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This paper proposes a new type of buckling-restrained braces (BRBs), namely shuttle-shaped buckling-restrained braces (SS-BRBs). The proposed SS-BRB is composed of a circular steel tube as the inner core, and a shuttle-shaped thin-walled steel tube as the external restraining member. The space between them is filled by a steel-plate isolation system. The shuttle-shaped restraining member of the SS-BRB significantly improves load-carrying efficiency and saves material in its strength design. Moreover, the SS-BRB is more aesthetically appealing and can be utilized as an exposed BRB in long-span or spatial structures. In terms of the concept of restraining ratio of a BRB, no design method of an SS-BRB is available currently because it concerns the solution of the elastic buckling load of an SS-BRB. Therefore, the elastic buckling load of a pin-ended SS-BRB is initially studied by adopting the equilibrium method and is further verified through finite element (FE) method. The lateral displacement function of an SS-BRB, and the longitudinal stress at the extreme fiber of the external restraining member are derived by considering an initial geometric imperfection that is consistent with the first order overall buckling shape of the SS-BRB. A correction factor considering shear deformation has been incorporated for a more accurate prediction. The lower limit of the restraining ratio for a load-bearing type of SS-BRBs is further obtained based on yielding of the extreme fiber of the restraining member. Furthermore, the proposed formula has incorporated a strain hardening factor for the SS-BRB that experiences strain hardening of the core after its initial yielding. The proposed formulas have been validated through FE numerical analysis. The findings in this paper provide fundamentals to develop the design method for an energy-dissipation type of SS-BRBs. [ABSTRACT FROM AUTHOR]

Buckling instability refers to a significant limit on the structures with I-section members, which causes severe decreasing of critical buckling load. Many mechanisms and techniques have been developed to increase the loading capacity of I-section structures, e.g., using composite materials or changing web geometry. This study aims at theoretically investigating the effect of geometry on the buckling capacity of wood composite I-beams with sinusoidal corrugated web. Experiments and numerical simulations are carried out to validate the theoretical predictions. The presented model is also reduced to flat web to validate with an existing study. Good agreements are observed from the validations. Parametric study is conducted to indicate the effects of web geometry on the critical buckling load. A significant increasing of buckling load (minimum 17.7%) is obtained between flat and sinusoidal web I-beams. Sensitivity study is carried out to evaluate the influences of web thickness, beam length and beam height on the loading capacity of sinusoidal I-beams. Optimal design is conducted to investigate the impact of the ratios of wavelength-to-beam length ( a L ) and wave amplitude-to-flange width ( A T ) on the critical buckling load and volume of wood corrugated I-beams. The findings in this study can be further used as guidance for the design of composite I-beams with sinusoidal corrugated web. [ABSTRACT FROM AUTHOR]

In the present work, attention is focused on the prediction of thermal buckling and post-buckling behaviors of functionally graded materials (FGM) beams based on Euler–Bernoulli, Timoshenko and various higher-order shear deformation beam theories. Two ends of the beam are assumed to be clamped and in-plane boundary conditions are immovable. The beam is subjected to uniform temperature rise and temperature dependency of the constituents is also taken into account. The governing equations are developed relative to neutral plane and mid-plane of the beam. A two-step perturbation method is employed to determine the critical buckling loads and post-buckling equilibrium paths. New results of thermal buckling and post-buckling analysis of the beams are presented and discussed in details , the numerical analysis shows that, for the case of uniform temperature rise loading, the post-buckling equilibrium path for FGM beam with two clamped ends is also of the bifurcation type for any arbitrary value of the power law index and any various displacement fields. [ABSTRACT FROM AUTHOR]

An effective way for improving the global load-carrying capacity of a steel arch with a welded hollow section is to increase the height of its webs. However, the high and thin web may buckle locally, which will affect the global load-carrying capacity and should be taken into account in predicting the global strength of the arch. This paper presents a numerical investigation for the in-plane strength and design for pin-ended circular steel arches with a welded hollow section, focusing on the effects of web local buckling by the large deformation inelastic analysis in association with a finite shell element model. The circular steel arches subjected to a radial load uniformly distributed along the arch length, a load uniformly distributed over the full span of the arch, or/and over the half span of the arch and their various combinations are considered in the investigation of their failure modes and strengths. The initial global and local geometric imperfections as well as residual stresses are included in the finite element model. It is found that web local buckling influences the global strength of the steel arches significantly and needs to be accounted in formulate their strength design formulas. The parameters related to the web local buckling and global buckling of the arch are thoroughly explored. It is found that the stability coefficients of arches under the nominal uniform axial compression are related to the equivalent normalized web height-to-thickness ratio of the cross-section and the normalized slenderness of the arch, and accordingly the design formula of the stability coefficients is proposed by including their effects. In addition, a design formula for predicting the strengths of the arches under a load uniformly distributed over the full span is developed by introducing a corrective coefficient into the stability coefficient, and it is found that the corrective coefficient is related to the arch rise-to-span ratio and slenderness of the arch. Furthermore, a general interaction design formula is developed for predicting in-plane strength of the arches under general in-plane loading such as a load uniformly distributed over the half span of the arch and various combinations of a full span uniform load and a half span uniform load. Comparisons with the finite element results demonstrate the proposed design formulas can provide good predictions and/or lower bound predictions for the strengths of the steel arches with a welded hollow section [ABSTRACT FROM AUTHOR]

In this paper, we give a targeted review of the state of the art in the study of planar elastic beams in large deformations, also in the presence of geometric nonlinearities. The main scope of this work is to present the different methods of analysis available for describing the possible equilibrium forms and the motions of elastic beams. For the sake of completeness, we start by giving an overview of the nonlinear theories introduced for approaching this argument and then we account for the variational principles and deformation energies introduced for modelling beams undergoing large deformations and displacements. We then consider different kinds of loads treated in the literature and the corresponding induced beam deformations. We conclude by accounting for the available analysis for stability and some considerations about problems where live loads are applied, as well as by describing some relevant numerical methods of use in the applications we have in mind. The selection criterion for the reviewed papers is dictated by the need to study large deformations and the dynamics of pantographic sheets. (Large deformations of planar extensible beams and pantographic lattices: heuristic homogenization, experimental and numerical examples of equilibrium. Proc R Soc A 2016; 472(2185): 20150790), dell'Isola et al. (Designing a light fabric metamaterial being highly macroscopically tough under directional extension: first experimental evidence. Z Angew Math Phys 2015; 66(6): 3473–3498), Turco et al. (Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Z Angew Math Phys 2016; 67(4): 1–28)]. [ABSTRACT FROM AUTHOR]

As a first attempt, optimum stacking sequences of thick laminated composite plate is obtained to maximize its buckling load via employing the finite element (FE), genetic algorithms (GAs) and particle swarm optimization (PSO) methods. The higher-order shear deformation theory (HSDT) is used to obtain governing equations of the plate. The finite element method (FEM) is employed to solve these equations and to gain buckling load of the plate. The FEM solution is linked with a developed optimization algorithm which is a mix of genetic algorithms (GAs) and particle swarm optimization (PSO) techniques. Some examples are solved to show applicability and usefulness of the proposed hybrid method for maximizing buckling load of the plate via finding optimum stacking sequences of the plate. Also, influences of different parameters on the optimum stacking sequences of the thick plate are studied. [ABSTRACT FROM AUTHOR]

Highlights • The differential system is solved with low computational cost. • The numerical results indicate a very good performance of the 6DE model proposed. • The 6DE model allows to obtain the equivalent properties for the beam-column model. • Practical expressions for the buckling loads exhibit an excellent agreement. Abstract Lattice towers and guyed masts are frequently used in the telecommunication industry, particularly to support antennas. These structural systems comprise a large number of elements (mainly, legs and diagonals) and for this reason, their representation by equivalent models is quite common and convenient. In a previous study, the authors derived a continuous model of a spatial lattice governed by nine differential equations (9DE). The legs trace forms a triangle and the diagonals with a zig-zag pattern are contained in three planes that join each two legs, defined as Pattern 1. Here and starting from an energy statement, the structural behavior of a 1D continuous model governed by six differential equations (6DE) which leads to a simpler representation of the lattice structure, is stated. This formulation considers the shear flexibility and the second order effect due to axial loads. Also, the inertial forces due to the legs and diagonals masses are taken into account. Numerical examples dealing with deflections, critical buckling loads and natural frequencies are solved with this 1D model. The results are compared with the outcomes found with finite element methods. A very good performance is attained with the proposed model. Finally, the equivalent properties for other patterns of diagonalization (Patterns 2, 3 and 4) different to the studied as well as the formulas to find the critical loads are included in Appendices. [ABSTRACT FROM AUTHOR]

Buckling mode interaction of elastic systems in the presence of initial imperfections is well known to have a detrimental effect on the response of a wide range of structural systems. This has been demonstrated mostly analytically for simple models, assuming small displacements, thus obtaining results with questionable validity in the post-buckling range. In order to acquire additional insight into this issue, in the first part of the present paper, two different versions of the well-known 2-DOF Augusti model, whose independent buckling modes are both stable, are studied analytically without any simplifying assumptions with respect to the magnitude of deformation, in order to accurately demonstrate the coupling phenomena in the presence of imperfections in the pre- and post-buckling range. Depending on the nature of the structure's rotational springs, its post-buckling equilibrium path may be either stable or unstable. Afterward, the elastic response of two examples of laced built-up columns is illustrated numerically, one characterized by interaction between in-plane global and local buckling and the other by in- and out-of-plane global buckling, featuring similar response to that of the two 2-DOF models, respectively, thus demonstrating occurrence of such behavior in actual structural systems. [ABSTRACT FROM AUTHOR]

In the present study a method for improving the reliability of measuring the elastic critical buckling load of sway frames is proposed. The critical load is obtained by extrapolating the dependence between the lateral stiffness and vertical load that acts on the frame up to zero value of the lateral stiffness. The reliability is improved by planning of testing procedure and nearing the testing load to the buckling one. The testing procedure includes planning and correction of the lateral load during the experiments in order to avoid plastic deformations under high vertical loads. Theoretical dependence of lateral stiffness on the vertical load is obtained considering the stiffness in connections between the frame elements is found. Errors due to extrapolation, limited measurements' quantity and measuring accuracy are considered. The theoretical results are further verified experimentally for various elements connection schemes. It is shown that using linear extrapolation of the dependence between lateral stiffness and vertical load provides high accuracy. Moreover, it's determined that increasing the maximum testing load decreases the difference between the experimental and analytical values of the buckling load. Therefore the proposed method can be successfully used for testing sway frames in laboratory and real conditions. [ABSTRACT FROM AUTHOR]

A numerical strategy is developed and used to investigate the localized lateral buckling of circular pipelines under thermal loading and friction. The constitutive relations for circular pipelines are derived for thermal stresses and finite strain based on a hyperelastic constitutive model. The prebuckling lateral expansion and localized postbuckling deformation are investigated. A critical included angle for circular profiles is studied. Beyond the critical included angle, increasing the included angle of the pipeline or changing the boundary conditions does not influence the localized buckling behavior. Parametric studies are performed and the results are validated with ansys. [ABSTRACT FROM AUTHOR]

This paper presents a new approach to the topology optimization of columns exposed to a loss of stability. The idea is to replace a conventional maximization of a buckling load by a locally formulated topology optimization problem based on compliance minimization. In order to do this, the standard instability analysis of a compressed column is performed first and the buckling mode is determined. Then the compressive loading is replaced by a transverse one which is selected so as to generate a bending moment, the distribution of which coincides with the one representing the considered buckling mode. Minimization of compliance is performed for the bent structure and optimal topology is generated. Finally, the critical load for the optimal column is calculated. The selected numerical results obtained with the use of the above technique, under the assumption that the buckling load is unimodal, are presented. The above approach allows generating optimal topologies using Cellular Automata (CA) method, which by nature requires local formulation of the design problem. [ABSTRACT FROM AUTHOR]

Many authors in the literature agreed that the flow theory of plasticity either fails to predict buckling or overestimates plastic buckling stresses and strains of plates and shells while the deformation theory succeeds in forecasting buckling and provides estimates that are more in line with the experimental results. Following a previous study by the same authors focused on compressed cylinders, the present work aims to investigate the reasons for the discrepancy between the flow and deformation theory predictions in the case of cylinders subjected to combined axial tensile load and increasing external lateral pressure. To this end, geometrically nonlinear finite-element calculations of selected cylindrical shells using both the flow theory and the deformation theory of plasticity have been conducted, and the results are compared with some accurate physical test results and with numerical results obtained by other authors using the code BOSOR5. It is found, contrary to common belief, that very good agreement between numerical and test results can be obtained in the case of the flow theory of plasticity. The reasons underlying the apparent plastic buckling paradox are discussed in detail. [ABSTRACT FROM AUTHOR]

In this research work, an exact analytical solution for thermal buckling analysis of functionally graded material (FGM) plates with clamped boundary condition subjected to uniform, linear, and non-linear temperature rises across the thickness direction is developed. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory accounts for parabolic distribution of the transverse shear strains, and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factor. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are solved analytically for a plate with simply supported boundary conditions. Resulting equations are employed to obtain the closed-form solution for the thermal force resultant for each loading case. Numerical examples covering the effects of the plate aspect ratio, side-to-thickness ratio and gradient index on thermal force resultant are discussed. [ABSTRACT FROM PUBLISHER]

The effect of distortional deformation on the elastic lateral buckling of thin-walled box beam elements under combined bending and axial forces is investigated in this paper. For the purpose, an analytical model is developed for the stability of laterally unrestrained box beams according to higher order theory. Ritz and Galerkin's methods are applied in order to discretize the governing equilibrium equations and then the buckling loads are obtained by requiring the singularity of the tangential stiffness matrix. The different solutions are discussed and then compared to the finite element simulation using Abaqus software where shell elements are used in the mesh process. The numerical results reveal that classical stability solutions as those adopted in Eurocode 3 overestimate the real lateral buckling resistance of thin-walled box beam members, particularly for the ones with high ratios between the height and the thickness of the cross-section. Numerical study of incidence of compressive forces on lateral buckling resistance of thin-walled box beam is investigated. [ABSTRACT FROM AUTHOR]

Abstract: The present study is concerned with the elastic/plastic buckling of thin rectangular plates under various loads and boundary conditions. The in-plane loads are placed uniformly and linearly varying in the uniaxial compression and biaxial compression/tension. The equilibrium and stability equations are derived and analyses are carried out based on two theories of plasticity, i.e. deformation theory (DT) and incremental theory (IT). The elastic/plastic behavior of plates is described by the Ramberg–Osgood model. Generalized Differential Quadrature (GDQ) discretization technique is used to solve the buckling of plate equation. To examine accuracy of the present formulation and procedure, several convergence and comparison studies are investigated and new results are presented. The differences between the IT and DT results increase by increasing loading parameter in linearly varying in-plane loading. Some new consequences are achieved regarding the validation range of two theories. Furthermore, effects of aspect, thickness to length and loading ratios, boundary condition, type of plasticity theory and linearly varying in-plane loading on the buckling coefficient are discussed. Contour plots of buckling mode shapes for various loading parameters are also illustrated. [Copyright &y& Elsevier]

Abstract: Axial deformation is not involved in the formulation of linear buckling caused by axial force. Likewise, twisting is not present in linear buckling caused by axial torque. The dynamic axial–torsional buckling of structural frames in the presence of follower axial force will be solved by means of dynamic stiffness using power series. Variationally consistent natural boundary conditions are given so that the resulting dynamic stiffness is symmetrical for conservative loading. Some parts of the boundary forces disappeared for follower axial forces due to consistent tangency to the neutral axis. The deficiency of the power series method to deal with non-uniform sections is highlighted. New instability phenomena for a simple column are studied in detail. It is shown that columns can buckle under direct follower tension. Follower tension decreases the natural frequency initially and then increases it rapidly after a turning point. The first pair of modes about the major axis and that about the minor axis of a rectangular section column meet at one crossing point. A very small axial torque will change the crossing into flutter-like tongues. These tongues are common in compressive follower force. These tongues caused by axial torque are reported here for the first time. [Copyright &y& Elsevier]

Semi-analytical models for the linear buckling analysis of unstiffened laminated composite cylinders and cones with flexible boundary conditions are presented. The Classical Laminated Plate Theory and the First-order Shear Deformation Theory are used in conjunction with the Donnell’s non-linear equations to derive the buckling equations. Axial, torsion and pressure loads can be applied individually or combined in the proposed models. The stiffness matrices are integrated analytically and for the conical shells an approximation is proposed to overcome non-integrable expressions. Comparisons with the literature show that the classical base functions available for axial compression cannot capture the buckling modes for non-orthotropic laminates. For torsion loads these classical shape functions do not catch the buckling modes even when applying the assumption of pure orthotropy, and it is shown how the proposed models correlate well with experimental data from the literature and finite element results. The use of elastic constraints at the boundaries allows the simulation of different boundary conditions in a versatile way and it is shown how those constants can be adjusted in order to change from one type of boundary condition to another. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the buckling analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under various in-plane mechanical loads, using the element-free kp-Ritz method. The first-order shear deformation plate theory is applied and a set of mesh-free kernel particle functions are used to approximate two-dimensional displacement fields. Effective properties of materials of the plates reinforced by single-walled carbon nanotubes (SWCNTs) are estimated through a micromechanical model based on either the Eshelby–Mori–Tanaka approach or the extended rule of mixture. Comparison study and numerical simulations with various parameters are conducted to assess efficacy and accuracy of the present method for analysis of buckling of SWCNT-reinforced composite plates. Results demonstrate that the change of carbon nanotube volume fraction, plate width-to-thickness ratio, plate aspect ratio, loading condition and temperature have pronounced effects on buckling strength of CNTRC plates as well as the boundary condition. [Copyright &y& Elsevier]

Abstract: In this work, we present analytic formulas for calculating the critical buckling states of some plastic axial columns of constant cross-sections. The associated critical buckling loads are calculated by Euler-type analytic formulas and the associated deformed shapes are presented in terms of generalized trigonometric functions. The plasticity of the material is defined by the Hollomon''s power-law equation. This is an extension of the Euler critical buckling loads of perfect elastic columns to perfect plastic columns. In particular, critical loads for perfect straight plastic columns with circular and rectangular cross-sections are calculated for a list of commonly used metals. Connections and comparisons to the classical result of the Euler–Engesser reduced-modulus loads are also presented. [Copyright &y& Elsevier]

Buckling of a column made of functionally graded material is investigated. The functional grading is performed in the longitudinal direction. The following problem is addressed: determine the variation of the elastic modulus with the axial coordinate such that the buckling load exceeds the preselected value. In this study, only polynomial variation of the buckling mode is considered and only the case of cantilever column is treated. [ABSTRACT FROM AUTHOR]

In this study, the influence of nonuniformity of eccentricity of stringers on the general axial buckling load of stiffened laminated cylindrical shells with simply supported end conditions is investigated. The critical loads are calculated using Love's First-order Shear Deformation Theory and solved using the Rayleigh-Ritz procedure. The effects of the shell length-to-radius ratio, shell thickness-to-radius ratio, number of stringers, and stringers depth-to-width ratio on the buckling load of nonuniformly eccentric shells, are examined. The research demonstrates that an appropriate nonuniform distribution of eccentricity of stringers leads the buckling load to increase significantly. [ABSTRACT FROM AUTHOR]

Abstract: The paper deals with the theoretical prediction of buckling loads for symmetric angle-ply and cross-ply laminated flat composite columns, consisting of two portions of different widths connected by fillets. The buckling loads of the column under axial compression were obtained for the following end conditions: simply supported, simply-clamped, clamped-clamped, and clamped free. Based on the first order shear deformation theory (FSDT), finite elements method (FEM) with FORTRAN computer language was exploited to obtain the critical buckling loads. The effects of orientation angles, fillet radius, column thickness and wideness, and modulus ratios on the buckling load were investigated. The results were presented in both graphical and tabular forms. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin''s approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented. [Copyright &y& Elsevier]

Abstract: Higher order shear deformation theory (HSDT) is reformulated using the nonlocal differential constitutive relations of Eringen. The equations of motion of the nonlocal theories are derived. The developed equations of motion have been applied to study buckling characteristics of nanoplates such as graphene sheets. Navier''s approach has been used to solve the governing equations for all edges simply supported boundary conditions. Analytical solutions for critical buckling loads of the graphene sheets are presented. Nonlocal elasticity theories are employed to bring out the small scale effect on the critical buckling load of graphene sheets. Effects of (i) nonlocal parameter, (ii) length, (iii) thickness of the graphene sheets and (iv) higher order shear deformation theory on the critical buckling load have been investigated. The theoretical development as well as numerical solutions presented herein should serve as reference for nonlocal theories as applied to the stability analysis of nanoplates and nanoshells. [Copyright &y& Elsevier]

Abstract: Dynamic buckling analysis of FGM plates has not been accomplished so far. In the present paper, vibration and dynamic buckling of FGM rectangular plates with surface-bonded or embedded piezoelectric sensors and actuators subjected to thermo-electro-mechanical loading conditions are investigated. A finite element formulation based on a higher-order shear deformation theory is developed. Both initial geometric imperfections of the plate and temperature-dependency of the material properties are taken into account. Dynamic buckling of plates already pre-stressed by other forms of loading conditions is assumed to occur under suddenly applied thermal or mechanical loads. A nine-node second order Lagrangian element, an efficient numerical algorithm for solving the resulted highly non-linear governing equations, and an instability criterion already proposed by the author are employed. A simple negative velocity feedback control is used to actively control the dynamic response of the plate. Results show that generally, initial geometric imperfections lead to an increased fundamental bending natural frequency and decreased buckling loads. Furthermore, buckling mitigation due to utilizing integrated piezoelectric sensors and actuators is mainly achieved in extremely high gain values. Therefore, the piezoelectricity effect on the buckling load is small in applicable voltages. It is also noticed that the temperature-dependency and initial geometric imperfections remarkably affect the buckling loads. [Copyright &y& Elsevier]

This article presents an analytical approach for evaluating the buckling load of sandwich panels made of hybrid laminated faces and a transversely flexible core. Useful design indications are obtained once the influence of main parameters influencing the structural response is examined. The proposed model is based on a priori assumption of the displacement field through the thickness, which is composed of two sets of modal configurations, one symmetric and one antisymmetric, besides a pure compressive mode. An equivalent `single layer approach', considering all displacement components (u, v, w) that linearly vary across the panel thickness, is used. For simply supported flat sandwich panels subjected to in-plane biaxial and shear loads, the Rayleigh-Ritz method is used to evaluate the buckling loads. Predictions of the proposed model are compared with those obtained by other available theoretical models and with experimental results. Finally, the best arrangement of sandwich panels, corresponding to the maximum buckling loads, is investigated by varying the parameters of both the faces and the core material. [ABSTRACT FROM AUTHOR]

Abstract: The load-resisting capacity of buckling-restrained braces (BRB) composed of an H-shaped core element and an external tube was investigated in this study by component testing. A study was carried out on the effect of the design parameters such as the thickness of the constraining tube and the length of the unconstrained length of the core ends on the maximum strength and the energy dissipation capability. The performance of the BRB was evaluated by comparing the test results with the recommended provisions for BRB. It was found that the thickness of the external tube and the unconstrained part of the core had a significant effect on the strength and hysteretic behavior of the BRB; with the correct thickness of external tube and unconstrained length, the BRB behaved stably throughout the cyclic loading history until the cumulative plastic deformation reached 330, which far exceeded the value of 200 required by the recommended provisions. [Copyright &y& Elsevier]

The paper deals with the effect of moisture and temperature on the buckling response of a laminated composite plate subjected to hygrothermomechanical loadings. Mechanical loading consists of uniaxial, biaxial, and shear. The distribution of temperature and moisture on the surface is considered to be uniform. The degradation in material properties due to moisture and temperature is taken into account using a micromechanical model. The mathematical formulation is based on higher order shear deformation theory and von Karman's nonlinear kinematics. A C0 finite-element method based on higher-order shear deformation plate theory is used for deriving the standard Eigenvalue problem. ATaylor series based mean-centered first-order perturbation technique is used to find out the second-order statistics of the hygrothermal buckling loads. The effects of temperature rise, moisture concentration, fiber-volume fraction, and plate parameters on buckling response of the plate are presented. [ABSTRACT FROM AUTHOR]

Post-buckling behaviour of sandwich plates with functionally graded material (FGM) face sheets under uniform temperature rise loading is considered. It is assumed that the plate is in contact with a Pasternak-type elastic foundation during deformation, which acts in both compression and tension. The derivation of equations is based on the first-order shear deformation plate theory. Thermomechanical non-homogeneous properties of FGM layers vary smoothly by the distribution of power law across the thickness, and temperature dependency of material constituents is taken into account. Using the non-linear von-Karman strain-displacement relations, the equilibrium and compatibility equations of imperfect sandwich plates with FGM face sheets are derived. The boundary conditions for the plate are assumed to be simply supported in all edges. The governing equations are reduced to two coupled equation in terms of stress function and lateral deflection. Employing the single mode approach combined with Galerkin technique, an approximate closed-form solution is presented to calculate the critical buckling temperature and post-buckling equilibrium path of the plate. Presented numerical examples contain the influences of power law index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation coefficients. [ABSTRACT FROM AUTHOR]

Abstract: This study presents the analytical, numerical, and experimental results of thin hemispherical metal shells into the plastic buckling range illustrating the importance of geometry changes on the buckling load. The hemispherical shell is rigidly supported around the base circumference against horizontal and vertical translation and the load is vertically applied by a rigid cylindrical boss at the apex. Kinematics stages of initial buckling and subsequent propagation of plastic deformation for rigid-perfectly plastic shells are formulated on the basis of Drucker–Shield''s limited interaction yield condition. The effect of the radius of the boss, used to apply the loading, on the initial and subsequent collapse load is studied. In the numerical model, the material is assumed to be isotropic and linear elastic perfectly plastic without strain hardening obeying the Tresca or Von Mises yield criterion. Both axisymmmetric and 3D models are implemented in the numerical work to verify the presence of non-symmetric deformation modes in the case of thin shells. In the end, the results of the analytical solution are compared and verified with the numerical results using ABAQUS software and experimental findings. Good agreement is observed between the load–deflection curves obtained using three different approaches. A secondary bifurcation point is detected in thin shells in which the deformation degenerates from symmetric to non-symmetric behavior. The bifurcation point depends on the (R/t 0) ratio and the material parameters. [Copyright &y& Elsevier]

Abstract: By means of geometrically non-linear modeling of the test process for high-quality specimens of thin-walled cylinders using a shell finite element implemented in ANSYS, it has been proved that this numerical approach is applicable for design of real axially compressed circular cylindrical shells under external local quasi-static loads. [Copyright &y& Elsevier]

Abstract: This paper presents and illustrates a GBT formulation to analyse the elastic localized web buckling of thin-walled steel beams under concentrated loads. The theme of localised web buckling is first introduced by describing the parameters that most influence the buckling behaviour of slender plates subjected to edge loads. After that, a GBT formulation to analyse the elastic localized web buckling of thin-walled steel beams under concentrated loads is presented: the GBT equations are derived and the determination of deformation modes is briefly addressed. Then, two illustrative examples are shown and validated by comparison with shell finite element results: (i) cold-formed steel plain channel beams with web crippling configurations and (ii) welded steel I-section beams with patch loading configurations. It is found that both pre-buckling longitudinal normal () and shear () stresses have to be included in the buckling analyses of cold-formed steel beams with External One Flange (EOF) and Internal One Flange (IOF) configurations as well as welded steel beams with Patch Loading Test (PLT) configuration. Furthermore, the pre-buckling transverse normal () stresses have to be included in the buckling analysis of cold-formed steel beams with External Two Flange (ETF) and Internal Two Flange (ITF) configurations as well as welded steel beams with Opposite Patch Loading Test (OPLT) configuration. In beams with EOF, IOF, PLT configurations, the GBT pre-buckling analysis should consider global and shear modes while the GBT buckling analysis may only consider local modes. In beams with ETF, ITF, OPLT configurations, the GBT pre-buckling analysis should consider transverse extension modes while the GBT buckling analysis may only consider local modes. [Copyright &y& Elsevier]

Abstract: The structural behaviour of elliptical hollow sections has been examined in previous studies under several loading conditions, including pure compression, pure bending and combined uniaxial bending and compression. This paper examines the elastic buckling response of elliptical hollow sections under any linearly varying in-plane loading conditions, including the most general case of combined compression and biaxial bending. An analytical method to predict the elastic buckling stress has been derived and validated against finite element results. The predictive model first identifies the location of the initiation of local buckling based on the applied stress distribution and the section geometry. The critical radius of curvature corresponding to this point is then introduced into the classical formula for predicting the elastic local buckling stress of a circular shell. The obtained analytical results are compared with results generated by means of finite element analysis. The comparisons between the analytical and numerical predictions of elastic buckling stress reveal disparities of less than 2.5% for thin shells and, following an approximate allowance for the influence of shear, less than 7.5% for thick shells. [Copyright &y& Elsevier]

Cellular beams with circular, oval and sinusoidal openings are used in construction practice now. The problems of determination of deformations of such beams and critical loads under local buckling of web are considered. Calculation of cellular I-beams deformations was performed using the finite element method. Critical loads were also determined with the numerical calculation by FEM. [ABSTRACT FROM AUTHOR]

Abstract: The flatwise compressive behaviour of tetrachiral and hexachiral honeycombs is analysed, using analytical and Finite Element simulations, both with explicit and implicit formulations. The tetrachiral and hexachiral cells are composed by cylinders connected by four and six tangent ligaments respectively. The ligaments act as mixed stiffeners-elastic foundations during flatwise compressive loading, providing different buckling mode shapes during deformation. The models are compared with experimental results obtained using RP-based honeycombs tested according to ASTM C 393-00 and ASTM C365-00. [Copyright &y& Elsevier]

Abstract: Thin-walled structures usually collapse in Eulerian buckling mode under oblique loads. Energy absorption capacity and crush force efficiency of the structure in this type of collapse are low. Collapse initiators are used to improve these properties. In this research, effect of collapse initiators on energy absorption characteristics of square tubes under oblique quasi-static loads is investigated both experimentally and numerically. Initiators are in the form of cuttings on the tube corners. Results show that collapse initiators in most of the specimens change deformation mode from general buckling to progressive buckling and decrease considerably the peak load; therefore increase crush force efficiency. Furthermore, effect of location and number of initiators is studied. There is good agreement between the numerical results and data from experiments. [Copyright &y& Elsevier]

This paper presents a study of buckling and postbuckling behaviour of simply supported composite plates subjected to nonuniform in-plane loading. The mathematical model is based on higher order shear deformation theory incorporating von Kármán nonlinear strain displacement relations. Because the applied in-plane edge load is nonuniform, in the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using these stress distributions, the governing equations for postbuckling analysis of composite plates are obtained through the theorem of minimum potential energy. Adopting Galerkin's approximation, the governing nonlinear partial differential equations are reduced into a set of nonlinear algebraic equations in the case of postbuckling analysis, and homogeneous linear algebraic equations in the case of buckling analysis. The critical buckling load is obtained from the solution of associated linear eigenvalue problem. Postbuckling equilibrium paths are obtained by solving nonlinear algebraic equations employing the Newton-Raphson iterative scheme. Explicit expressions for the plate in-plane stress distributions within the prebuckling range are reported for isotropic and composite plates subjected to parabolic in-plane edge loading. Buckling loads are determined for three plate aspect ratios (a/b=0.5, 1, 1.5) and three different types of in-plane load distributions. The effect of shear deformation on the buckling loads of composite plate is reported. The present buckling results are compared with previously published results wherever possible. [ABSTRACT FROM AUTHOR]

Some 250 years after the systematic experiments by Musschenbroek and their rationalization by Euler, for the first time we show that it is possible to design structures (i.e. mechanical systems whose elements are governed by the equation of the elastica) exhibiting bifurcation and instability (‘buckling’) under tensile load of constant direction and point of application (‘dead’). We show both theoretically and experimentally that the behaviour is possible in elementary structures with a single degree of freedom and in more complex mechanical systems, as related to the presence of a structural junction, called ‘slider’, allowing only relative transversal displacement between the connected elements. In continuous systems where the slider connects two elastic thin rods, bifurcation occurs both in tension and in compression, and is governed by the equation of the elastica, employed here for tensile loading, so that the deformed rods take the form of the capillary curve in a liquid, which is in fact governed by the equation of the elastica under tension. Since axial load in structural elements deeply influences dynamics, our results may provide application to innovative actuators for mechanical wave control; moreover, they open a new perspective in the understanding of failure within structural elements. [ABSTRACT FROM AUTHOR]

Abstract: This paper addresses the buckling and vibration analysis of isotropic and laminated plates by a first-order shear deformation theory. The numerical approach is based on collocation with radial basis functions. The model allows the analysis of arbitrary boundary conditions and irregular geometries. It is shown that the present method, based on a first-order shear deformation theory produces highly accurate natural frequencies and modes of vibration, as well as critical loads and modes. [Copyright &y& Elsevier]

This paper presents an analytical approach for pre-buckling and buckling analyses of thin-walled members implemented within the framework of the Generalised Beam Theory (GBT). With the proposed GBT cross-sectional analysis, the set of deformation modes used in the analysis is represented by the dynamic modes obtained for an unrestrained frame representing the cross-section. In this manner, it is possible to account for the deformability of the cross-section in both pre-buckling and buckling analyses. Different loading conditions, including both axial and transverse arrangements, are considered in the applications to highlight under which circumstances the use of the GBT deformation modes is required for an adequate representation of the pre-buckling and buckling response. The numerical results have been validated against those determined using a shell element model developed in the finite element software ABAQUS. [ABSTRACT FROM AUTHOR]

Abstract: The critical buckling load of a structure undergoing lateral buckling can be determined experimentally by using the extrapolation or plotting techniques, without having to subject the structure to loading in the vicinity of critical. To achieve this, it is only necessary to have data relating load to a deformation characteristic. A search of the literature reveals that only certain and just a few deformation characteristics such as lateral displacement and/or twist have mostly been used by researchers in this regard. In this paper, the feasibility of application of various deformation variables for experimental determination of the critical buckling load is investigated in case of I-beams with different initial geometrical imperfections undergoing the elastic lateral–distortional mode of buckling. It is demonstrated that lateral displacement of the I-beams is directly coupled with different deformation variables such as web transverse and longitudinal strains, vertical deflection, and angles of twist of top and bottom flanges. Based on these key findings, the Southwell, Massey, Modified, and Meck Plot methods are applied on these various deformation variables, and consequently satisfactory and reliable estimates are obtained for the critical buckling loads. Finally, it may be concluded that the application of the extrapolation techniques does not actually need to be limited to some certain deformation variables. [Copyright &y& Elsevier]

In the present study, the buckling behaviour of laminated composite skew plates with different boundary conditions subjected to linearly varying in-plane loads are presented. The skew plate is modelled based on higher order shear deformation theory, which accurately predicts the buckling behaviour for the thick plate. The in-plane stress distribution within the skew plate due to linearly varying in-plane load is equal to the applied in-plane edge load in the pre-buckling range. Using these in-plane stress distributions, the total potential energy functional is formulated. Total potential energy is a function of the total strain energy of skew plate and potential energy due to in-plane stress distributions. The total strain energy of skew plate contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total potential energy functionals mapped from physical domain to computational domain over which a set of orthonormal polynomials satisfying the essential boundary conditions is generated by Gram–Schmidt orthogonalization process. Using a Rayleigh-Ritz method in conjunction with Boundary Characteristics Orthonormal Polynomials, the total potential energy functional is converted into sets of algebraic equations. Finally, these algebraic equations are rearranged as a linear eigenvalue problem, which is solved to obtain the critical buckling loads. The numerical results are presented for different skew angles, boundary conditions, length to thickness ratios, aspect ratios and in-plane loadings. It is observed that the critical buckling load increase with the increase of skew angle as well as change in the mode shape at a lower aspect ratio with the increase of skew angle. [ABSTRACT FROM AUTHOR]

Highlights: [•] Timoshenko column in presence of an arbitrary number of concentrated cracks is considered. [•] Cracks have been modeled as concentrated reduction of the flexural stiffness. [•] Explicit expressions of buckling shapes and the buckling load equations are proposed. [•] Tensile buckling phenomenon is captured by the proposed explicit solutions. [•] The influence of multiple cracks on the tensile and the compressive buckling is assessed. [Copyright &y& Elsevier]

In this research, a size-dependent first-order shear deformable model is developed based on the Mindlin's strain gradient elasticity theory to analyze the free vibration and axial buckling of circular cylindrical micro-/nano-shells. The size-dependent governing equations and corresponding boundary conditions are established through Hamilton's principle. For some specific values of the gradient-based material parameters, the most general form of shell formulation can be reduced to those based on simple forms of the strain gradient elasticity theory such as the modified strain gradient theory (MSGT), modified couple stress theory (MCST) and strain gradient theory (SGT). To illustrate the characteristics of a micro-/nano-shell obtained by the size-dependent shell formulation, the axial buckling and free vibration problems of a simply-supported (SS) microshell are analyzed by employing a Navier-type solution. Selected numerical results are presented to get an insight into the effects of dimensionless material length scale parameters, length-to-radius ratio and circumferential mode number on the non-dimensionless natural frequencies and buckling loads. For comparison purpose, the non-dimensional natural frequencies and buckling loads predicted by MSGT, MCST, SGT and classical theory (CT) are also presented. It is shown that the effect of small scale is more prominent for lower values of dimensionless length scale parameter. [ABSTRACT FROM AUTHOR]

An unconstrained gusset connection for buckling restrained braces in reinforced concrete frame structures is proposed and tested as an effort to mitigate the complicated and usually harmful interactions between the steel gusset plate and the adjoining reinforced concrete column. Local damage control incorporating the rearrangement of beam flexural strength is also proposed to enhance the reliability of the gusset connection by moving the potential plastic hinge of the beam away from the connection region. Two different connecting methods, one with posttensioned steel rods and the other embedded stud groups, were considered. The results of the cyclic loading tests on reinforced concrete (RC) beam-gusset connection subassemblies confirmed that both connecting methods are available as long as the local damage control is implemented, which is not only helpful in eliminating the unfavorable deformation loss at the connection, but more importantly, can prevent the buckling restrained braces (BRBs) from being dislocated as a result of the beam end failure in extreme earthquake events. [ABSTRACT FROM AUTHOR]

Abstract: A solution is proposed to the buckling problem formulated for a rectangular sandwich plate having all the edges fully clamped (CCCC plate) and subjected to a uniaxial compressive loading. The analysis of the out-of-plane deformation of the buckled plate is based on the equations of the first order shear deformation theory (FSDT). Galerkin method has been employed to solve the problem. Variations of the plate deflection and angles of rotation between the unloaded edges have been approximated using the solution to the bending problem for the shear deformable beam with clamped ends. The approximation of these variables between the loaded edges has been performed using trigonometry series. The solution to the problem is reduced to the calculation of the eigenvector of corresponding homogeneous system of linear equations and determination of its least component. Verification of the solution obtained has been performed using finite-element analysis. [Copyright &y& Elsevier]

Abstract: A semi-analytical method is developed for pre-buckling and buckling analyses of thin, symmetrically laminated composite panels with an elliptical cutout at an arbitrary location and orientation under general thermo-mechanical loading conditions. Both the pre-buckling and buckling analyses are based on the principle of stationary potential energy utilizing complex potential functions and complete polynomials. The complex potential functions capture the steep stress gradients and local deformations around the cutout, and the “complete” polynomials improve the global buckling response of the laminate. The complex potential functions in the pre-buckling state automatically satisfy the in-plane equilibrium equations, thus reducing the first variation of the total potential energy in terms of line integrals only. Because the complex potential functions for out-of-plane displacements are augmented by the “complete” polynomials, the area integral terms in the second variation of the total potential energy, referred to as the Treftz criterion, are retained in the buckling analysis. The kinematic boundary conditions are idealized by employing extensional and rotational springs (elastic restraints) with appropriate stiffness values. Based on the numerous validation problems, this analysis is proven credible for predicting the buckling load of rectangular and non-rectangular panels with a cutout. [Copyright &y& Elsevier]

Long-term large deformation geohazards can impose excessive deformation on a buried pipeline. The ground displacement field may initiate pipeline deformation mechanisms that exceed design acceptance criteria with respect to serviceability requirements or ultimate limit states. The conventional engineering approach to define the mechanical performance of pipelines has been based on combined loading events for in-air conditions. This methodology may be conservative, as it ignores the soil effect that imposes geotechnical loads, and also provides restraint, on buried pipelines. The importance of pipeline-soil interaction and load-transfer mechanisms that may affect local buckling of buried pipelines is not well understood. A three-dimensional continuum finite element model, simulating the local buckling response of a buried pipe, using the software package ABAQUS/Standard was developed and calibrated. A comprehensive parametric study was previously conducted to investigate the effect of several parameters on local buckling response of pipelines buried in firm clay. A new strain criterion for local buckling of buried pipelines in firm clay through response surface methodology was developed. In this paper, the new criterion is compared with several existing in-air criteria to study the effect of soil restraint on the local buckling response of buried pipelines. The criterion developed in this study predicts greater characteristic critical strain capacity than in-air based criteria that highlights the influence of soil restraint. [ABSTRACT FROM AUTHOR]

In this paper the correlation of deformation energy and critical buckling loads is examined. An advanced analysis technique is derived for the investigation of z-section frames typically applied in composite aircraft fuselage. This technique is verified through closed form solutions of z-section columns under quasi-static loading conditions. The method is applied to study the effects of flange width and laminate thickness on the critical failure modes of composite frames. Therein, the focus is on composite structural elements favourable for deformation kinematics in aerospace applications subjected to crash loads. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an efficient mathematical model for studying the buckling behavior of geometrically perfect elastic two-layer composite columns with interlayer slip between the layers. The present analytical model is based on the linearized stability theory and is capable of predicting exact critical buckling loads. Based on the parametric analysis, the critical buckling loads are compared to those in the literature. It is shown that the discrepancy between the different methods can be up to approximately 22%. In addition, a combined and an individual effect of pre-buckling shortening and transverse shear deformation on the critical buckling loads is studied in detail. A comprehensive parametric analysis reveals that generally the effect of pre-buckling shortening can be neglected, while, on the other hand, the effect of transverse shear deformation can be significant. This effect can be up to 20% for timber composite columns, 40% for composite columns very flexible in shear (pyrolytic graphite), while for metal composite columns it is insignificant. [Copyright &y& Elsevier]