverse direction did not significantly increase the load carrying capacity. Increase in GF density in parallel to axis direction increased the load carrying capacity. [ABSTRACT FROM AUTHOR]

A laboratory experimental program has been conducted to investigate three hinge buckling failure (THB) using a newly developed THB testing apparatus and methodology. The novel apparatus differs from buckling experimental programs used in the past in that it allows for direct control of axial load throughout the test similar to a horizontal in situ stress. The objective of the study was to gain quantifiable insight into the THB failure mechanism under a range of controlled axial stress conditions to inform future development of stability analysis methods. Specimens (two block) of the relatively homogeneous Wallace sandstone formation were selected and a total of seven tests were conducted to parametrically explore a range a specimen thickness (3.2 to 5 cm) and two levels of axial 'clamping' stress (10 and 15 MPa). In addition to load and displacement monitoring, high-speed camera images and acoustic emission (AE) data was collected during each test. The tests revealed relatively consistent characteristic behaviour with identifiable thresholds of yield, peak and failure (collapse). A brittle-ductile response transition was observed based on the tested parameters, although not clearly identified from the limited testing. A clear relation was developed for specimen thickness and axial stress. A calibrated distinct element modelling simulation of the experiment was conducted that showed a reasonable match to the characteristic experimental behaviour. This provided greater insight into the THB failure mechanism and showed that this method of simulation is suitable for this mode of failure. Highlights: Three Hinge Buckling of laminated rock was investigated experimentally using a novel testing apparatus. A parametric testing program was conducted to explore the effect of specimen thickness on buckling under different axial 'clamping' loads. The experimental tests were supported by high-speed video image capture and acoustic emission hit count monitoring. The tests revealed several characteristics regions of the lateral load – lateral displacement response. Micro-mechanical distinct element modelling using UDEC Voronoi tessellated simulation provided further insight into the experimental results. [ABSTRACT FROM AUTHOR]

Axially loaded micro/nano-beams supported on foundations are extensively applied in micro/nano-electro-mechanical systems. This paper deals with the problems of free vibration, buckling and dynamical stability of Timoshenko micro/nano-beam supported on Winkler–Pasternak foundation subjected to a follower axial periodic load. Based on Hamilton's principle, the governing equations of the system are derived in conjunction with nonlocal strain gradient and Timoshenko theory. The transition parameter is introduced to describe the follower direction of axial load during the deformation of the micro/nano-beam. Employing the weighted residual method, the variational consistency boundary conditions (BCs) can be derived according to the governing equations. Using differential quadrature method (DQM), the governing equations are discretized and numerical solutions of the natural frequencies, critical buckling load and instability region are obtained. Numerical examples are performed to verify present solutions by those available in the literature. Significant effects of the transition parameter and variational consistency BCs are revealed on the free vibration, buckling and dynamical stability of the axially loaded micro/nano-beam. The present analysis is of significance to axially-loaded micro/nano-beam mechanical system, especially for determination of the direction of follower axial force. [ABSTRACT FROM AUTHOR]

The newest version of shells buckling standard prEN 1993‐1‐6 (2021) adopts linear elastic buckling stress expressions for steel perfect cylinders under axial, circumferential, and torsional effects separately. However, there are no explicit detailed rules that cover the influence of two or more loading combinations on the cylinder buckling resistance, considering a full‐length domain and different boundary conditions. Consequently, this paper looks into such a topic, which will be a useful reference for future research extensions. The examined cylinders were subjected to three loading configurations: axial plus pressure, axial plus torsion, and axial, pressure, and torsion altogether. The finite element (FE) buckling capacities were compared with the prEN 1993‐1‐6 (2021) buckling strengths, from which several findings were obtained. Aspects such as the load configuration applied to a cylinder, the length domain in which a cylinder falls, and the boundary type of a cylinder's ends each led to distinctive and complex descriptions of buckling behavior. The outcomes of this study will in turn assist in developing the current standard prEN 1993‐1‐6 (2021) and its recommendation ECCS EDR5 (2013), particularly the chapter that is relevant to cylindrical shells of constant wall thickness under general loading. [ABSTRACT FROM AUTHOR]