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This article considers a bidirectional functionally graded (BDFG) beam with various distributions of volume fraction. The impact of these distributions on the buckling and bending response of BDFG beam with general boundary conditions is investigated via a quasi-3D solution. It is assumed that the beam is exposed to a set of in-plane varying compressive loads and there mechanical characteristics change in both directions. Also, the BDFG beam is considered to be exposed different external mechanical loads. Hamilton's principle is employed to derive the governing equations, which are then solved using analytical solution to obtain buckling and bending characteristics. The precision of the current formulation is investigated via a comparison with available data in literature. Some numerical results are presented and discussed to assess the effect of different parameters such type of volume fraction, boundary condition, varying load, and beam geometry on the buckling and bending of BDFG beam. [ABSTRACT FROM AUTHOR]

In this paper, a new model for porous structures in functionally graded plates (FGPs) is introduced that under significant differences in constitutive material properties and high porosity ratios, the difference in elasticity modulus of the suggested pattern reaches twice as many as the previous model. This study is based on the finite strip method, incorporating Eringen nonlocal elasticity and third-order shear deformation theory, to create standard and geometric stiffness matrices for mechanical and thermal buckling analyses of functionally graded porous nanoplates (FGPNPs). The procedure is founded on Lagrangian and Hermitian shape functions to account for significant shear deformation effects in thick plates, and all in-plane displacements are applied in the geometric matrix based on the virtual work principle. Various factors like boundary conditions, porosity distributions, temperature variations, and nonlocal parameter are investigated for their impact on the mechanical and thermal buckling loads of FGPNPs. The findings reveal the substantial influence of size effects on thick porous nanoplate evaluations. Mechanical analysis shows that O-, V-, X-shaped and uniform patterns exhibit the best performance against mechanical loads, respectively. Despite the material properties deteriorating with increased porosity ratios, thermal resistance is improved. The new uniform pattern performs the best under uniform loading, and V-shaped porous structures excel at strength against nonlinear loading. However, the X-shaped model exhibits the lowest thermal resistance in both conditions. [ABSTRACT FROM AUTHOR]

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]

Fragility and the presence of a poisonous substance (lead) are the two major issues with traditional piezoceramics and structures that include them. This work suggests an active structure that is lightweight, flexible, and eco-friendly such that a polymeric foam plate is sandwiched between two piezoelectrically activated nanocomposite layers. A combination of a polymer and piezoelectric nanowires (NWs) of zinc oxide (ZnO) is used in the nanocomposite layers. For the proposed active structure, two types of void distributions and functionally graded (FG) distributions of the NWs have been assumed in each corresponding layer. The buckling characterization of the proposed eco-friendly active sandwich plate (EFASP) under biaxial mechanical loads has been conducted using an extended meshless solution based on a third-order theory. An in-depth parametric study on the EFASPs' biaxial buckling resistance revealed that increasing NW content considerably enhances buckling resistance, with this enhancement strongly reliant on the distribution profile of the NWs. Moreover, it was observed that embedding voids in the substrate layer can lead to a large structural weight reduction while only marginally lowering the buckling performance of suggested EFASPs. [ABSTRACT FROM AUTHOR]

An analytical investigation on buckling behavior of thick functionally graded shells with nearly cylindrical shapes and porosities under mechanical loads is presented in this paper. Loading conditions considered are that axial compressive load, lateral pressure and combined mechanical loads in thermal environments. Porosities are evenly or unevenly distributed within the shell. Governing equations are established based on a higher order shear deformation theory taking into account interaction between the shell and surrounding elastic medium. Two-term form of deflection is assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive closed-form results of buckling loads. [ABSTRACT FROM AUTHOR]

Thermo-mechanical buckling analysis of laminated spherical shells bounded with the piezoelectric actuator layers has been presented in this article. Applied loads are a combination of thermal, mechanical and electrical loads. Derivations of equilibrium and stability equations are based on the classical laminated shell theory and Sanders's nonlinear kinematic relations. The analysis employs the Galerkin method to achieve closed-form formulas for the buckling loads of the piezo-laminated spherical shell. Effects of applied actuator voltage, voltage sign, geometrical parameters of the shell (length, diameter, and thickness), material properties, and layout of composite layers on the buckling strength are investigated. Analytical solutions are obtained for three types of thermal loading, and one thermo-mechanical loading condition. The results are validated by the known data in the literature. [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]

Based on Eringen's nonlocal elastic theory, the vibration characteristics and critical buckling load of porous functionally graded rectangular nanoplates under thermomechanical load are studied. The material properties of porous FGM nanoplates are characterized by Voigt mixing power rate and arbitrarily distributed porous model, and the correlation between material and temperature is further considered, the temperature distribution along with the thickness direction is uniform. The numerical solution of the vibration and critical buckling loads of porous functionally graded material (FGM) rectangular nanoplates under thermo‐mechanical loading are investigated using the numerical solution method‐differential transformation method (DTM), and the governing differential equations are established in the classical plate theory and Hamilton system. The effects of boundary conditions, nonlocal parameters, gradient index, temperature rise, porosity, compression load, and aspect ratio on the vibration and critical buckling load of porous FGM nanoplates under thermo‐mechanical loading effects are mainly investigated utilizing arithmetic examples. [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]

The high temperature environment makes the buckling of composite laminated plate happen earlier. Further weight savings can be achieved once the plate has a favorable postbuckling stiffness. This study aims to address this issue by developing a ROM-driven lamination optimization to maximize the buckling and postbuckling performance of compressed plates under initial temperature field. The reduced-order model(ROM) constructed using the improved Koiter theory is reformulated to be suitable for thermal-mechanical buckling problems. A linear subspace of the force space is represented to be the span of the mechanical load, the thermal load and a set of predefined perturbation loads. The thermal load related to the initial temperature field is constant during the increase of in-plane compressive load. An independently additional degree of freedom corresponding to the thermal load is implemented into the construction of the reduced-order model. The buckling and postbuckling performance can be extracted from the solution of reduced-order model, and then subsequently selected as inputs to achieve the optimal laminate. The main novelty of this work is to achieve the thermal-mechanical buckling and postbuckling optimization, benefitting from the highly efficient single run of thermoelastic geometrically nonlinear analysis. Various numerical examples have been selected to validate the performance of the proposed method, considering the influences of length-to-width ratio, α1/α2, ply number and nonuniform temperature field. [ABSTRACT FROM AUTHOR]

This article presents the axial buckling analysis of polymer-CNT-fiber nanocomposite annular system (PCFCAS) resting on Winkler-Pasternak substrates under various temperature gradients. With the aid of Hamilton's principle and the higher-order shear deformation theory (HSDT), the governing equations are derived. For developing an accurate solution approach, a generalized differential quadrature method (GDQM) is finally employed. Various geometrically parameters are taken into account to investigate the axial buckling analysis of the PCFCAS subjected to a high-temperature environment. Finally, the presented results demonstrate that different parameters such as outer to inner radius ratio (Ro/Ri), patterns of temperature increase, volume fraction and orientation angle of the carbon fibers (CFs), weight fraction and distribution patterns of carbon-nanotubes (CNTs), and other geometrical and physical parameters have an important role in the axial buckling load of the current structure. The fundamental and golden results of this paper could be that when the PCFCAS is in an environment with sinusoidal, and uniform temperature change, the structure encounters with the highest axial buckling load. In contrast, the lowest buckling load occurs for the uniform temperature change. Also, when the effect of the Winkler and Pasternak foundation is considered, there is a sinusoidal effect from the Ro/Ri parameter on the axial buckling load of the disk, and this matter is true for all boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, the nonlinear time history response and dynamic-buckling of functionally graded material (FGM) shell structures in thermal environments with temperature-dependent material properties is studied. An implicit conservative/decaying time integration scheme and a curved 8-node degenerated shell element are used for time and spatial discretization respectively. Numerical results show that the developed shell element formulation with the implicit time integration scheme is capable of solving nonlinear dynamic-buckling and large displacement dynamic problems of FGM shells in severe thermal environments. Th influence of material constituents, power-law indexes and thermo-mechanical loadings on the transient dynamic response and dynamic-buckling phenomena are considered. [ABSTRACT FROM AUTHOR]

Buckling and sound radiation characteristics of curved sandwich panels subjected to combined thermo-mechanical loads are presented in the paper. The panel comprises a 3-D functionally graded graphene porous core sandwiched between FG-V Λ CNT reinforced composite face sheets (3DGrF-CF). The governing differential equations of 3DGrF-CF sandwich panels are derived using the parabolic shear deformation theory (PSDT), and the vibration responses are predicted using Navier's approach. The vibration response thus obtained is fed into the Rayleigh integral to capture the acoustic pressure. The buckling and sound radiation characteristics were found to vary significantly with the core's porosity coefficient and porosity grading pattern. However, the impact of this influence also depends on the magnitude of thermal & mechanical loading. This implies that selecting a core for acoustic comfort depends on the dominance of loading conditions and is illustrated using octave band analysis. • Buckling & vibro-acoustic analysis of 3DGrF-CF panels under thermo-mechanical loads. • Analytical prediction using Navier's & Rayleigh's approach considering PSDT. • Optimum porosity coefficient & grading pattern for different loading conditions. [Display omitted] [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]

Buckling load estimation of continua modeled by finite element (FE) should be based on non-linear equilibrium. When such equilibrium is obtained by incremental solutions and when sensitivity analysis as well as iterative redesigns are included, the computational demands are large especially due to optimization. Therefore, examples presented in the literature relate to few design variables and/or few degrees of freedom. In the present paper a non-incremental analysis is suggested, and a simple sensitivity analysis as well as recursive redesign is proposed. The implicit geometrical non-linear analysis, based on Green-Lagrange strains, apply the secant stiffness matrix as well as the tangent stiffness matrix, both determined for the equilibrium corresponding to a given reference load, obtained by the Newton-Raphson method. For the formulated eigenvalue problem, which solution gives the estimated buckling load, the tangent stiffness matrix is of major importance. In contrast to formulations based on incremental solutions, the tangent stiffness matrix is here divided into two matrices, the stress stiffness matrix that is linear depending on stresses and the remaining part of the tangent stiffness matrix. Examples verify the effectiveness of the proposed procedure. [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]

Objective of this work is to optimize the structural configuration of laminates in terms of design for the maximization of buckling resistance of laminates under the effect of constraints. The predominant design parameter is the orientation of the fibers in the layers of the laminate. High-order deformation theory is used in the mathematical formulation in the buckling analysis of stratified composite plates. For this purpose, we will use the optimization technique genetic algorithm taking into account the various factors: number of fibers, geometric ratio, load ratio and boundary conditions. [ABSTRACT FROM AUTHOR]

Thin steel shells in the form of spherical segments, loaded by external pressure, have a tendency to sudden buckling under a lower pressure than their plastic resistance. The buckling phenomenon of spherical shells was the subject of research done by many authors and the previous results of theoretical and experimental research were used in the European Design Recommendations published in 2008 by European Convention for Constructional Steelwork. This article presents experimental research done on a specially designed and manufactured stand. Specimens were manufactured with a metal spinning technique from steel sheets usually used for deep drawing and stamping of metal objects. The actual shape of every specimen was determined with the three-dimensional scanning technique. Material research was also done on the steel sheets. Pressure was exerted with an air compressor and displacement was measured with the optical measurement system ARAMIS. The deformation modes of the whole specimen were registered precisely at every step of pressure exertion till the final postbuckling stage. All the data measured were registered automatically by two computers. The result of every experiment is presented in the form of an equilibrium path as the relationship of the pressure p as a function of a chosen displacement parameter. This article also presents a comparison between the critical pressures obtained during the experiments and the results obtained from the numerical simulations done with COSMOS/M. The experimental and the numerical results were also compared with the buckling resistances proposed by Rotter and Schmidt and Błażejewski and Marcinowski. [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]

The effects of the delamination in the critical buckling load failure of E-Glass/epoxy composite laminates are analysed. The buckling load of rectangular composite plates is determined by carrying out the experimental work for different aspect ratios of range 2 to 3. The specimens are made with unidirectional fibres of orientation (90°/45°/-45°/°/)s. The width of long 100 mm and 50 mm at the centre of the plate, a single substantial delamination is made at the mid layer produced by Teflon film using hand lay-up technique. The buckling loads of plates were found by using simply supported boundary condition and kept the other side edges free. The experimental buckling loads were found from the graph drawn for vertical displacement vs load. By drawing the graph for the vertical displacement vs. load, the experimental buckling load can be calculated. Using finite element software of ANSYS 10, the experimental results were validated. [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]

Post-buckling analysis of functionally graded material (FGM) plates resting on Winkler and Pasternak elastic foundations subjected to thermomechanical loadings with circular cut-outs at centre and random material properties is presented. The material properties of each constituent's materials, volume fraction index, thermal expansion coefficients, foundation stiffness parameters and thermal conductivities are taken as independent basic random input variables. The basic formulation is based on applying Reddy's higher order shear deformation theory, which requires C1 continuous element approximation. A modified form C0 continuity is applied in the present investigation. A serum-free expansion medium with mean-centred first-order regular perturbation technique for composite plates is extended for FGM plates to solve the random eigenvalue problem. Typical numerical results are presented to examine the second-order statistics for effect of the volume fractions index, plate length-to-thickness ratios, plate aspect ratios, types of loadings, amplitude ratios, support conditions and various shape and size of holes with random thermomechanical properties. The results obtained by the present solution approach are validated with published papers and the robust method of simulation. It is found that the laminates with round cuts (FGM plates resting on Winkler and Pasternak elastic foundations) have a significant influence on the post-buckling response under Thermomechanical loading conditions. Present investigations are useful for the applications and further research. [ABSTRACT FROM AUTHOR]

This article aims to investigate the post-buckling behavior of plates and cylindrical panels made of functionally graded materials (FGM) and carbon-nanotubes reinforced composites (FG-CNTRC) under mechanical loads. Unlike the other high order shear deformation theories, the proposed formulation is elaborated within a double directors finite shell element which allows a parabolic distribution of the transverse shear strains, guarantee the zero condition of the transverse shear stresses on the extreme surfaces of the shell and introduces large deformations and finite rotations through a non-linear framework. Newton-Raphson with arc length control solution strategy is used to resolve the equilibrium paths. A power-law distribution and the extended rule of mixture are used to determine the effective material properties of functionally graded materials and carbon-nanotubes reinforced composites. The effectiveness and the accuracy of the formulation is checked via several comparisons with published results in the literature. Especially, some complex post-buckling curves of FGM and FG-CNTRC curved panels and plates with different mechanical loadings are provided that could be useful for future references. The effects of various parameters are also reported. [ABSTRACT FROM AUTHOR]

In this paper, the buckling behavior of a complete spherical shell under external pressure and of a half-sphere under torsion are first investigated. Several parametric studies are performed, which rely on the European Recommendations framework (ECCS text), so as to identify the different key parameters of the corresponding buckling capacity curves and lead up to both a qualitative and quantitative discussion about the imperfection sensitivity of such structures under each fundamental load. The related results allow us to completely describe the buckling behavior of a spherical shell under combined external pressure and circumferential shear by means of interactive buckling curves, without the need of many supplementary computations for any arbitrary combined loading case. [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]

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 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]

In this paper, the non-linear dynamic buckling of laminated composite rectangular plates is studied using finite element method. The laminated composite plates are subjected to in-plane dynamic compressive loads. The non-linear dynamic equations are solved using Abaqus/Explicit. Volmir's criterion is used to calculate the dynamic buckling loads. In order to observe the actual phenomenon, imperfections are incorporated in the plate. The results are validated using results from the available literature. The effect of ply orientation, loading function and imperfections on the non-linear dynamic buckling loads are studied. Non-linear dynamic buckling loads for rectangular pulse loads are found to be critical when compared to sinusoidal loading function. [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]

In order to determine the nonlocal critical buckling loads of chiral double-walled carbon nanotubes embedded in an elastic medium, the nonlocal Timoshenko beam theory is implemented. The solution for the nonlocal critical buckling loads is obtained using governing equations of the nonlocal theory. The effect of the elastic medium, the buckling mode number, chirality, and aspect ratio on the nonlocal critical buckling loads of double-walled carbon nanotubes are studied and discussed. The Young's modulus of three types of double-walled carbon nanotubes, with armchair, zigzag, and chiral tubules, are calculated based on molecular dynamics simulations. The nonlocal critical buckling loads in relation to the chirality of double-walled carbon nanotubes, buckling mode number, and length-to-diameter (aspect} ratio, in the presence and absence of an elastic medium, are examined. [ABSTRACT FROM AUTHOR]

The Hencky bar-net model (HBM) has been shown to be a physical structural representation of the finite difference plate model (FDM). This paper extends the HBM to tackle buckling problems of rectangular plates under in-plane non-uniform loads. This class of problems requires a pre-buckling stress analysis involving plane-stress elasticity equations in order to establish the non-uniform stress distributions in the plate domain for input loads to the HBM. The converged results given by HBM compare well with existing reference solutions; thereby verifying the model. The HBM is also used to generate some new buckling solutions for rectangular plates under various point loads and partially distributed loads. [ABSTRACT FROM AUTHOR]

The double rectangular tube assembled buckling-restrained brace is a new type of buckling energy consumption buckling-restrained brace. Because of its external restraining members, which are bound by high-strength bolts, its mechanical mechanism is more complicated and its failure modes are more varied. In this study, the double rectangular tube assembled buckling-restrained brace composition and three types of end constructions are introduced in detail. The influences of different design parameters on the performance of double rectangular tube assembled buckling-restrained brace are studied by numerical analysis methods; the possible failure modes and the influence of the end strengthening construction of double rectangular tube assembled buckling-restrained brace are also investigated, and a number of suggestions are proposed to improve this design. This study shows that the pinned double rectangular tube assembled buckling-restrained brace has four types of typical failure modes, namely, overall buckling failure, external end local pressure-bearing failure, bending failure of the extended strengthened core region and bolt threading failure. Rational design can prevent a buckling-restrained brace from losing its load-bearing capacity. In addition, compared with the end strengthening scheme with an external hoop, the end strengthening scheme with a strengthened bench can improve the load-bearing capacity of the double rectangular tube assembled buckling-restrained brace more effectively, and a reasonable design can also save materials. [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]

The design of cold-formed steel columns must consider flexural buckling, torsional buckling, and flexural-torsional buckling. The American Iron and Steel Institute incorporated equations for the critical elastic buckling loads corresponding to these failure modes in the North American Specification for the Design of Cold-Formed Steel Members. These equations were originally developed for columns with consistent boundary conditions for all three modes. However it is common in practice to have different unbraced lengths for major axis flexure, minor axis flexure, and torsion. Furthermore, it is common for certain members to be oriented such that intermediate bracing restraint directions do not align with the principal axes. This paper investigates and develops a general formulation of the column buckling equation to incorporate unequal unbraced lengths and non-principal axes. [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]

This paper considers the application of the buckling restraining concept in reinforced-concrete (RC) columns subjected to seismic-type loading. The main objective of the experimental study is to investigate the seismic performance of RC short columns with buckling-restrained casing provided to the main reinforcement at the critical region. The debonding of reinforcement by providing a rebar restraining collar is carried out at the plastic hinge region where maximum bending moment occurs. The columns are subjected to quasi-static cyclic lateral loading combined with a constant axial loading to simulate seismic-type loading. The performance of these columns is compared – in terms of ultimate load, ductility, load displacement envelope and energy dissipation capacity – with that of counterpart short columns designed as per Indian Standard code IS:456-2000 and ductile detailing as per IS:13920-2016. The main variables selected in this investigation are the axial load ratio and the length of the buckling-restrained casing of reinforcement. The test results indicate that the columns with buckling-restrained casings have improved performance in terms of lateral load-carrying capacity, energy dissipation characteristics and reduced stiffness degradation relative to columns without casing. [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]

The paper is concerned with the sensitivity analysis of structural responses in context of linear and non-linear stability phenomena like buckling and snapping. The structural analysis covering these stability phenomena is summarised. Design sensitivity information for a solid shell finite element is derived. The mixed formulation is based on the Hu-Washizu variational functional. Geometrical non-linearities are taken into account with linear elastic material behaviour. Sensitivities are derived analytically for responses of linear and non-linear buckling analysis with discrete finite element matrices. Numerical examples demonstrate the shape optimisation maximising the smallest eigenvalue of the linear buckling analysis and the directly computed critical load scales at bifurcation and limit points of non-linear buckling analysis, respectively. Analytically derived gradients are verified using the finite difference approach. [ABSTRACT FROM AUTHOR]