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This paper presents an arch structure called the circular box arch with sinusoidal corrugated webs (CBASCW). This study investigates the out-of-plane elastic buckling behavior and elastoplastic stability capacity of the arch through a combined approach of theoretical derivation and finite element simulation. The section stiffness of the arch, including flexural stiffness, shear stiffness, and torsional stiffness, is achieved through theoretical derivation. Additionally, the elastic buckling load in both pure compression and pure bending states is derived. A simplified model is also introduced, which can conveniently simulate the internal force and deformation of the arch. The elastoplastic instability mechanism and failure mode are studied under various loading conditions, including uniform radial load, end bending moment, vertical load uniformly distributed in full-span, and vertical load uniformly distributed in half-span. Furthermore, the stability curves of the arch under conditions of pure compression and pure bending are graphed by incorporating stability coefficient and regularized slenderness ratio. According to the simulation results obtained from the simplified model and the analysis of stability curves, a design formula for stability capacity is proposed. [ABSTRACT FROM AUTHOR]

The impact test of tubular components is usually carried out by way of drop hammer impact. In fact, in many ships’ equipment, the form of load is often carried out by way of drop impact test. In this paper, the drop impact test is used to study the buckling of tubular structure under impact load, so as to make it closer to the impact form of components in actual ship structure. Firstly, the stress, strain, acceleration at each moment and the buckling deformation mode of the tubular member after the impact are obtained through the drop impact experiment, and then the impact process is analyzed. Secondly, the finite element method is used for numerical simulation of the impact process, and the accuracy of the finite element analysis results is verified by comparing with it. Thirdly, the finite element method proved to be effective and was used to simulate single and multiple drop impacts under more working conditions, and a large amount of data was obtained. Finally, according to the existing impact criteria based on the results of drop weight impact, it is applied to the drop impact process, and the accuracy of each impact criterion is analyzed and compared. This method makes up for the deficiency of the traditional experimental method of using falling weight to simulate impact, and provides a reference for the critical buckling condition of similar thin-walled cylindrical shells under impact. [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]

This paper presents a novel analytical solution for the buckling load in 3D of columns that fills a gap in the existing literature by accounting for shear deformation and spatial effects. The latter means that a column can be supported and buckle in any direction. We build on the foundational work of Simo and use a 3D beam model to derive a set of equations that form the basis for our analytical solution. The paper outlines the axioms of the Simo model, presents the corresponding equations, and describes the linearization procedure in details. By linearizing the equations we obtain a set of algebraic equations with boundary conditions, which we manipulate into an analytical solution for the buckling load. An illustrative example using a column with an elliptical cross-section shows how different boundary conditions and the spatial orientation of the column influence the buckling load. This research work not only contributes to the verification of numerical programs, but also provides engineers with a valuable tool for optimizing structural configurations. [ABSTRACT FROM AUTHOR]

Buckling may cause drill string damage or even drilling failure. For the 3 000-m-long horizontal section drill string, a simplified analysis model of drill string in horizontal well is established, and the dynamic response results of axial displacement, angular displacement and contact force are obtained. When buckling, the closer the position of drill string is to the bottom, the later the buckling time, the smaller the buckling deformation degree, the slower the growth rate of axial displacement, and the smaller the attenuation degree of angular displacement and contact force amplitude. After buckling, drill string undergoes tensile deformation and eventually remains stable in the tensile state. After stabilization, from the top of drill string to the bottom of drill string, axial displacement increment increases first, then remains unchanged and then decreases, and the relative torsion angle between different positions gradually decreases. The drill string is always in horizontal contact with the wellbore, resulting in the same contact force values at different locations. The change of well inclination angle does not affect the change law of displacement and contact force. The absolute value of angular displacement is negatively correlated with the change of well inclination angle, and the value of axial displacement increment and contact force is positively correlated with the change of well deviation angle, but the value of contact force is quite close. The research results can provide reference for alleviating the buckling of drill string in horizontal wells. [ABSTRACT FROM AUTHOR]

This paper studies electro-thermal buckling in a flexoelectric microbeam. This first-of-a-kind study focuses on two case-specific types of buckling in microbeams, which are essential to microstructures. Because of the electric fields and high temperatures in their environments, microbeams are susceptible to electro-thermal buckling more often than mechanical buckling. In addition, microstructures can exhibit flexoelectricity. As such a thorough understanding of electro-thermal bucking is extremely important. In this paper, we begin with extracting the equations governing flexoelectric microbeams from size-dependent flexoelectric theories. We then derive closed-form solutions for said equations. We explore various boundary conditions and, with respect to the load, analyze the various pre-buckling and buckling modes. Our study shows that buckling does not occur in some boundary conditions, and electrical curvature is very important in isotropic and homogeneous flexoelectric microbeams. In the end, the paper presents electro-thermal buckling results for specific boundary conditions as well the probability of buckling. [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]

The woven structure made of naturally curved (in-plane) ribbons has smooth geometry and fewer geometric imperfections, but there is no study of its buckling mechanical properties under vertical loads. The aim of this paper is to investigate buckling mechanical properties of spherical woven structures. Three spherical woven structures with different ribbon types and six new spherical woven structures with different ribbon widths and thicknesses were designed and the quasi-static vertical compression tests were carried out. The buckling load of spherical woven structures were studied by nonlinear finite element and ring buckling theory. Results indicate that the failure mode of the spherical weave structure under vertical loading can be divided into two stages, where a flat contact region forms between the spherical weave structure and the rigid plate and inward dimple of ribbons. Spherical weave structures using naturally curved (in-plane) ribbon weaving have better buckling stability than those woven with straight ribbon. Based on theoretical and finite element analysis, we propose a buckling load equation and buckling correction factor equation for the new spherical weave structure under vertical compression load. The formula is validated and has good agreement with the test results, which could help to design the stability of spherical weave structures with in-plane ribbons. [ABSTRACT FROM AUTHOR]

This study investigates the elastic buckling behavior of oblate hemi-ellipsoidal shells (OHES) subjected to non-uniform external hydrostatic pressure. The virtual work-energy of OHES consists of virtual strain energy due to membrane, bending, in-plane stress resultants, and virtual work of hydrostatic pressure. For buckling analysis, the geometric stiffness matrix is obtained from the strain energy due to in-plane stress resultants. A finite element procedure via a C1 continuity axisymmetric element is applied to solve the critical hydrostatic pressure from the eigenvalue buckling problem. The buckling pressure of the hemi-ellipsoidal dome subjected to uniform external pressure is verified with the previous research and FEM commercial software. Present results also indicate that the maximum in-plane stress of the hemi-ellipsoidal shell shapes are near the apex point as the axisymmetric buckling shape. In the case of hydrostatic pressure, the critical hydrostatic pressure of OHES is determined and are in good agreement when compared with the experimental results in published research. Furthermore, the shape ratio influences the difference in critical load results between uniform pressure and hydrostatic pressure, especially when the shape ratio is higher than 0.5 and the a / t ratio is less than or equal to 100. Seawater depth limitations in subsea engineering are also presented and found that the shell thickness and shape ratio are the major factors affecting critical seawater depth. [ABSTRACT FROM AUTHOR]

In this paper, buckling and nonlinear post-buckling behaviors of a bidirectional porous (BDP) beam are investigated under bidirectional hygrothermal environment. Euler–Bernoulli beam theory with the von Kármán nonlinearity is employed to derive the nonlinear variable coefficient governing differential equations based on Rayleigh quotient method. Analytical solutions of critical buckling load and load–deflection equilibrium path in post-buckling are deduced for the single directional varying (SDV) porous beam. The general numerical solutions for bidirectional varying (BDV) porous beam are obtained by differential quadrature finite element method (DQFEM) with Newton–Raphson iteration method based on the variation principle. The high accuracy of the present numerical method with higher computing efficiency is verified by comparison with published reports and the analytical results in this work. Parametric analysis on effects of the porosity bidirectional distributions, porosity coefficients, distributions of hygrothermal environment and boundary conditions on buckling load and post-buckling response is carried out to enhance the buckling and deformation resistances in design, manufacture and usage of porous structures. The results show that the bidirectional porosity pattern, linear and nonlinear hygrothermal distribution and boundary conditions play a significant role on buckling critical external load and critical hygrothermal increments, buckling form and post-buckling path. [ABSTRACT FROM AUTHOR]

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young's modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson's ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates. [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]

Steel sheeting is usually provided at the upper flange of purlin in steel roof with screw connections. The resulting diaphragm effect provided by the sheeting enhances the buckling resistance of the purlin. However, this diaphragm effect will be reduced due to any abnormality in the screw connection caused by wind-induced fatigue particularly from typhoon. This would reduce the buckling resistance of the purlin with sheeting (the purlin-sheeting system), and it would affect subsequent condition evaluation during their service life. This problem is addressed in this paper with a framework of time-dependent reliability evaluation of the buckling limit state of the purlin-sheeting system. The buckling resistance reduction due to the degradation of the diaphragm effect from typhoon is taken into account in the resistance model. The randomness of wind intensity and landfall occurrence of typhoon during the service life of purlin are also accounted for in the wind load effect model. The time-dependent reliability of the purlin at different positions of a roof is studied. Then the variation of reliability of the system due to the effect of climatic changes in the design service life is discussed. The proposed strategy is then applied to the evaluation of a purlin-sheeting system in eleven cities in China with typhoon occurrences with some useful results for future studies in the provisions of the design code. [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]

A torsional buckling model of cylindrical shells with asymmetric local thickness defect is established based on the Hamiltonian system. The critical load and torsional buckling mode of cylindrical shells with defects are obtained by the symplectic eigensolution expansion method, which overcomes the difficulty of constructing the deflection function of the traditional semi-inverse method. Local buckling modes can be captured by this new analytical model with the superposition of symplectic eigensolutions. To ensure accuracy and validity of the symplectic method, the analytical solution with torsional buckling of a cylindrical shell is compared with the classical solution and the finite element method (FEM) solution. The results show that the most detrimental position of the defect is only related to the width of the defect, not to the depth. The local defect changes the circumferential buckling wave number of the cylindrical shell and concentrates the torsional corrugation on the side containing the defect. Torque symmetry is broken due to the asymmetric defect, and the most detrimental defect direction for buckling is the same as the direction of torsional buckling wavelet. [ABSTRACT FROM AUTHOR]

In this paper, the isogeometric method is developed to study mechanical buckling behavior of nanocomposite plates reinforced by graphene sheets with temperature-dependent (TD) material properties in thermal environment. The plate is separately subjected to in-plane uniaxial, biaxial and shear loadings. It is assumed that the plate has different number of layers. By considering different volume fraction for each layer of graphene sheets, different functionally graded (FG) patterns of graphene sheets may be achieved. Furthermore, in some cases, it is considered that more than one FG patterns exist along the plate thickness. The energy statement of the plate is obtained using a logarithmic higher-order shear deformation theory (HSDT). Then, the isogeometric method is used to establish the desired eigenvalue problem. The comparison and convergence studies are presented for a wide range of numerical examples in all considered cases to show the correctness and ability of the solution. Afterwards, by presenting a set of numerical examples, the effects of plate significant parameters on the critical buckling load of the plate are examined. It is shown that the highest critical buckling loads occur when the plate has the minimum number of layers. [ABSTRACT FROM AUTHOR]

New accurate buckling analysis for rectangular orthotropic thin plates with complicated non-classical boundary restraints are conducted through adopting the finite Fourier integral transform approach. Non-classical boundaries such as rotationally restrained edges increase the mathematical difficulty in processing problems of plates, which leads to rare analytical results for benchmark use. The proposed approach is implemented in the framework of integral transform theory, in which trial function for the deflection is not necessary, and offers uniform solution procedures for problems of plates with various boundaries via adopting different integral kernels. The main merits of the approach employed is to enable one to change the complicated title problem into dealing with linear algebraic equations easily solved. Via altering the rotational spring factors introduced, buckling behaviors of plates with Levy-type boundaries and non-Levy-type boundaries can also be studied. Finally, all the given results including critical load factor and mode shape match the FEM analysis exactly, which illustrate the accuracy and validity of the method. [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]

The aim of this work is to investigate the free vibration and buckling characteristics of sigmoid functionally graded (FG) nanoplate with the influence of porosity. The modified rule of the mixture is utilized to calculate the effective material properties of porous sigmoid functionally graded (P-SFGM) nanoplate. Three schemes of porosity distribution, including uniform, symmetric and nonsymmetric are investigated. The first-order shear deformation theory is utilized to simulate the displacement fields of P-SFGM nanoplate. Eringen's nonlocal elastic theory and isogeometric analysis (IGA) are used to establish the governing equations for free vibration and buckling analysis of nanoplate structure with small size effect. By using NURBS as a basic function, IGA can fulfill the higher-order derivative requirement of governing equations. The accuracy of the presented solution is verified. By taking the nonlocal parameter into account, the stiffness of the plate is softened. Also, the effects of porosity distribution across the plate's thickness, porosity parameter, material power index, boundary conditions (BCs) and aspect ratio on the frequency response of P-SFGM nanoplate are presented. [ABSTRACT FROM AUTHOR]

This presents a mathematical model proposed by the author for description of deformation process of a shell structure under the action of a load that depends linearly on time. Material orthotropy, geometric nonlinearity, transverse shifts are taken into account. A distinctive feature of the model is the use of a refined discrete method for taking into account stiffeners, proposed by the author earlier. Prior to this, the method was used only in static or isotropic dynamic problems. It is proposed to add correction normalizing factors, which makes it possible to obtain the most accurate values of critical loads. The methodology of the calculation algorithm under dynamic loading is based on the Kantorovich method and the Rosenbrock method, which allows solving rigid ordinary differential equation (ODE) systems. New numerical results for cylindrical panels are obtained. The influence of the number of stiffening elements on the values of the critical load is shown. A comparison with the classical discrete method of taking into account stiffeners is carried out. For the problems considered in this paper, the phase portraits of the system are shown. [ABSTRACT FROM AUTHOR]

Perforated cold-formed steel (PCFS) beams are regarded as an economical option for steel construction industry owing to its various advantages. They can provide access for the facilities like electric wires and pipelines to penetrate the web so that extra building space could be saved. However, the web openings might change the web stress distribution as well as reduce the cross-sectional properties, which make the PCFS beams more susceptible to buckling and may have effect on their load-bearing capacity. In this paper, a simplified spring model was proposed based on the use of energy method, to predict the critical moment of lateral-torsional buckling of PCFS channel beams with circular holes in web subject to pure bending. The effect of hole sizes and lateral restraint at the tension flange was examined by using the derived analytical solution. In addition, eigenvalue buckling analysis was conducted by using finite-element package ANSYS to validate the accuracy of the proposed analytical model. The results demonstrated that the proposed analytical solution was reliable and the critical moment predicted can be used for the extension of DSM formulae for the design of PCFS beams when considering the failure caused by lateral-torsional buckling of the beams. [ABSTRACT FROM AUTHOR]

This paper presents some new analytic thermal buckling solutions of temperature-dependent moderately thick functionally graded (FG) rectangular plates with non-Lévy-type constraints within the symplectic solution framework in the Hamiltonian system. An original problem is reduced to the superposition of two constructed subproblems that are analytically solved via the rigorous symplectic elasticity approach with mathematical techniques such as variable separation in the symplectic space and symplectic eigen expansion. The physical neutral surface is employed to remove the stretching-bending coupling in constitutive equations. The main characteristic of the present symplectic superposition strategy is on the rational derivation without assumption on solution forms, which, however, is hard to achieve by conventional semi-inverse methods. Comprehensive benchmark results are presented, including critical buckling temperatures as well as mode shapes of typical non-Lévy-type FG plates in uniform and nonlinear temperature fields, and are verified by available numerical results. The effects of boundary constraint, aspect ratio, volume fraction exponent, and thickness-to-width ratio on buckling temperatures are quantitatively investigated. The occurrence of thermal buckling is further studied by presenting a failure mode map covering a wide range of geometric parameters. [ABSTRACT FROM AUTHOR]

Cylindrical shell subjected to axial compression is very sensitive to the initial geometric imperfection. Even very small initial imperfection would significantly reduce the critical load. In this paper, the post-buckling behaviors of functionally graded (FG) porous magneto-electro-elastic (MEE) cylindrical shell with initial geometric imperfection is investigated by using the high-order shear deformation theory. The post-buckling equilibrium paths for different imperfection amplitudes are obtained by Galerkin's method. Several numerical examples are presented to demonstrate the accuracy of the proposed model and reveal the effects of geometrical parameters, material properties, external magneto-electric loads on the post-buckling equilibrium path. In addition, the imperfection sensitivity of FG porous MEE cylindrical shells is also discussed. [ABSTRACT FROM AUTHOR]

Lateral distortional buckling (LDB) mode has been investigated as one of the failure modes in steel I-beams. The LDB mode in such beams is known by simultaneous lateral deflection, twist, and cross-sectional change due to web distortion. However, many studies have been conducted to investigate the behavior of this failure mode; so far, no formula has been found to calculate the ultimate LDB resistance of I-beams, which also takes into account the effect of different loading conditions. Consequently, in the current paper, by conducting an extensive parametric study, it was tried to investigate the effect of all main parameters as well as the effect of different loading conditions on the ultimate LDB resistance of I-shaped beams. Then, based on the provided database, the artificial neural network (ANN) method was employed, and based on it, a high-precision formulation was proposed to predict the ultimate LDB strength of steel I-beams. In addition to the ANN method, a regression-based formula was also developed as a classical method to examine the differences between the two methods. Finally, the proposed formulas were compared with other existing formulas for estimating the LDB strength. The results showed that the proposed formula based on ANN not only presents a reasonable accuracy compared to the existing formulations but also can be used by engineers as practical equations in the design of I-beams. [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]

The straight-beam approach is a simple and efficient means for analyzing the buckling of curved beams. Although previous researchers showed that the straight-beam approach is capable of simulating the lateral buckling of solid curved beams, the warping effect had been neglected and thus its practical application in engineering was limited. In this study, thin-walled curved I-beams will be dealt with by assuming the warping degrees of freedom (DOFs) to be identical at the common node for non-aligned connected elements. One feature of the present formulation is that the moments induced by initial nodal moments undergoing out-of-plane rotations are duly considered in the geometric stiffness matrix, while the compatibility and equilibrium are enforced for angled joints at the deformed position. With high computational efficiency, the present approach obtains buckling loads that agree well with the theoretical curved-beam solutions or the ones obtained by ABAQUS using shell elements. Compared with the modern curved-beam elements, the straight-beam element is locking free, invariant and simple in formulation, since the effect of curvature is not involved in global assembly. [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]

This paper focuses on dynamic buckling of composite structures subjected to impulse loads. Using the Lyapunov exponent, the Budiansky–Hutchinson criterion is improved and its algorithm is constructed. Based on it, the nonlinear dynamic buckling loads are evaluated for typical composite structures such as a fiber-reinforced composite plate, composite laminated cylindrical shells and a laminated plate with delaminations and matrix cracks that are all subjected to impulse loads. The improved criterion of dynamic buckling is validated through comparisons with the results in the published literatures. [ABSTRACT FROM AUTHOR]

Because structures made of FG material often operate in high temperature environments, it is critical to understand the mechanical behavior of these structures while taking temperature into consideration. As a result, the phase-field model is employed in this work to investigate the thermal buckling of fractured functionally graded material (FGM) plates. Additionally, this study demonstrates the difference between the plate's static stability response to thermal load in the case of temperature-dependent (TD) material mechanical properties and in the case of temperature-independent (TID) material mechanical properties, illustrating that the calculation for these two cases will appear to be highly skewed. This provides a scientifically valid foundation for scientists to adopt a more realistic computation model. The equations are based on the third-order shear deformation plate theory (TSDT) of Reddy. This work proves that this discrepancy strongly depends on the material, boundary condition, crack length as well as thickness of the crack plate, it has never been explored in published work, the results give very useful and needful information for scientists to choose the best accuracy case to calculate and apply in practice. [ABSTRACT FROM AUTHOR]

This paper investigates the possibility for implementing machine learning-aided prediction in analyzing the buckling phenomena of ballasted railway tracks induced by extreme temperature. In this study, artificial neural networks (ANNs) have been developed to identify the relationship between various ballasted track conditions and outputs, namely safe temperature and buckling temperature. The variables included in the objective function of the optimization problems are the lateral resistance of ballasted track provided by ballast-sleeper interaction, torsional resistance provided by fastening systems, and misalignment of the track. Due to its complexity in parameter combinations, the objective of this study is to create predictive models with the aim of minimizing the usage of scarce resources. Thus, this paper is the first to develop a novel machine learning-aided prediction of railway track buckling due to extreme temperature. Comprehensively, all 353 datasets of the safe and buckling temperatures derived from previous finite element (FE) simulation results have been collected and trained. Note that the mean squared error (MSE) and the coefficient of determination ( R 2) are considered to quantify the performance of the ANN architectures. The optimal ANN architecture with a very high rate of accuracy has been determined and highlighted. Thus, the suggested neural network model can be applied conveniently to help estimate safe and buckling temperatures of the complex track models in order to improve track conditions and thus prevent track buckling in summer. [ABSTRACT FROM AUTHOR]

To develop large-span but ultralight lattice truss columns, a hierarchical IsoTruss column (HITC) was proposed. The multi-buckling behavior of the axially compressed HITC was analyzed by the finite element method (FEM) using a parametric approach in the framework of ANSYS parametric design language (APDL). It was demonstrated that the program enables efficient generation of the finite element (FE) model, while facilitating the parametric design of the HITC. Using this program, the effects of helical angles and brace angles on the buckling behavior of the HITC were investigated. Depending on the helical angles and brace angles, the HITCs mainly have three buckling modes: the global buckling, the first-order local buckling and the second-order local buckling. Theoretical multi-buckling models were established to predict the critical buckling loads. Buckling failure maps based on the theoretical analyses were also developed, which can be useful in preliminary design of such structures. [ABSTRACT FROM AUTHOR]

Steel slit shear walls (SSSWs), made by cutting slits in steel plates, are increasingly adopted in seismic design of buildings for energy dissipation. This paper estimates the seismic energy dissipation capacity of SSSWs considering out-of-plane buckling. In the experimental study, three SSSW specimens were designed with different width-thickness ratios and aspect ratios and tested under quasi-static cyclic loading. Test results showed that the width-thickness ratio of the links dominated the occurrence of out-of-plane buckling, which produced pinching in the hysteresis and thus reduced the energy dissipation capacity. Out-of-plane buckling occurred earlier for the links with a larger width-thickness ratio, and vice versa. Refined finite element model was built for the SSSW specimens, and validated by the test results. The concept of average pinching parameter was proposed to quantify the degree of pinching in the hysteresis. Through the parametric analysis, an equation was derived to estimate the average pinching parameter of the SSSWs with different design parameters. A new method for estimating the energy dissipation of the SSSWs considering out-of-plane buckling was proposed, by which the predicted energy dissipation agreed well with the test results. [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]

In this paper, an evaluation of the influence of atmospheric humidity on the critical buckling load of reinforced concrete columns is performed. A particular case consisting of a real, extremely slender reinforced concrete pole was taken for the study. The chosen mathematical procedure for calculating the critical load is based on the Mechanics of Deformable Solids due to variations of structure vibration frequency over time. The rheological behavior of concrete related to creep and shrinkage, which illustrates the time-dependent aspect of the problem, was also considered in the analysis following normative recommendations from the Brazilian Association of Technical Standards (ABNT). In order to evaluate value changes of critical buckling loads, different time instants after loading the structure as well as different relative humidity from 0% to 100%, in 10% increments were considered. According to the selected criteria, it was possible to verify that a higher atmospheric humidity decreases the water transport from the interior out to the exterior surfaces of concrete, hence positively influencing structure stiffness. Therefore, the lowest reduction on critical buckling was 41.9% at 100% relative atmospheric humidity, versus the highest 60.7% at 0% relative humidity. A period of 7500 days after loading the structure was considered in the analysis. [ABSTRACT FROM AUTHOR]

Nonlinear buckling analysis for honeycomb auxetic-core sandwich toroidal shell segments with CNT-reinforced face sheets surrounded by elastic foundations under the radial pressure is presented in this study. The basic equation system of shells is established based on the von Kármán–Donnell nonlinear shell theory, combined with Stein and McElman approximation. Meanwhile, the foundation-shell elastic interaction is simulated by the foundation model based on the Pasternak assumption. The Galerkin procedure is utilized to achieve the pre-buckling and post-buckling responses for the shell, from which the radially critical buckling load is determined. Numerical analysis shows the various influences of auxetic-core layer, CNT-reinforced face sheets, and elastic foundation on the pre-buckling and postbuckling behavior of sandwich shells with CNT reinforced face sheets. [ABSTRACT FROM AUTHOR]

Buckling design of axially compressed cylindrical shells is still a challenging subject considering the high imperfection-sensitive characteristic in this kind of structure. With the development of various design methods, the energy barrier concept dealing with buckling of imperfection-sensitive cylindrical shells exhibits a promising prospect in recent years. In this study, buckling design of imperfection-sensitive cylindrical shells under axial compression based on the energy barrier approach is systematically investigated. The methodology about buckling design based on the energy barrier approach is described in detail first taking advantage of the cylindrical shells whose buckling loads have been extensively tested. Then, validation and discussion about this buckling design method have been carried out by the numerical and experimental analyses on the cylindrical shells with different geometrical and boundary imperfections. Results in this study together with the available experimental data have verified the reliability and advantage of the buckling design method based on energy barrier approach. A design criterion based on the energy barrier approach is therefore established and compared with the other criteria. Results indicate that buckling design based on energy barrier approach can be used as an efficient way in the lightweight design of thin-shell structures. [ABSTRACT FROM AUTHOR]

In this research, nonlinear thermal buckling and post-buckling behaviors of composite plate with the circular/elliptical cut-out are investigated using particle semi-energy (PSE) method. The semi-energy method is based on the solution of compatibility equation via an Airy force function and out-of-plane displacement function. The unknown parameters of these functions are determined by minimizing the potential energy. The integral of potential energy are replaced with summation of particles energy at perforated plate. The cut-out is modeled easily using these particles. The advantages of this method are easily cut-out modeling by particles and proposing just one of the displacement fields (i.e. out-of-plane). Based on the results, there is a good agreement (1.25%) between the post-buckling loads derived from PSE of this paper and experimental test of other literature. The accuracy of the finite element method (FEM) is 7.5% with respect to experimental test. The influences of temperature distribution, the cut-out size and elliptical cut-out rotating on post-buckling load and deflection of perforated plate are investigated. [ABSTRACT FROM AUTHOR]

This paper presents a computational methodology to compute the critical buckling stress of built-up cold-formed steel columns joined with discrete fasteners. The fasteners are modeled as three-dimensional beam elements, and their effect is integrated into the spline finite strip framework, evolving the compound strip methodology. Although this technique has been presented in the literature, this paper presents yet another robust framework for the buckling load evaluation of compound cold-formed steel columns with arbitrarily located fasteners. The proposed framework is applied to study the effect of fasteners on the formation of local, distortional, and global buckling modes of built-up section and a comparison is drawn with the buckling behavior of a single section. In this study, the proposed formulations are also used to get insights into the stability behavior of single-span and multi-span compound cold-formed steel columns in the presence of (i) fasteners with varied spacings with respect to span and (ii) the presence of the additional restraining system such as wall panels. For different buckling modes, a significant increment in buckling stress for a built-up section from a single section is observed when the fastener spacing is kept less than the critical buckling half-wavelength of the respective buckling modes. The study on the effect of wall panels shows that in comparison to unsheathed wall studs, the sheathed wall studs that produce additional constraints lead to the elimination of the global buckling deformations. The proposed formulations are simple, yet rigorous and have been validated using finite element-based numerical results. [ABSTRACT FROM AUTHOR]

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force F , bending moment M and distributed load q (or concentrated load P) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads. [ABSTRACT FROM AUTHOR]

Unstiffened plates in structures are usually welded or fastened to supporting members, providing rotational restraint stiffness to the plate. Previous studies have shown that neglect of rotational restraint stiffness at the edges of a plate in a structure can introduce deviations in the analysis of dynamic elastic buckling. In this study, the in-plane impact-induced dynamic elastic buckling responses of isotropic imperfect unstiffened plates with four elastically restrained edges are analytically investigated, based on the large-deflection theory of thin plate. The evolution of the peak deflection predicted by the proposed analytical method is found to be consistent with the responses available from the literature. Then the method is further used to estimate the deformation map of an unstiffened plate with four elastically restrained edges, and the effects of rotational restraint stiffness, initial geometric imperfection and shock duration on the dynamic buckling response of the plate are examined. The results show that the critical dynamic buckling load and the maximum deflection response of the plates are significantly influenced by the rotational restraint stiffness as well as the first-order initial geometric imperfection, and thus cannot be neglected in the analysis of dynamic buckling. [ABSTRACT FROM AUTHOR]

The dynamic failure behavior of double-layer-domes subjected to impact is studied numerically through the nonlinear finite element software LS-DYNA. The parameters considered in this work include the mass, velocity, and size of impactor, impact direction, roof weigh, geometric imperfection, rise-to-span ratio, and depth of dome. The dynamic time-history response and energy conversion of the structure are utilized to distinguish between the failure mechanism types. For the cases studied, it is found that failure of the structures falls into one of the three categories: (1) local shear failure, (2) partial progressive failure, and (3) full progressive failure. Non-failure case dominates the dome response when the kinetic energy of the impactor is small enough, and the structure can convert most of the kinetic energy into the strain energy, thereby absorbing the impact. Local shear failure occurs in a double-layer-dome when an impactor with very high kinetic energy strikes the dome. For an impactor striking with a mass of 5 to 300 ton and a velocity of 50 to 120 m/s, the double-layer-dome studied will suffer from partial progressive failure. Varying mass and velocity of the impactor in the range of 1 to 300 ton and 200 to 400 m/s, respectively, results in a tendency of the dome to exhibit local shear failure. Although impact direction does not cause a change in the failure mechanism type, there is a reduction in the severity of failure of the system as the impact angle increases. Roof weight has no dominant effect on the failure mechanism of the double-layer-dome. A small initial member imperfection with amplitude 0.001 L does not change the progressive failure type. A large member imperfection of 0.01 L triggers member buckling and leads to local shear failure of the dome. Except for some loading cases, the change in the rise to span ratio and depth of the dome does not seriously affect the failure mode. [ABSTRACT FROM AUTHOR]

Instabilities in nanosized, externally pressurized spherical shells are important for their applications in nano and biotechnology. Mechanics at such length scale is described by nonlocal and Strain Gradient (SG) field theories. However, analysis of shell buckling is involved and becomes even more complicated in presence of nonlocal and SG interactions. This paper demonstrates that such analysis can be largely simplified by a shallow segment representation of the shell by assuming short wave lengths for the incipient buckling modes. The governing equations are derived and linearized equations are solved to obtain a closed form solution for the critical external pressure causing buckling for a pressurized nonlocal shell. Nonlocal interactions are shown to reduce, whereas the SG interaction increases the critical pressure. The relative reduction/increase becomes more prominent for higher modes of buckling and for increasingly thinner shell. A constricting relationship between the two set of wave numbers expressing the buckling modes is also shown to be modified by the nonlocal and SG scale parameters. Consequent wave numbers increase/decrease, accompanied by decreasing/increasing number of wavelengths, thereby further justifying the shallow segment representation employed herein. [ABSTRACT FROM AUTHOR]

This study addresses the analytical treatment of a closed-form buckling equation for lateral-torsional stability of thin web composite cantilever beams under mid-height tip force. The beam is composed of random ply fiber orientations. Classical lamination theory is embedded into the Vlasov plate formulation to make up the framework of the analytical treatment. A closed-form solution is realized when an innovative dimensional reduction is extended to the 3D constitutive stiffness matrix. This was made possible through a two-step process in which the shear strain, lateral curvature, and twisting curvature are retained first. By condensing the shear strain variable, effective lateral, torsional, and coupling stiffness terms were formulated. Applying the equilibrium conditions in the deformed configuration, two differential equations are obtained in terms of the lateral curvature and twisting angle. Eliminating the lateral curvature, the twisting angle differential equation with nonconstant coefficients is generated. This equation is solved using a hybrid numerical-analytical approach yielding an analytical buckling expression. Finite element results are generated to verify the accuracy of the buckling load predictions indicating very good correlation with the buckling equation results regardless of the random lamination applied. [ABSTRACT FROM AUTHOR]

This paper presents an analytical investigation on dynamic buckling of cylindrical shells with general thickness variations under exponentially increasing external pressure over the time. Different from the previous studies in literatures, the shell thickness varies arbitrarily and is common in actual engineering, which leads to failure of the existing methods. A new analytical method is first developed to solve the fourth-order governing partial differential equations with variable coefficients for the shell subjected to varying external pressure. Then the asymptotic formulae for dynamic buckling loads considering general thickness variations are derived and expressed by geometry sizes of the shell and thickness variation functions. To validate the presented results, two specific non-axisymmetric thickness cases are discussed in detail. The critical dynamic buckling loads show a great agreement with the previous ones by other researchers for simple and axial thickness variation situation. Finally, example calculations and parametric discussion are performed, and influences of thickness variation types, speed of external pressure and the power exponent of time on the critical dynamic buckling loads are discussed. [ABSTRACT FROM AUTHOR]

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed. [ABSTRACT FROM AUTHOR]

This paper deals with the lateral buckling behavior of an axially compressed beam interacting with the ground on which it is resting. Such a simple model is supposed to reproduce the same trends as observed during the lateral buckling of offshore pipelines on the seabed. In such practical analyses, the pipe-soil interaction relates the ground to the neutral axis of the pipeline. It is shown that, although such a constraint significantly affects the buckling behavior of the pipeline, it cannot reflect the torsional component of the buckling modes. However, this component is encountered in practice and may further modify the critical loads. Therefore, in this present preliminary study, the interaction between the beam in hand and the surrounding ground is modeled by a connection (a continuous distribution of lateral springs) related to the bottom line of the beam. In this way, the real contact between the soil and the bottom line of a pipe is mimicked, allowing for both flexural and torsional deformations in the buckling response. The problem is investigated analytically using an Euler–Bernoulli beam model with an isotropic linear elastic constitutive law and also an elastic interaction law. Original analytical solutions are derived and compared to numerical results obtained through finite element computations. In comparison with classical solutions (with the connection related to the neutral axis), new types of buckling modes may appear when considering torsional effects, depending on the boundary conditions, with generally much lower critical loads. These first results are certainly representative of some features of the global/localized lateral buckling of offshore pipelines, indicating that torsional effects should also be taken into account in such more comprehensive analyses. [ABSTRACT FROM AUTHOR]

An accurate buckling response analysis for functionally graded graphene platelet (GPL) reinforced piezoelectric cylindrical nanoshells subject to thermo-electro-mechanical loadings is presented by a rigorous symplectic expansion approach. Three types of GPL reinforced patterns are considered, and the modified Halpin–Tsai model is employed to determine their effective material properties. By using Eringen's nonlocal stress theory and Reissner's shell theory, new governing equations are established in the Hamiltonian form. Exact solutions are expanded into symplectic series and three possible forms are derived. A comparison with the existing study is presented to validate the solution and very good agreement is observed. The effects of material and geometrical properties of GPLs, electric voltage and temperature rise on critical buckling stresses are investigated and discussed in detail. [ABSTRACT FROM AUTHOR]

The Refined Zigzag Theory (RZT) is a structural theory developed for the analysis of composite multilayer and sandwich beams. However, the accuracy of RZT for buckling analysis of sandwich beams has not been experimentally investigated, and for RZT and Timoshenko Beam Theory (TBT) the effect of the degree of heterogeneity on their accuracy requires further study. The aim of this work was to validate the use of the RZT for predicting the critical buckling loads of sandwich beams, even with highly heterogeneous material properties, and to assess the use of the TBT for the same application. Buckling experiments were conducted on five foam-core sandwich beams, which varied in geometry and included highly heterogeneous configurations. For each beam, two finite element (FE) models were analyzed using RZT- and TBT-beam FEs. The comparison between the numerical and the experimental results highlighted a major capability of RZT to correctly predict the critical buckling load for all the beams considered. The dependence of the TBT results on the beam characteristics was further investigated through a parametric analysis, which showed the dominant effect to be a close to linear relationship between the TBT error and the beam face-to-core thickness ratio. The work demonstrated the outstanding accuracy of the RZT predictions, including the superior capabilities with respect to TBT, and has application for rapid and accurate analysis of industrial structures. [ABSTRACT FROM AUTHOR]

Lateral buckling of cantilevered circular arches under various end moments is studied using an analytical approach. Three types of conservative moments are considered, i.e. the quasi-tangential moments of the 1st and 2nd kinds, and the semi-tangential moment. The induced moments associated with each of the moment mechanisms undergoing three-dimensional rotations are included in the Newman boundary conditions. Using the differential equations available for the out-of-plane buckling of curved beams, the analytical solutions are derived for a cantilevered circular arch, which can be used as the benchmarks for calibration of other methods of analysis. [ABSTRACT FROM AUTHOR]