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Curved nanobeams are one of the essential components in manufacturing nano-electromechanical systems needing nonlinear stability design. In the current investigation, the nonlinear buckling characteristics of functionally graded porous reinforced curved (FGPRC) nanobeams having different degrees of curvature are analyzed by counting the higher-order gradients of the classical strain tensor as well as nonlocal-type interatomic interactions. In this regard, two independent length-scale constants within the framework of the nonlocal strain gradient theory (NSGT) of continuum elasticity are taken into account. Via employing the promising low computational cost and geometrically adaptable method of isogeometric collocation, various branches of NSGT-based equilibrium graphs of FGPRC nanobeams are plotted relevant to each considered degree of curvature. It is extrapolated that the quantity of graphene platelet (GPL) weight fraction has a negligible influence on the significance of nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect in the value of the maximum deflections or lateral loads at the detected limit points, especially attributed to a higher degree of curvature. Besides, it can be remarked that, in the FGPRC nanobeam owning a small degree of curvature, lessening the quantity of porosity index results in an increment in the significance of the nonlocal-type of interatomic size dependency as well as the strain gradient kind of small-scale effect on the maximum deflection at both upper and lower limit points. However, in the FGPRC nanobeams owning medium and large degrees of curvature, it gets lesser at the upper limit point, but becomes higher at the lower limit one. [ABSTRACT FROM AUTHOR]

Natural fibers have been extensively researched as reinforcement materials in polymers on account of their environmental and economic advantages in comparison with synthetic fibers in the recent years. Bamboo fibers are renowned for their good mechanical properties, abundance, and short cycle growth. As beams are one of the fundamental structural components and are susceptible to mechanical loads in engineering applications, this paper performs a study on the free vibration and buckling responses of bamboo fiber reinforced composite (BFRC) beams on the elastic foundation. Three different functionally graded (FG) layouts and a uniform one are the considered distributions for unidirectional long bamboo fibers across the thickness. The elastic properties of the composite are determined with the law of mixture. Employing Hamilton's principle, the governing equations of motion are obtained. The generalized differential quadrature method (GDQM) is then applied to the equations to obtain the results. The achieved outcomes exhibit that the natural frequency and buckling load values vary as the fiber volume fractions and distributions, elastic foundation stiffness values, and boundary conditions (BCs) and slenderness ratio of the beam change. Furthermore, a comparative study is conducted between the derived analysis outcomes for BFRC and homogenous polymer beams to examine the effectiveness of bamboo fibers as reinforcement materials, demonstrating the significant enhancements in both vibration and buckling responses, with the exception of natural frequencies for cantilever beams on the Pasternak foundation with the FG-⟡) fiber distribution. Eventually, the obtained analysis results of BFRC beams are also compared with those for carbon nanotube reinforced composite (CNTRC) beams found in the literature, indicating that the buckling loads and natural frequencies of BFRC beams are lower than those of CNTRC beams. [ABSTRACT FROM AUTHOR]

The present paper provides an analysis to obtain the critical buckling load and vibration frequencies of the sandwich cylindrical panel with functionally graded (FG) face sheets and FG porous core resting on an elastic foundation, subjected to mechanical load and in thermal environments. The panel is formulated within the framework of the nonlocal strain gradient theory for shell model and classical shell theory. Based on Hamilton's principle and Galerkin's method, the effects of nonlocal and strain gradient parameters, materials and geometrical characteristics, porosity, temperature and elastic foundation on buckling load, fundamental frequencies, and dynamic response of the panel are considered. [ABSTRACT FROM AUTHOR]

In this work, a nonlocal strain gradient model for the buckling analysis of functionally graded Euler–Bernoulli beam subjected to thermo-mechanical loads is developed. The governing equations are derived by incorporating the effects of nonlocal and strain gradient parameters. Thermal properties over the cross section are graded using the power law. The resulting sixth-order differential equation is solved analytically for various boundary conditions. The effect of strain gradient and nonlocal parameters on the variation of critical buckling temperature under three different boundary conditions and three different thermal loading conditions is studied. The proposed model compares well with the existing literature in the limiting sense of no nonlocal and gradient effects. [ABSTRACT FROM AUTHOR]

Abstract This paper was dealt with buckling and post-buckling behavior of short thin-walled Z-columns made of a carbon-epoxy laminate, subjected to eccentric compressive load. The buckling mode and the buckling load of real structures versus load eccentricity were discussed. The study involved both experimental tests were carried out on real laminated structures and numerical simulations by the finite element method. The buckling load of real structures was determined by approximation methods on the basis of experimental and numerical post-buckling equilibrium paths of the structure. Additionally, in numerical simulations, the bifurcation load value was determined by solving an eigen problem. In all cases, experimental findings and numerical results show high agreement. The study determined the quantitative influence of the direction and value of compressive load eccentricity on the buckling load and rigidity of the structure in the post-buckling state. [ABSTRACT FROM AUTHOR]

Abstract The suggested before energy barrier criterion for design buckling pressure is extended to the case of clamped shallow spherical caps. It is developed for shells with geometrical imperfections and a new adjusted formula is obtained for design buckling load of imperfect structures. The method is applied to shells with elastic-perfectly plastic material. It is validated by experimental data and proved by numerical analysis based on finite element method. Calculation results were obtained and analysed for different values of shell geometrical parameter. A simple formula for design buckling pressure is suggested and validated. [ABSTRACT FROM AUTHOR]

Abstract Repair of a composite laminate with delamination using micro-bolts is studied parametrically. The effects on compressive buckling load of delamination crack length, bolt material, bolt diameter and arrangement, and bolt–laminate clearance are considered. For 45- and 65-mm crack lengths, buckling load recovery rates using brass bolts are 90% and 73%, respectively. Using steel increases the rate by 6.6% compared to the intact specimen. Tests are performed fixing the number of steel bolts for bolt diameters of 0.6, 1.0, and 1.2 mm. The buckling load recovery rate using 1.2- versus 0.6-mm bolts increases by 6.8%. Finite element analysis confirms the effect of the bolt–laminate gap: 27% larger buckling load for no clearance than for a 0.1-mm gap. 18% higher buckling load, which is 97% of intact-specimen buckling load, is obtained for a 1.2-mm-diameter bolt repair by gluing bolts and holes and then tightening them compared with using bolts alone. [ABSTRACT FROM AUTHOR]

Abstract The present paper deals with the description of the stability loss and postbuckling for multilayered composite structures. Both, the experimental results and theoretical predictions are presented and discussed. The wide literature review is also pointed out considering the issue of both experimental and theoretical buckling analyses for composite rectangular plates and shells. A special attention is focused on the buckling and postbuckling behaviour od structures with cutouts and reinforcement. [ABSTRACT FROM AUTHOR]

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]

Abstract In this work, a formulation for buckling and geometrically nonlinear analysis of functionally graded plates under thermo-mechanical loading is presented. The influence of high temperature environment on deflections due to mechanical loading as well the deflections produced by thermal loads acting alone or combined with mechanical loads is analysed. The implemented finite element model is based on a non-conforming triangular flat plate/shell element, with three nodes and eight degrees of freedom per node, associated with a higher order shear deformation theory. The solutions of some illustrative examples are evaluated involving the variation of volume fractions of constituent materials, temperature range and material combinations, which have significant impact on the deflections of plates. The numerical results obtained with the present model are presented and compared with alternative solutions. [ABSTRACT FROM AUTHOR]

Design specifications in North America, unlike their European counterpart, use same equations for design of rolled and welded shape beams for lateral torsional buckling (LTB). A recent study by MacPhedran and Grondin (2011) has shown that the current Canadian design equations might overestimate the capacity of welded wide flange (WWF) beams, which are welded I-shapes, requiring further investigation. This paper evaluates the performance of the current design equations for LTB capacities of welded I-shape beams. Nonlinear Finite Element (FE) analysis is performed for simply supported WWF beams subjected to constant moment, linear and nonlinear moment gradient. Three types of linear moment gradients are investigated: end moment ratios of 0.5, 0.0, and − 1.0. Also, two types of transverse loadings are considered: a concentrated load at mid-span and uniformly distributed load along the length, and applied at the top flange, shear center, and at the bottom flange. In total, 416 FE models are analyzed and it is observed that for constant moment loading both CSA and AISC overestimate the LTB capacity of welded I-shape beams by as much as 37%. FE analysis also shows that current CSA strength curve overestimates significantly the strength of WWF beams by as much as 40% for end moment ratio of 0.5. For transverse loading, current CSA strength curve overestimates the capacity significantly for top flange loading and underestimates for bottom flange loading. Also, Eurocode is found to be conservative for all cases and the proposed equation by MacPhedran and Grondin (2011) provides better predictions of LTB strengths of WWF shapes than the current CSA approach. [ABSTRACT FROM AUTHOR]

Compressed reinforcements on reinforced concrete (RC) and steel fibre reinforced concrete (SFRC) columns are generally submitted to cyclic and monotonic loading, which can buckle. This phenomenon can cause the reduction of both ductility and peak loads, which is why design standards propose constructive details to avoid this. Although the bibliography mentions that steel fibres in concrete can delay buckling of reinforcements, design codes do not distinguish between concrete types (with and without fibres) in these constructive details. Analytical models that determine the length and critical buckling stress of reinforcements may consider this effect. Nowadays, analytical models can be classified as discrete and distributed depending on whether they consider transverse reinforcement stiffness and the stiffness of the concrete cover that concentrates on transverse reinforcements, or if they are distributed along the element, respectively. Both discrete and distributed models are valid for small transverse reinforcement separations, while distributed models that only consider the concrete cover effect are valid for large transverse reinforcement separations. This paper proposes a mixed model to determine critical buckling loads of compressed reinforcements subjected to monotonic loading to use the stress-strain relationships of reinforcing bars, including buckling, that are found in the scientific-technical literature. This model considers transverse reinforcements discretely and concrete cover distributedly. The model can be applied to any transverse reinforcement configuration, and to any concrete type (with or without fibres). An analytical equation is also proposed to determine critical compressed reinforcement loads, whose result is presented as abaci. Finally, to calibrate the model in normal-strength concrete columns under eccentric loading, with or without fibres, a programme is presented in which the critical load of longitudinal reinforcements is experimentally determined. The proposed analytical model is calibrated and a procedure to determine critical buckling loads of compressed reinforcements under monotonic loading is proposed. [ABSTRACT FROM AUTHOR]

Stability is an important problem in applications of plate and shell structures as well as newly arisen nano-structures, such as nanotubes and graphene sheets. Most classical methods for stability analysis require buckling modes, which are difficult to be accurately predicted, especially for the structures with complex boundary boundaries and load conditions. In this paper, we propose a half-analytical method to predict the critical buckling of structures, named mode-independent energy-based buckling analysis method (MIEM), in which the buckling mode is not needed to be presupposed. The proposed MIEM shows great superiority in dealing with structure buckling under complicated loads and constraints. Besides, it is more suitable for large-scale nanostructures due to its extremely small amount of calculations, and the calculation amount can be further reduced for periodic structures. With the MIEM, the critical buckling of substrate-supported graphene sheets under complex strain states is investigated comprehensively. Furthermore, a unified criterion to predict the critical buckling of substrate-supported graphene is given by a simple expression, which could be of great help in design and manufacture of graphene-based electronics and devices. The MIEM developed in this paper can be used in buckling analysis of structures such as beams and plates as well. [ABSTRACT FROM AUTHOR]

In this paper, a new analytical approach is developed for global buckling of composite sandwich cylindrical shells with lattice cores under uniaxial compression by using the smeared stiffener method. The stiffness contribution of stiffeners is evaluated through the new force and moment effect analysis of the stiffener network on a general unit cell. In these analyses, outer skin-stiffener and inner skin-stiffener interactions are considered, appropriately. The equivalent stiffness of the composite sandwich cylindrical shells with lattice cores is then computed by superimposing the stiffness contribution of stiffeners, outer and inner skins. The critical buckling load is calculated by Rayleigh–Ritz method. Finally, various test examples with different scales of the structure, outer and inner skins ply stacking sequence, outer and inner skins thicknesses were analyzed and the results were compared with results obtained by finite element methods and other works. The results show that the proposed approach has high prediction accuracy and low computational cost for the global buckling analysis of composite sandwich shells with lattice cores. Also, another advantage of the developed approach is able to prediction of the global buckling load of stiffened composite cylindrical shells with better accuracy. Therefore, the proposed approach is highly attractive for the preliminary design of composite sandwich structures in the aerospace industry. [ABSTRACT FROM AUTHOR]

In this paper, we study buckling of radially FGM circular plates. In a previous study, a fourth-order polynomial expressing the exact solution of a linear elastic problem was used as buckling mode shape. To generalise such investigation, in this contribution the buckling mode is postulated to take the shape of a fifth-order polynomial function of the radial coordinate. The flexural rigidity is consequently sought as a polynomial of suitable order, expressing the functional grading. New solutions in closed form are then obtained by a semi-inverse method. It is found that suitable choices of functional grading may increase the buckling load up to 246% with respect to the homogeneous and uniform cases. [ABSTRACT FROM AUTHOR]

An exact free vibration and buckling analysis of a tapered beam-column with general connections is calculated. All structural elements are made of functionally graded material. In this study, a power function is assumed for the variation of the elastic modulus along the cross-section’s height. Extensional-coupling effects are considered in the proposed formulation. By solving the related fourth-order differential equation, the exact answers are obtained. The Bessel functions are utilized in this solution. In addition, the effect of connection flexibility is assessed by considering rotational and transitional springs at the two ends of the element. The suggested stiffness matrix can analyze the free vibration and buckling of a frame made of functionally graded material tapered beam-columns with semi-rigid connections and supports. To validate the proposed formulation, several benchmarks and novel examples are separately analyzed. All numerical findings clearly demonstrate the usefulness of the authors’ scheme. [ABSTRACT FROM AUTHOR]

Buckling loads of laminated panels calculated by analytical approaches are usually based on the assumptions that the panels are subjected to uniform in-plane edge loads without cutouts, despite of the fact that real structural components are subjected to various kinds of non-uniform in-plane edge loads along with different sized cutouts. The main objective of this paper is to study the effects of reinforced/unreinforced circular cutouts and non-uniform in-plane edge loads on the buckling behavior of composite panels with different ply-orientations by the finite element technique. Furthermore, it addresses the effects of different boundary conditions and thickness of panels. To carry out the analyses, a nine-noded heterosis plate element and a compatible three-noded beam element are developed, including the effect of shear deformation and rotary inertia for both the plate and the stiffeners. In structural modeling, the plate and the stiffener elements are treated separately, with their displacement compatibility maintained using transformation matrices. It has been illustrated in this study that presence of larger-sized reinforced cutouts predominantly increases the buckling strength of the panel as compared to those with smaller sized cutouts. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive test database of concentric compression experiments on pultruded fiber-reinforced polymer (PFRP) specimens that failed in a global flexural buckling mode published in literature between 1969 and 2016. A new closed-form equation to determine the reduction factor for global flexural buckling of PFRP structural struts under axial compression is developed on the basis of the Ayrton-Perry formula and observed initial out-of-straightness of PFRP members measured by other researchers. Recognizing that data on initial imperfections may be unavailable, a second new empirical closed-form equation is derived based upon the experimental database. Validation of the two explicit expressions is performed by both comparison to experimental data and comparison with validated numerical simulations. In addition, the accuracies of the two proposed equations are compared with those of five closed-form solutions available in the literature; both results in more accurate predictions than the extant equations. Both new proposed equations can be conveniently used by structural engineers at the preliminary engineering design stage for accurately assessing the reliability and safety of composite structures under concentric compressive loading. [ABSTRACT FROM AUTHOR]

This paper presents an exact model for studying the global buckling of concrete-filled steel tubular (CFST) columns with compliant interfaces between the concrete core and steel tube. This model is then used to evaluate exact critical buckling loads and modes of CFST columns. The results prove that interface compliance can considerably reduce the critical buckling loads of CFST columns. A good agreement between analytical and experimental buckling loads is obtained if at least one among longitudinal and radial interfacial stiffnesses is high. The parametric study reveals that buckling loads of CFST columns are very much affected by the interfacial stiffness and boundary conditions. [ABSTRACT FROM AUTHOR]

Elastoplastic buckling behaviors of rectangular plates made from functionally graded materials (FGMs) are investigated in this paper. The elastoplastic material properties are assumed to vary smoothly through the thickness of the plates. The three dimensional material constitutive relation of FGMs is found by introducing the material homogenization method, named Tamura-Tomota-Ozawa(TTO) model, into J 2 deformation theory or J 2 flow theory. The uniform strain hypothesis helps to simplify the prebuckling state and derive the analytical expression of the position of the material elastoplastic interface. The buckling governing equations and the buckling critical condition of the structures are formulated under the framework of the classical plate theory. An iterative algorithm is designed to obtain the elastoplastic buckling critical load, a converging result between the prebuckling and the buckling critical internal forces. ABAQUS simulation well verifies the present theoretical predictions from J 2 flow theory, and is resorted to investigate the postbuckling behaviors of FGM plates. Discussions are addressed for the effects of the constituent distribution, the material plastic flow, the preloaded states of the plates, and the regions of buckling types are plotted as well. [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]

In the present paper, the post-buckling behavior of a simply supported piezoelectric hybrid microplate subject to thermal, electrical and mechanical loads is studied. The size effect in the mechanical behavior of the microplate is captured by using the modified couple stress theory. The Mindlin plate theory is adopted to describe its deflection behavior with the von Karman’s geometric nonlinearity taken into account. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical thermal/mechanical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the material length scale parameter to thickness ratio, the applied electric field and in-plane boundary conditions on the buckling and post-buckling behavior of the piezoelectric hybrid microplate are discussed in detail. [ABSTRACT FROM AUTHOR]

Highlights • Experimental tests were conducted on doubly-symmetric welded Q460GJ steel beams against lateral torsional buckling. • Numerical models were developed for steel beams to quantify their lateral torsional buckling resistances. • Comparisons were made between numerical results and design curves from different national codes. Abstract This paper presents an experimental and numerical study on the global buckling behaviour of doubly-symmetric Q460GJ steel beams under three-point bending. A total of eight simply-supported beams with different slendernesses and height-to-width ratios were tested in the experimental programme. To achieve the required loading and boundary conditions, a special loading system was designed for the beams so that the vertical load applied at the mid-span through a hydraulic jack could move with the beams in the lateral direction, and a set of steel rollers was placed in the supports. All eight beams failed in lateral-torsional buckling. Finite element models were also developed for the beams, in which initial geometric imperfections and residual stresses were considered. The model was validated against experimental results, and a reasonably good agreement was obtained. A series of parametric study was carried out to gain a deep understanding of the effects of slenderness and height-to-width ratio on buckling factor. Comparisons were made between numerical data and calculated values in accordance with different national codes. [ABSTRACT FROM AUTHOR]

Research is limited with respect to load-deflection behavior of slender concrete columns internally reinforced with Fiber Reinforced Polymer (FRP) spirals and longitudinal bars. An analytical buckling model based on numerical integration is presented to predict the load versus deflection performance of slender concrete columns reinforced with FRP spirals and longitudinal bars, subjected to eccentric loads. The model can be used to predict the behavior of slender concrete columns with various configurations including FRP and/or steel reinforcement, single or double spiral, and number of longitudinal bars. The longitudinal bars considered include steel, FRP, or hybrid reinforcement consisting of steel and FRP bars. The model is found to predict the experimental performance of slender concrete columns reinforced with Glass FRP longitudinal bars and spirals with satisfactory accuracy. The model is used to create interaction diagrams for FRP spiral-confined circular concrete columns with various slenderness ratios, reinforced with steel, FRP or hybrid reinforcement. [ABSTRACT FROM AUTHOR]

Abstract Cylindrical lattice structures are types of lightweight structures and can utilize the orthotropy of fiber-reinforced composite materials. Maximization of the buckling loads is important because they dominate the strength of the structures. On the basis of the fact that a hyperboloidal shape deviation increases the buckling loads of cylindrical homogeneous shells, the changes in the buckling loads of cylindrical lattice structures with a hyperboloidal shape deviation are discussed. Further, the buckling loads of both conventional cylindrical lattice structures and shape-deviated hyperboloidal lattice structures with respect to the compressive, bending, and torsional loads are calculated using a finite element method. The results show that the shape deviation decreases the buckling loads, while the change in mass is negligible. The effects of the shape deviation on the buckling loads differ between homogeneous shell structures and lattice structures. [ABSTRACT FROM AUTHOR]

This paper presents a theoretical and experimental analysis of buckling load of the circular tube with flattened ends. The buckling tests were conducted on the steel tubes with different length and diameter, and the critical buckling force was determined from the measured relation between the lateral displacement and axial force. Analytical solutions for the critical buckling force of the circular tubes were derived in the series form, and a numerical procedure based on the finite difference method and quasi-Newton method was developed to determine the critical buckling load. The results show that both analytical and numerical solutions were in agreement with those measured from the experiment. Moreover, the effect of flattened part length on the value of the critical buckling force was investigated there. The paper provides a mathematical model of mentioned case and gives us some simplifications calculating the critical buckling force. [ABSTRACT FROM AUTHOR]

A new type of core-separated buckling-restrained braces, namely a core-separated battened buckling-restrained brace (B-BRB) has been proposed. Its load-carrying capacity and hysteretic response are investigated theoretically and experimentally in this paper. The B-BRB has a remarkable advantage over a common buckling-restrained brace (BRB), in which the newly formed cross-section of the B-BRB is spread outwards by spacing two cores, hence resulting in higher material utilization efficiency in its structural design. In addition, the two independent all-steel BRBs, each having a single plate core simply in-filled in a narrow hollow section, are connected by longitudinally distributed battens rather than continuous plates. Based on the elastic-plastic FE analysis of a B-BRB under monotonic compressive load, its ultimate resistance and failure modes are investigated numerically, considering the effect of its overall initial geometric imperfection. An interaction formula between normalized slenderness ratio and buckling factor of the B-BRB is proposed for predicting its ultimate load-carrying capacity. Consequently, the hysteretic response of the B-BRB is explored through elastic-plastic FE analysis. The maximum normalized slenderness ratios of the B-BRBs required for a load-bearing type and an energy-dissipation type are proposed in their strength designs, respectively. Ultimately, hysteretic responses of five B-BRB specimens have been experimentally investigated. The experimental results are compared with the FE numerical analysis, which considers plate local buckling of all components of the B-BRBs. The comparison has verified the rationality of the proposed design method. [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]

A general analytical procedure is proposed to design tapered laminated composite structures. It is based on: 1) the introduction of two variables representing a laminate configuration, 2) the analytical determination of the lower bound of the number of layers in each of the segments constituting the construction, 3) the definition of the reference sublaminate which configuration is transferred to all segments/parts of the construction, 4) the gradual building of configurations for symmetric balanced laminates having odd or even number of plies. The solution is verified by the comparison with results existing in the literature for both inner and outer tapers. A multi-panel composite structure is considered to demonstrate the applicability of the proposed method. As usual, in a such class of problems, the whole construction is divided into segments/panels. The individual segments are subjected to the simultaneous action of in-plane, tensile or compressive and shear loads. The present results demonstrate the simplicity and effectiveness of the method and non-uniqueness of solutions. The paper intends to clarify the physical sense of the discussed problem. [ABSTRACT FROM AUTHOR]

Double-coped beams are usually employed to avoid spatial interference when similar elevations of both the top and bottom flanges of the connected beams are required. Due to the removal of the flange parts, the load resistance can be significantly compromised. This paper discusses the effectiveness of various reinforcing strategies aiming to increase the load resistance of newly designed double-coped beams or to upgrade the existing ones. A series of full-scale tests are conducted first, covering a set of reinforcement types and varying coping dimensions. Local web buckling is found to be the governing failure mode for the unreinforced specimens, and the presence of the considered stiffeners can effectively increase the load resistance. In particular, a pair of longitudinal stiffeners for the top cope edge is shown to completely mitigate the risk of local web buckling, and the final failure mode is tensile cracking at the bottom cope corner. The doubler plates, either full-depth or partial-depth, can delay the initiation of local web bucking, and as a result the load resistance is remarkably increased. The effects of the varying reinforcement types and coping dimensions on the utilisation efficiency of section capacities are discussed in detail. A finite element study is subsequently conducted to enable further understanding of key structural characteristics and to help explain some test phenomena. Preliminary design comments and recommendations are finally proposed based on the exiting test and numerical data. [ABSTRACT FROM AUTHOR]

In this work, the bending-induced buckling of elliptical composite cylinders is significantly improved by using curvilinear fiber paths. The orientation angle in the composite plies are designed to circumferentially vary in elliptical multi-layered composite cylinders for the best bending-buckling performance. To this end, a metamodeling based design optimization approach is successfully employed. The resulting elliptical cylinders with so-called variable stiffness (VS) laminates are shown to have bending buckling capacities up to 70% higher than their constant stiffness (CS) counterparts made with traditional straight-fiber laminates. Unlike the circular cylinders, the non-uniform curvature of the elliptical cylinders adds more complexity to the buckling behavior when the direction of the bending moment is changed. The effect of loading direction on the buckling performance of VS and CS elliptical cylinders is then investigated. Finally, a VS elliptical composite cylinder is designed for having maximum bending buckling capacity in two opposite directions simultaneously, and its buckling performance in different directions is compared with its CS counterpart. [ABSTRACT FROM AUTHOR]

Grid-stiffened composite structures not only allow for significant structural weight reduction but also are competitive in terms of structural stability and damage tolerance compared with conventional stiffened candidates. As the development of Automated Fibre Placement (AFP) technology matures, a unitized construction of skin and stiffeners is easily manufacturable. In this paper, a curved stiffener layout is optimized to enhance the structural buckling resistance. A linear variation of stiffener angles is used, resulting in the formation of a locally rhombic lattice pattern. Due to the spatial variation of angle and spacing induced by the use of curved stiffeners, analytic solutions for the responses are not generally applicable. Thus, global and local buckling loads are calculated based on finite element models by a previously-developed global/local coupled strategy. Since the stiffeners are not explicitly modelled in the finite element calculations, a fixed mesh is used for gradient-based optimization. Both parametric design and optimization are performed in order to find the optimal curved grid pattern, whose practical performances are assessed by post-buckling analysis. A comparison between the performances of structures with curved stiffeners, with straight stiffeners, and variable-stiffness skins with curved fibres, demonstrates the potential of curved stiffener configurations in improving the structural efficiency. [ABSTRACT FROM AUTHOR]

A solution of the buckling problem for a shear loaded composite anisogrid lattice plate with the clamped edges based on the Galerkin method is presented in this paper. The lattice plate is modelled as an equivalent continuous orthotropic plate with effective stiffness parameters. The deflection of buckled plate is presented in the form of a double series containing clamped–clamped beam functions. The critical in-plane shear load is found solving the generalised eigenvalue problem for a homogeneous system of algebraic equations in which the unknowns are the coefficients of the double series. Based on this solution, the effects of the plate dimensions and parameters of lattice structure on the value of critical load are investigated and analysed. Results of these analyses are successfully verified using the finite element method. An approximate analytical expression providing fast and reliable way of calculation of the critical buckling load is obtained for the lattice plate composed of the ribs made of the same composite material and with the same size of their cross-sections. [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]

A new model depicting the full phase of tubular string buckling in vertical wellbores is proposed. The buckling modes of the tubular string are divided into: no buckling, 2D lateral buckling, 3D lateral buckling, continuous contact buckling and helical buckling. For the 2D lateral and 3D lateral buckling, the tubular string is respectively depicted by two and four suspended sections; for the continuous contact and helical buckling, the tubular string includes four suspended sections and one continuous contact section. With the suspended and continuous contact sections respectively depicted by beam-column model and buckling differential equation, the general buckling configurations of the entire tubular string are deduced. Substituting relevant continuity, boundary and stability conditions, the tubular string buckling problem is converted into a system of nonlinear equations. Solving these equations with iteration method, the critical buckling loads and the buckling configurations under different buckling modes for a weightless tubular string are obtained. Later, the weightless model is extended to the case for a tubular string with weight. On the basis of the new buckling model, the axial force and torque transfer along the tubular string under the coupling effect of friction force and buckling is discussed. The results show that the existence of tubular string weight increases the complexity of buckling mechanism and calculation. The continuous contact between the tubular string and wellbore reduces the axial force and torque transfer along the tubular string. To increase the axial force and torque transfer and inhibit buckling, the installation of stabilizers of low friction and buckling inhibition on the buckling-prone sections is wiser than unilaterally increasing the diameter and thickness of the tubular string. Compared with the previous results, the new model provides a more sophisticated description of tubular string buckling in vertical wellbores. [ABSTRACT FROM AUTHOR]

Stiffened cylindrical shells are widely used in modern engineering structures, especially in aircraft, oil-transmitting pipeline, spacecraft industry and ocean engineering. Due to the increasing demands for high structures performances, this paper presents the effect of stiffeners on the nonlinear buckling of cylindrical shells with functionally graded (FG) coatings under torsional load. The cylindrical shell is reinforced with external axial stiffeners. The material properties are assumed to vary continuously through the thickness direction. Equilibrium and stability equations for cylindrical shells are derived by using the classical shell theory (CST) with von-Karman nonlinear kinematic relations. Using analytical approach, Galerkin procedure, and the Airy stress function, the resulting equations are employed to obtain the closed-form expression for the critical buckling loads and load–deflection relation. The influences of the number of stiffeners, volume fraction exponent, the thickness of the metal layer, and geometric parameters on the nonlinear buckling behavior of the cylindrical shell with FG coatings are examined in details. [ABSTRACT FROM AUTHOR]

An analytical method for vibration and buckling behaviours of Functionally Graded (FG) beams with various boundary conditions under mechanical and thermal loads is presented. Based on linear strain-displacement relations, equations of motion and essential boundary conditions are derived from Hamilton’s principle. In order to account for thermal effects, three cases of the temperature rise through the thickness, which are uniform, linear and nonlinear, are considered. The exact solutions are derived using the state space approach. Numerical results are presented to investigate the effects of boundary conditions, temperature distributions, material parameters and slenderness ratios on the critical temperatures, critical buckling loads, and natural frequencies as well as load-frequencies curves, temperature-frequencies curves of FG beams under thermal/mechanical loads. The accuracy and effectiveness of proposed model are verified by comparison with previous research. [ABSTRACT FROM AUTHOR]

The stability of a nonuniform column subjected to a tip force and axially distributed loading is investigated based on the Timoshenko beam theory. An emphasis is placed on buckling of a standing column with varying cross-section and variable material properties under self-weight and tip force. Four kinds of columns with different taper ratios are analyzed. A new initial value method is suggested to determine critical tip force and axial loading at buckling. The effectiveness of the method is confirmed by comparing our results with those for Euler-Bernoulli columns for the case of sufficiently large shear rigidity. The effects of shear rigidity, taper ratio, and gravity loading on the buckling loads of a heavy standing or hanging column are examined. [ABSTRACT FROM AUTHOR]

In this study, a finite element method (FEM) based on the size dependent nonlocal integral elasticity theory is implemented for buckling analysis of nanoscaled beams with various boundary conditions. The method is based on the principle of total potential energy. The variations of buckling load with respect to the scaling effect parameter and to the length-to-thickness ratio are investigated. Furthermore, the effect of attenuation function type on the buckling load is examined. The results are compared with the corresponding solutions of governing stability equations which are derived in the context of nonlocal differential elasticity theory. It is found that the small scale coefficient has a noticeable effect on the buckling load of nanobeams. [ABSTRACT FROM AUTHOR]

This work presents a study of the behavior, performance and failure of thinwalled composite channel section columns. The study is carried-out using nonlinear finite element models of laminated columns, including geometric imperfections and material failure, as well as approximate analytical solutions based on the Classical Lamination Theory. The accuracy of the numerical model is assessed using experimental results available in the literature and very good results were obtained. The results show the influence of the column layup and wall thickness on the structural behavior of laminated columns, including the buckling mode and ultimate failure load. Finally, the numerical model is used to assess the accuracy of approximate closed-form expressions for evaluation of the local buckling loads of composite channel section columns. [ABSTRACT FROM AUTHOR]

Since economic quantities are more meaningful to decision makers than dynamic response parameters, this paper examines the economic benefits of using Buckling-Restrained Braces (BRBs) in hospitals located in the very soft soils of the lakebed zone of Mexico City. Since non-structural elements and contents are far more expensive than the structure itself, they are included in detail in the analyses. The results of analyses on three-, six-, and nine-storey frames, which represent short-period structures, show that the expected (or probable) losses and lifecycle costs are smaller when structures are equipped with BRBs. Different cases (defined by the contribution of the BRBs to the strength capacity of the structure) were analysed and compared. The best design options were identified from a comparison of lifecycle costs. As an example, a comparison of cost-benefit analysis between a bare frame and a frame designed under gravity loads and equipped with BRBs, shows that the latter is more economical; because, for the same initial cost, the lifecycle costs are significantly smaller. [ABSTRACT FROM AUTHOR]

In order to understand the formation of one-dimension periodic structures by electrospinning, an approximate mechanical approach for the critical load and the number of half waves in the buckled shape have been conducted based on the energy method. Diameter of circular cross-section electrospun fiber is assumed to be equal to the length of the rectangular cross-section spitted fiber. Fiber with rectangular cross section buckles more easily than that with circular cross section because of the different flexural rigidity. For rectangular-section fiber, increase of length to width ratio can result in the increase of the number of half waves. Detailed simulation results for buckling responses of circular-section fiber and rectangular-section fiber have been conducted by commercial finite element analysis software (ABAQUS). [ABSTRACT FROM AUTHOR]

We present a nonlinear finite element method to investigate the nonlinear stability of stiffened functionally graded materials (FGM) plates considered as a whole unit. The plates are subjected to mechanical and thermal loads. The material properties are assumed to be temperature dependent and varied gradually across the thickness according to a power law distribution. The nonlinear equations of FGM plates are based on the first-order shear order plate theory. The influence of material, geometrical properties of stiffeners and initial deflections on the buckling and post-buckling response of the stiffened plates are studied in detail. Including the latest information no work has been oriented towards post-buckling analysis of stiffened FGM plates considered as a whole unit. [ABSTRACT FROM AUTHOR]

The buckling response and load carrying capacity of thin-walled open cross-section profiles made of Fibre Metal Laminates, subjected to static axial compression loading are considered. These include thin-walled Z-shape and channel cross-section profiles adopting a 3/2 FML lay-up design, made of 3 aluminium layers. The objective of the investigation is the comparison of standard thickness Fibre Reinforced Plastic layers versus thin-ply material technology. Whilst thin ply designs differ only by the layer thickness, they offer an exponential increase in stacking sequence design freedoms, allowing detrimental coupling effects to be eliminated. The benefit of different hybrid materials are also considered. The comparisons involve semi-analytical and finite element methods, which are validated against experimental investigations. [ABSTRACT FROM AUTHOR]

The paper presents the application of the differential transformation method (DTM) to the stability analysis of nonuniformly loaded beams under bending. The main advantage of the method is the possibility to obtain the semi-analytical solution for the critical loads of the beam undergoing lateral-torsional buckling. To determine the critical load, the system of two coupled ordinary differential equations with variable coefficients and parameters have to be solved. Numerical analyses were carried out for three different types of load functions: (i) Uniformly distributed load, (ii) linearly varying load and (iii) sinusoidally distributed load. The results were compared with the solutions computed by the finite element method (FEM) and those obtained by the authors using the variational iterative method (VIM). In each case, it was found that the difference with reference to the existing one does not exceed 3%, which testifies the effectiveness of the DTM used. Nevertheless, it should be emphasized that the number of terms of the approximation series used is fairly large and therefore the calculation of higher critical loads can be very time-consuming. [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]

Applicability of the vibration correlation technique (VCT) for nondestructive evaluation of the axial buckling load is considered. Thin-walled cylindrical shells with and without circular cutouts have been produced by adhesive overlap bonding from a sheet of aluminium alloy. Both mid-surface and bond-line imperfections of initial shell geometry have been characterized by a laser scanner. Vibration response of shells under axial compression has been monitored to experimentally determine the variation of the first eigenfrequency as a function of applied load. It is demonstrated that VCT provides reliable estimate of buckling load when structure has been loaded up to at least 60% of the critical load. This applies to uncut structures where global failure mode is governing collapse of the structure. By contrast, a local buckling in the vicinity of a cutout could not be predicted by VCT means. Nevertheless, it has been demonstrated that certain reinforcement around cutout may enable the global failure mode and corresponding reliability of VCT estimation. [ABSTRACT FROM AUTHOR]

In the present article, the buckling of a fluid-infiltrated porous plate is investigated using Mindlin plate theory and an analytical procedure. A cosine rule for the pore distribution across the plate thickness is assumed with a coefficient defining porosity level. The governing stability equations are rewritten in terms of four auxiliary functions and decoupled with the aid of some mathematical manipulations. The decoupled partial differential equations are solved analytically by assuming simply supported radial edges for the plate. The critical buckling loads are calculated by considering fluid-saturated and fluid free conditions for the interconnected network of pores for different sector angles, thickness-radius ratios, coefficients of plate porosity, aspect ratios, and boundary conditions. It is found that the pore fluid compressibility affects the buckling load significantly. [ABSTRACT FROM AUTHOR]

This paper presents a numerical investigation into the buckling behaviour of cold-formed steel zed purlins when subjected to transverse distributed uplift loading. The study uses both linear and non-linear finite element methods (ABAQUS shell Finite Element analyses) to investigate the pre-buckling, buckling and post-buckling behaviour of zed-section purlins in purlin-sheeting systems. The numerical modelling strategy is carefully validated using the results of available experimental data. Influences of boundary conditions and restraints from sheeting on web shear buckling, local, distortional and lateral-torsional buckling behaviour, and the buckling interactions of the purlins are discussed. Furthermore, the strengths and failure modes of the purlins obtained from numerical results are compared with the design strengths predicted using the direct strength method (DSM) specified in the ‘North American Specification’ (AISI S100). The comparisons show that the ultimate strengths of buckling interactions are generally underestimated. Hence, the DSM is modified to cover the partially restrained zed-sections in purlin-sheeting systems. [ABSTRACT FROM AUTHOR]

In this paper, an analytical model is developed to determine the torsional-flexural buckling load of a channel column braced by unevenly distributed batten plates. Solutions of the critical-buckling loads were derived for three boundary cases using the energy method in which the rotating angle between the adjacent battens was presented in the form of a piecewise cubic Hermite interpolation (PCHI) for unequally spaced battens. The validity of the PCHI method was numerically verified by the classic analytical approach for evenly battened columns and a finite-element analysis for unevenly battened ones, respectively. Parameter studies were then performed to examine the effects of loading eccentricities on the torsional-flexural buckling capacity of both evenly and unevenly battened columns. Design parameters taken into account were the ratios of pure torsional buckling load to pure flexural-buckling load, the number and position of battens, and the ratio of the relative extent of the eccentricity. Numerical results were summarized into a series of relative curves indicating the combination of the buckling load and corresponding moments for various buckling ratios. [ABSTRACT FROM AUTHOR]