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This paper investigates the buckling mechanism of the steel core of buckling-restrained braces. The development of buckling mode is revealed with increasing axial load. The formulae of the maximum contact force and the maximum bending moment of the restraining member are obtained. The analytical results are validated by the finite element analysis. Compared to the results by conventional analysis, the number of contact points or buckling waves is much less; for hinged ends, the contact force for the lower mode is the identical while the contact force for higher modes is 1/4 lower; for fixed ends, the contact force is half of the conventional method. [ABSTRACT FROM AUTHOR]

The purpose of this paper was to study the effect of I-shape stiffener stiffness on the buckling and post-buckling, up to collapse behavior of stiffened composite panel under the uniform uniaxial compression load. Six stiffened composite panel configurations, which were orthogonally designed with two skin configurations and three I-shape stiffener configurations, were took into account in the experimental investigation. Three specimens for each configuration (18 specimens in total) were manufactured for test. Before tests, the key dimensions of I-stiffener and skin were measured. Furthermore, all the specimens were also inspected visually and detected by the ultrasonic C-scan system. No initial delamination or debonding area was found on all the specimens according to their C-scan images. The experimental results show that the equivalent compression stiffness of I-shape stiffener has great influence on the buckling load and failure mode of stiffened panel, but a little effect on the failure load of stiffened panel. The skin thickness has great impact on the buckling load and the final failure load. [ABSTRACT FROM AUTHOR]

Current study is concentrated on the extraordinary properties of defective carbon nanotubes (CNTs). The role of vacancy defects in thermal buckling response of precompressed CNTs is explored via molecular dynamics (MD) simulations. Defective CNTs are initially compressed at a certain ratio of their critical buckling strain and then undergo a uniform temperature rise. Comprehensive study is implemented on both armchair and zigzag CNTs with different vacancy defects including monovacancy, symmetric bivacancy and asymmetric bivacancy. The results reveal that defects have a pronounced impact on the buckling behavior of CNTs; interestingly, defective CNTs under compressive pre-load show higher resistance to thermal buckling than pristine ones. In the following, the buckling response of defective CNTs is shown to be dependent on the vacancy defects, location of defects and chirality. [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]

Buckling analysis of nanobeam is significantly important for design of nano-electro-mechanical systems (NEMS), especially for those under non-uniform temperature induced commonly by the operation of NEMS. In this work, such issue is investigated with the aids of size-dependent model, i.e. nonlocal thermoelasticity, and size effect of heat conduction on buckling property is considered for the first time. Euler–Bernoulli beam is adopted and reformulated within nonlocal theory. Analytical solution to critical load for various boundary conditions, e.g. SS, CF, CS and CC, is obtained using eigenvalue method. And the temperature distribution is determined using nonlocal heat conductive law. The effect of elastic and thermal nonlocal parameter on the critical load is systematically discussed. It is observed that classical models over-predict the critical load, which may be dangerous in practical applications. The present work is expected to be helpful for design of nanobeam-based devices and systems. [ABSTRACT FROM AUTHOR]

Beams (columns) subjected to axially distributed load (e.g., self-weight) are commonly treated using the classical Euler-Bernoulli beam theory, which ignores the transverse shear effect. Adopting the Engesser and Haringx shear theories, respectively, we study in this article the stability and initial post-buckling of sandwich (or laminated composite) beams under terminal force and axially distributed load. Nonlinear governing equations are derived from geometrical compatibility, equilibrium of forces, and moments. The critical buckling load, modal shapes of deformation, and shear force together with bending moment at buckling can be obtained by using the Galerkin's method in terms of trigonometric functions, and the initial post-buckled configuration of the beam is determined employing the shooting method. Predictions based on the Engesser theory agree with finite element simulation results, while the Haringx theory overestimates the buckling load. The effects of transverse shear and various different end constraint conditions on static buckling and initial post-buckling of sandwich beams are systematically explored. [ABSTRACT FROM AUTHOR]

Unstiffened cylindrical shells are very sensitive to geometric imperfections such as production-related deviations from the ideal geometry (conventional imperfections) as well as imperfect boundary conditions, material and wall thickness imperfections (non-conventional imperfections). The load carrying capability of unstiffened shells is reduced significantly by those imperfections. The NASA SP-8007 design guideline from 1968 is currently used for shell design. This guideline provides knock-down factors for the buckling loads and is based on experimental data of isotropic and orthotropic test specimen. Therefore the structural behavior of composite material is not considered adequately. Based on the single-perturbation load approach (SPLA), this paper introduces a new physical based approach, to determine a lower bound for the buckling load of unstiffened composite cylindrical shells with respect to conventional and non-conventional imperfections, the constant single-buckle imperfection (CSBI) principle. The CSBI principle is based on the theory of the metastability of the geometric imperfect cylindrical shell which is introduced within this paper. The results indicate that the CSBI principle has the potential to provide an improved shell design in order to reduce weight and cost of thin-walled shells. [ABSTRACT FROM AUTHOR]

The current article analyses the buckling response of piezoelectric cylindrical composite panels reinforced with carbon nano-tubes subjected to axial load. Classical laminated plate theory (CLPT) is employed to reach stress and displacement correlations embracing mechanical and magnetic terms. Stress–strain equations for piezoelectric cylindrical panels reinforced with carbon nanotubes are then written by using Mori–Tanaka method. The coupled electro-mechanical governing equations, Donnell theory as well as minimum potential energy method are thereafter utilized to calculate buckling loads and modes. The effects of such parameters as volume fraction of nano-tube, geometrical characteristics as well as two loading types of axial and biaxial on buckling load of the composite panel are investigated. The results show that increasing the volume fraction of nano-tube eventuates in increasing the buckling load. The results were compared with those already available in the existed literature using different shell theories for isotropic and composite cylindrical panels and a very good agreement was observed. [ABSTRACT FROM AUTHOR]

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

An analytical approach is presented to investigate the linear buckling of eccentrically stiffened functionally graded thin toroidal shell segments subjected to axial compression, lateral pressure, and hydrostatic pressure. On the basis of classical thin shell theory, the smeared stiffener technique and the adjacent equilibrium criterion, the governing equations of buckling of eccentrically stiffened functionally graded toroidal shell segments are derived. The functionally graded toroidal shell segments with simply supported edges are reinforced by a ring and stringer stiffener system on an external surface. The resulting equations in the case of compressive and pressure loads are solved directly. The obtained results show the effects of stiffeners and input factors on the buckling behavior of these structures. In this paper, the results are also compared with the solutions published in the literature for the specific cases of a toroidal shell. [ABSTRACT FROM AUTHOR]

Design of stiffened panels requires evaluating their behavior under any loading circumstances by considering initial geometric imperfections and the altering effects resulting from eventual material degradation. Both static and dynamic loading scenarios are to be investigated in order to assess safety for buckling strength of these vital structures. In this work, dynamic buckling under in-plane uniform axial compression loading having the form of finite duration pulse is analyzed through nonlinear finite element modeling of the structure. Welding induced defects that consist of initial geometric imperfections modifying the skin plate curvature in the longitudinal direction were incorporated. Material degradation in the heat affected zone was also taken into account. The Budiansky and Roth buckling criterion was employed to predict instability under a given dynamic load pattern. Various profiles including rectangular, triangular, double-triangular and half-sine were considered. The obtained results have shown that both the pulse period and the pulse shape have a drastic effect on the buckling strength. For the considered boundary conditions, pulses having periods that are comparable to two times the period of the first natural mode of vibrations were found to reduce the static buckling strength up to 66% in the elastic regime and 33% in the elastic plastic regime. [ABSTRACT FROM AUTHOR]

The present study is concerned with an analysis of load and frequency interaction effects in the dynamic buckling of sandwich plates and shells with a soft, transversely flexible core. The analysis is based of a general geometrically nonlinear soft-core sandwich model presented and a corresponding extended Galerkin solution strategy presented earlier. In the present study, the formalism is adopted and transformed into an eigenvalue problem. Assuming large transverse average displacements but small amplitudes for the vibration problem, a partially decoupled problem is obtained where in a first step the static buckling and face wrinkling problems can be addressed without consideration of the dynamic problem. In a second step, the dynamic eigenvalue problem can be solved, using the static solution as input parameters. The model is applied in parametric studies on the vibration response of plane and doubly curved sandwich panels with rectangular projection. In all cases, strong interaction effects between the external static preload and the natural frequencies are observed. The development of overall buckling or local face wrinkling instabilities enabled due to the transverse flexibility of the core result in distinct drops of the first natural frequency. [ABSTRACT FROM AUTHOR]

In the present work, an innovative approach is developed and employed to investigate the buckling load of composite laminated plates using polar representation of the fourth-order flexural stiffness tensor. Based on the Rayleigh-Ritz method for calculating the buckling load of orthotropic uncoupled laminates, a new approach is proposed for calculating the critical buckling load as a function of fiber orientation and the number of layers. A new formula is also represented for measuring the possible numbers of buckling modes based on the length-to-width ratio of the plate. Moreover, the new methods make it easy to handle buckling problems, optimization and design of laminated plates subjected to in-plane loads. The efficiency and precision of this method are proved by numerical examples. The anisotropic parts of the buckling load are calculated, and their polar variations are investigated. [ABSTRACT FROM AUTHOR]

A numerical study is carried out using finite element method, to examine the effects of square and rectangular cutout on the buckling behavior of a sixteen ply quasi-isotropic graphite/epoxy symmetrically laminated rectangular composite plate [0°/+45°/-45°/90°] subjected to various linearly varying in-plane compressive loads. Further, this paper addresses the effects of size of square/rectangular cutout, orientation of square/rectangular cutout, plate aspect ratio(a/b), plate length/thickness ratio(a/t), boundary conditions on the buckling bahaviour of symmetrically laminated rectangular composite plates subjected to various linearly varying in-plane compressive loading. It is observed that the various linearly varying in-plane loads and boundary conditions have a substantial influence on buckling strength of rectangular composite plate with square/rectangular cutout. [ABSTRACT FROM AUTHOR]

Experimental study on thin-walled welded steel beam-to-column connections under cyclic large plastic strain loading was conducted. Severe shear buckling in panel zones was observed during the testing. The connections have stable and excellent seismic performance, and finally failed due to the post-buckling ductile fracture. This paper aims to numerically simulate the post-buckling ductile cracking process using a proposed micro-mechanism based ductile fracture model, and further investigate critical factors, such as equivalent panel zone width-to-thickness ratio, axial load ratio and initial geometrical imperfection, that affect cracking behaviors of the connections. The cyclic ductile fracture model is verified with the experimental data, and employed to conduct the parametric analyses. Deterioration of stress-carrying capacity is also considered, so the fracture model can successfully simulate the load decrease in the load-displacement curves of the experimental results. [ABSTRACT FROM AUTHOR]

Practical applications such as airplane wings are usually subjected to combined thermal and mechanical loads, and they hence are prone to buckling failure. Preceding works on the buckling of advanced materials, e.g., functionally graded materials, under combined thermal and mechanical loads are rather rare in literature. In this paper, we report new numerical results of thermal-mechanical buckling of functionally graded rectangular and skew plates (FGPs) under combined thermal and mechanical loads. The numerical responses of buckling are computed using isogeometric analysis (IGA) based on the first-order shear deformation plate theory (FSDT) without shear-locking effect. We present formulations and then provide validation of numerical results computed by the proposed formulation against reference existing solutions. Parametric study is also performed to explore insight into the effects of various numerical aspect ratios such as gradient index, plate aspect ratio, loading type, skew angle, and boundary condition, etc. on mechanical response of FGPs. The stability diagrams are also presented. [ABSTRACT FROM AUTHOR]

A numerical approach for the study of the elastic buckling of slender columns with unilateral supports is proposed. This new approach is based on the numerical solution of a special type of eigenvalue problems that takes into account the complementarity character of the pair (displacement, obstacle reaction) at each unilateral support. The implementation of the proposed approach is illustrated by the determination of bifurcation loads and corresponding modes for several finite element models of columns. [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]

The present paper deals with the axisymmetric vibrations of multi-directional functionally graded circular plate under uniform in-plane loads resting on elastic foundation. The mechanical properties of the plate material are assumed to vary in both radial and transverse directions. Generalized differential quadrature method has been employed to obtain the frequency equations from the differential equation governing the motion of such simply supported plates. The effect of volume fraction index, in-plane force parameter, foundation parameter, heterogeneity parameter and density parameter has been studied on the natural frequencies of vibration. The critical buckling loads have been computed. Three-dimensional modes shapes for first three natural frequencies have been presented. [ABSTRACT FROM AUTHOR]

In this article, an analytical approach is presented to analyze static stability of defective annular graphene sheet. Due to production process and constrains conditions, graphene sheet may be opposed to structural defect. Some of the defects can be modeled as an eccentric hole. The graphene sheet is elastically restrained at the bottom surface. Nonlocal thin plate theory as well as the translational addition theorem are employed to solve the problem. The stability and accuracy of results are examined by the literature and the finite element analyses. Effects of eccentricity of defects, nonlocality, Winkler and Pasternak foundation parameters and various boundary conditions on the critical buckling load of an annular graphene sheet are investigated. It is observed that the eccentricity and size of defects have significant effect on the critical load. [ABSTRACT FROM AUTHOR]

Functionally graded carbon nanotube reinforced nanocomposites have drawn great attention in both research and engineering communities. The weak interfacial bonding between carbon nanotubes and the matrix, which traditionally hinders the application of carbon nanotube reinforced nanocomposites, can be remarkably improved through the graded distribution of carbon nanotubes in the matrix. Within the framework of classical beam theory, this paper investigates the dynamic buckling behavior of functionally graded nanocomposite beams reinforced by single-walled carbon nanotubes and integrated with two surface bonded piezoelectric layers. The governing equations of the beam subjected to an applied voltage, a uniform temperature and an axial periodic force are derived by applying Hamilton's principle. Numerical results are presented for beams with different distribution patterns and volume fractions of carbon nanotubes and end support conditions. The influences of the beam geometry, temperature change, applied voltage, static axial force component, boundary condition, carbon nanotube volume fraction and its distribution on the unstable regions of FG-CNTRC piezoelectric beams are discussed in detail. [ABSTRACT FROM AUTHOR]

The free vibration and buckling behaviors of foam-filled composite corrugated sandwich plates under thermal loading are investigated theoretically. A refined shear deformation theory is extended incorporating two different combinations of hyperbolic and parabolic shear shape functions. Equivalent thermoelastic properties of the foam-filled corrugation are obtained using the method of homogenization based on the Gibbs free energy. Based on hyperbolic-polynomial variation of all displacements across the thickness of both face sheets and sandwich core, the shear plate theory accounts for both transverse shear and thickness stretching effects. The theoretical predictions are validated against existing results as well as finite element simulations. The effects of geometric and material parameters on natural frequency and critical temperature change for buckling are systematically investigated. The proposed theory is not only accurate but also simple in predicting the free vibration and thermal buckling responses of composite sandwich plates with foam-filled corrugated cores. [ABSTRACT FROM AUTHOR]

A semi-analytical method named Galerkin strip distributed transfer function method (GSDTFM) is employed to solve the buckling and vibration of a single-layered graphene sheet (SLGS) nanomechanical resonator subjected to initial in-plane loads within the framework of the nonlocal Kirchhoff plate theory. The buckling load and the frequency shift are obtained by using the GSDTFM. And the effects of the initial in-plane load, the nonlocal parameter as well as the attached nanoparticle location on the frequency shift are investigated. The simulated results show that the buckling load of the SLGS depends on not only the side length of the SLGS, but also the small scale effects. The impact of the initial in-plane load on the fundamental frequency is significant. The frequency shift at an initial tensile load is larger than that at an initial compressive load. These results are consistent with the previously reported ones. [ABSTRACT FROM AUTHOR]

A semi-analytical solution of thermal buckling and postbuckling equilibrium paths of rectangular composite plates subjected to localized thermal heating over the plate area with uniform temperature rise through its thickness is reported here. The plate is either simply supported or clamped for out-of-plane displacements and immovable for in-plane displacements. The thermal buckling of the composite plate subjected to localized thermal loading is solved in two steps as the prebuckling stress distributions within the plate are not known a priori. In the first step the explicit analytical expressions for these in-plane prebuckling stress distributions within the composite plate are developed by solving the thermoelasticity problem using Airy's stress function. Using the computed in-plane stress distributions within the plate, the plate nonlinear stability equations are formulated using a variational principle. First-order shear deformation theory incorporating von-Kármán geometric nonlinearity is used to model the plate. The generalized differential quadrature method in conjunction with the modified Newton-Raphson method is used to solve the nonlinear governing partial differential equations for nonlinear thermal stability of composite plates. The influence of aspect ratio, area of heated region, and the boundary conditions on the critical buckling temperature and equilibrium paths are examined. [ABSTRACT FROM AUTHOR]

This paper presents a unified nonlinear analytical solution of bending, buckling and vibration for the temperature-dependent functionally graded (FG) rectangular plates subjected to thermal load. Geometric nonlinearity resulted from mid-plane stretching is considered. Material properties of FG plates are assumed to vary with temperatures and the volume fractions of the constituents. Newly proposed higher order shear deformation theories in present available literature are sorted out and given a unified application. Three types of mathematical models, P-FG, S-FG and E-FG models, describing effective material properties of functionally graded materials (FGMs) are discussed. Finally, based on the unified nonlinear analytical solution, influences of material heterogeneity, thermal load, and plate geometry on bending, buckling and vibration of FG plates are studied. Outcomes reveal that the nonlinear solution exhibits better accuracy in calculation of shear stress in bending responses. The thermal load plays an important role in determining the bending, buckling and vibration of the FG plate. In addition, the characteristics of these three types of mathematical models to simulate effective material properties of FGMs are numerically compared and discussed. [ABSTRACT FROM AUTHOR]

The computational methods for solving buckling loads of thin-walled members with open sections are not unique when different concerns are emphasized. In this paper, the buckling loads of thin-walled members in linear-elastic, geometrically nonlinear-elastic, and nonlinear-inelastic behaviors are investigated from the views of mathematical formulation, experiment, and numerical solution. The differential equations and their solutions of linear-elastic and geometrically nonlinear-elastic buckling of thin-walled members with various constraints are derived. Taking structural angle as an example, numerical analysis of elastic and inelastic buckling is carried out via ANSYS. Elastic analyses for linearized buckling and nonlinear buckling are realized using finite elements of beam and shell and are compared with the theoretical results. The effect of modeling of constraints on numerical results is studied when shell element is applied. The factors that influence the inelastic buckling load in numerical solution, such as modeling of constraint, loading pattern, adding rib, scale factor of initial defect, and yield strength of material, are studied. The noteworthy problems and their solutions in numerically buckling analysis of thin-walled member with open section are pointed out. [ABSTRACT FROM AUTHOR]

To obtain accurate buckling load for rectangular plates under compressive point loads, one of the important factor is that the in-plane stress distributions within the plate prior to buckling should be accurate enough. Although the differential quadrature method (DQM) has been successfully used in a variety of fields including the buckling analysis of thin rectangular plates under non-uniformly distributed edge compressions, however, the DQM has some difficulty in dealing with singular functions such as the Dirac-delta function appeared in the stress boundary condition. In this paper, novel formulations are presented to overcome the difficulty encountered in dealing with the Dirac-delta functions by using the DQM. The normal stress boundary condition is numerically integrated before being discretized in terms of the differential quadrature. Detailed formulations are given. Buckling of rectangular plates under either uniaxial or biaxial compressive point loads is successfully analyzed. It is demonstrated that accurate buckling loads can be obtained by the DQM for rectangular plates with nine combinations of boundary conditions and various aspect ratios. The compactness and computational efficiency of the DQM are retained in solving the partial differential equations with boundary conditions involving Dirac-delta functions. The accuracy of the differential quadrature (DQ) results is verified by comparing them with existing analytical solutions and finite element data. New results are tabulated which can be a reference for other researchers to develop new numerical methods. [ABSTRACT FROM AUTHOR]

This paper presents an analytical study on the thermal buckling analysis of axially loaded columns of thin-walled open section with nonuniform sectional properties. Obtained herein are critical loads related to flexural, torsional and flexural-torsional buckling of an I-section column subjected to an axial compressive load applied at the geometric centroid, and under linearly varied non-uniform temperature distribution scenarios. The analysis is accomplished using traditional energy methods. The influences of thermal strain, nonuniform distribution of pre-buckling stresses, and variation of pre-buckling stresses along the longitudinal axis of the column on critical buckling loads are examined. The present results highlight the importance of nonuniform sectional properties in the buckling analysis of columns of doubly symmetric section. [ABSTRACT FROM AUTHOR]

An approximate analytical solution of the buckling problem formulated for a composite sandwich cylindrical shell subjected to a uniform external lateral pressure is presented in the paper. Both ends of the shell of finite length are fully clamped. The problem is solved using the Galerkin method. The analytical formula for the critical load has been obtained and verified by comparison with a finite-element solution. Based on this formula buckling analyses of sandwich pipes with different types of core materials normally used in underwater applications have been performed. Applications of the formula to the solutions of design problems have been demonstrated for the clamped–clamped sandwich pipes considering constraints imposed on the value of critical pressure. [ABSTRACT FROM AUTHOR]

In this paper, a re-look into the upper and lower bound solution to the buckling of composite columns is presented in details and this includes the complete derivation of the expressions for the kinematical compatibility conditions. Included in this contribution are also the results of the current finite element simulation together with the results of the experiments. Moreover, further investigations are conducted to test whether the proposed three methods of calculating the effective flexural stiffness can be employed in cooperation with the developed mathematical model to form the desired upper and lower bounds for the buckling loads of both the perfect and single-delaminated fiber-reinforced composite beams for the various parameters that are studied. In these analyses, single-delaminated fiber-reinforced composite beams which consist of random ply-orientations and stacking sequences are employed to put up a stringent test on the generalness and applicability of these three methods. It is observed that for all the cases that were examined, these three means of evaluating the effective bending modulus of a fiber-reinforced composite beam pass are validated. [ABSTRACT FROM AUTHOR]

This work presents a metamodel strategy to approximate the buckling load response of laminated composite plates. In order to obtain representative data for training the metamodel, some laminates with different stacking sequences are generated using the Latin hypercube sampling plan. These stacking sequences are converted into lamination parameters so that the number of inputs of the metamodel becomes constant. The buckling load for each laminate of the training set are computed using finite elements. In this way the inputs-outputs metamodel training pairs are the lamination parameters and the corresponding bucking load. Neural network and support vector regression metamodels are employed to approximate the buckling load. The performances of the metamodels are compared in a test case and the results are shown and discussed. [ABSTRACT FROM AUTHOR]

Morphing aircraft aim to increase the performance of aircraft over multiple flight conditions, by enabling shape changes in flight in order to optimise their aerodynamic properties for the current conditions. The skin of a morphing aircraft is a critical component. It must be compliant in degrees of freedom that are required for actuation, to minimise the actuation loads. However, it must also carry structural loads, and therefore be stiff in load bearing degrees of freedom. This leads to a requirement for extremely anisotropic material systems. A common solution is the use of a corrugated panel. However, previous work on corrugations has not addressed the problem of compressive buckling loads. This work analyses the performance of corrugated panels under buckling loads, and optimises corrugation patterns for the objectives of weight, buckling performance, and actuation compliance. Simplified analytical models that derive properties equivalent to conventional plates are used to obtain approximate estimates of the buckling loads. Furthermore a new mode of buckling, that occurs entirely in-plane and is unique to panels with extreme anisotropy is analysed. The simple models allow optimisation to be performed, and both a single-objective and a multi-objective approach are demonstrated. The results are compared to Finite Element Analysis. [ABSTRACT FROM AUTHOR]

This article deals with the buckling analysis of rectangular functionally graded material (FGM) plates using classical plate theory (CPT). Finite element method has been applied for the modelling and buckling analysis of FGM plate. Uniaxial and biaxial compression loads along with simply supported boundary conditions on rectangular FGM plates are investigated. Convergence of the solution obtained by MATLAB has also been studied by varying the mesh size. Obtained results are compared with the existing literature, it shows that the buckling characteristics are closer to the reference results. By varying the geometric parameter a/b critical buckling load variation has been calculated and Power law index is also been evaluated. [ABSTRACT FROM AUTHOR]

In practice, voltage would be stored in actuators due to applied mechanical loads or voltage specified as input to them. The effect of stored voltage in actuators on buckling analysis has not been studied so far. This article addresses fully coupled electromechanical buckling analysis of active laminated composite thin to thick plates using partial hierarchical Rayleigh–Ritz solution. The formulation is derived from variational principle with consideration for shear deformation plate theory. Another major contribution is to postpone the initiation of buckling of a laminated plate by increasing its flexural stiffness using feedback piezoelectric control. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for the buckling and free vibration analysis of laminated beams by using a refined and generalized shear deformation theory which includes the thickness expansion. The eigenvalue equation is derived by employing the Rayleigh quotient, and the Ritz method is used to approximate the displacement field. The functions used in the Ritz method are chosen as either a pure polynomial series or a hybrid polynomial-trigonometric series. The hybrid series is used due to the superior convergence and accuracy compared to conventional pure polynomial series for certain boundary conditions. The boundary conditions are taken into account using the penalty method. Convergence of the results is analyzed, and numerical results of the present theory are compared with other theories for validation. Nondimensional natural frequencies and critical buckling loads are obtained for a variety of stacking sequences. The effect of the normal deformation on the fundamental frequencies and critical buckling loads is also analyzed. [ABSTRACT FROM AUTHOR]

The lateral buckling problem for continuous welded rail tracks under thermal loading has been well researched and is known to involve a localisation buckling phenomenon where only a limited region of the track buckles. In this paper, a sandwich column model is formulated to model the rail track-tie structure as sandwich column. The constitutive relations for the thermally induced stresses and finite strain are based on a hyperelastic constitutive model. A hyperbolic function for the nonlinearity of the axial and lateral resistance between the tracks and ballast was used. A critical track length is proposed beyond which the localisation is unaffected. Increasing the track length or changing the boundary conditions does not influence the localised buckling behaviour for track lengths beyond the critical length. The use of fasteners with large rotational stiffness substantially increases the lateral stability of the track-tie structure. Nonlinear numerical solutions are compared with the results in the literature. The variation in the axial compressive force within the localisation zone in the rail is studied and discussed. Parametric studies are performed on examples to identify the influence of track imperfections on the localised lateral buckling and safe temperature change. [ABSTRACT FROM AUTHOR]

In this study, we use transport equations to investigate the dynamic buckling of an imperfect elastoplastic beam, including the effect of axial stress waves, when subjected to an impulsive load. Thus, the governing equations for the elastoplastic behavior of the material are extracted using mass, energy, and momentum transport equations. We assume that the passage of the shock wave through the control volume creates five phases with four boundary discontinuities, i.e., the initial elastic phase, initial plastic phase, fluid phase, secondary plastic phase, and secondary elastic phase. Transport equations are used in integral form as well as non-physical variables to eliminate the discontinuity conditions in the governing equations. These equations are also used for continuum modeling of the elastoplastic behavior of the beam under an impulsive load and a continuous model is presented. Finally, the time histories of stress, strain, and velocity wave propagation along the beam are presented, and the results are validated based on comparisons with known solutions. [ABSTRACT FROM AUTHOR]

Abstract The present paper shows an experimental and numerical modelling investigation of the flexural-torsional buckling behaviour and load-carrying capacities of fixed-ended hot-rolled austenitic stainless steel equal-leg angle section columns. The testing programme was conducted on four austenitic stainless steel angle sections and involved material testing, initial global and torsional imperfection measurements and sixteen fixed-ended column tests. This was followed by a numerical simulation study, where the numerical models were firstly developed to validate against the experimental data and then utilised to perform numerical parametric studies to generate additional results over a broader range of member lengths and cross-section geometric dimensions. The derived test and finite element results were carefully analysed and then utilised to evaluate the accuracy of the established design rules in Europe, America and Australia/New Zealand. Comparisons of the failure loads derived from the experimental and numerical studies with the corresponding codified flexural-torsional buckling strength predictions revealed an unduly high level of conservatism and scatter. Extension of the direct strength method to carbon steel equal-leg angle section columns has been recently made, and the applicability of the approach to fixed-ended hot-rolled austenitic stainless equal-leg steel angle section columns was also assessed. The new approach was generally shown to yield more precise flexural-torsional buckling resistance predictions than the existing design standards, but a large portion of the predictions were unsafe, indicating that further improvements are required. Highlights • 16 fixed-ended hot-rolled austenitic stainless steel equal-leg angle section columns have been tested. • FE models have been validated against tests and used to perform parametric studies. • Current international design codes and other recent proposals have been described and discussed. • The accuracy of each approach has been evaluated against test and FE results. [ABSTRACT FROM AUTHOR]

Cellular and castellated members are usually produced by performing cutting and rewelding operations on a hot-rolled I-section member. As illustrated in previous work, these operations will influence the residual stresses present in the members in a manner which is detrimental for the flexural buckling resistance. Up to now, this has not been considered in the limited amount of literature concerning the flexural buckling resistance of these members. In this paper, the weak-axis flexural buckling resistance is examined, taking into account the influence of the modified residual stress pattern and the modified geometry of cellular and castellated members. Therefore, the critical buckling load and the buckling resistance of simply supported cellular and castellated members were investigated numerically. In the numerical model, a modified residual stress pattern was introduced, based on earlier measurements. As the amount of measurements was relatively limited, the results of these simulations should be considered as preliminary results, in attendance of a confirmation of the utilized residual stress pattern. The results of the simulations illustrate the detrimental influence of the expected residual stress pattern modification on the buckling resistance. By comparing the results with the European buckling curves, preliminary best fit curves could be selected. This comparison was executed with a 2T approach, in which all cross-sectional properties are calculated for the 2T section at the centre of the opening. [ABSTRACT FROM AUTHOR]

An analytical solution for buckling of an eccentrically stiffened sandwich truncated conical shell is investigated. The shell consists of two functionally graded material (FGM) coating layers and a core layer which are metal or ceramic subjected to an axial compressive load and an external uniform pressure. Shells are reinforced by stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution. Two models of coated shell-stiffener arrangements are investigated. The change of the spacing between stringers in the meridional direction is taken into account. A couple set of three-variable-coefficient partial differential equations in terms of displacement components are solved by the Galerkin method. A closed-form expression for determining the buckling load is obtained. The numerical examples are presented and compared with previous works. [ABSTRACT FROM AUTHOR]

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

Abstract: Various methods can be used to investigate buckling phenomena in a steel compression member. Among these methods, experimental formulas, semi-empirical formulas, closed-form solutions and classic methods based on differential equations as well as numerical methods based on finite elements are most commonly used. All of these methods have associated complexities. Thus, it is very difficult to perform a comprehensive parametric study on the buckling phenomenon of a compression member using these methods. The simplicity of the mathematical concepts used in ANNs (artificial neural networks) and their ability to model complex problems have led to the popularity of ANNs. After the learning step of an ANN, a function can be determined as a relationship between the input variables and output parameters, which is a load–displacement relationship in this article. It is then possible to perform an extensive parametric study on the buckling behavior of a compression member. In this research, the network can also extract the critical load–slenderness relationship. Using this network, it is possible to conduct an accurate study on the effects of various parameters at the critical load as well as to evaluate the sensitivity of the critical load to each variable used in the ANN training. [Copyright &y& Elsevier]

A theoretical (semi-analytical) approach was proposed to estimate the dynamic in-plane response of corrugated core sandwich columns against suddenly applied loads with a compression rate less than 5m/s. The model has been constructed so as to effectively include various dynamic effects such as stress wave propagation, material rate dependence and lateral inertia. The practical and theoretical complexities caused from the dynamic phenomena and the established governing equations (e.g. coupled non-uniform axial force distribution) have been resolved by employing Galerkin's method. The proposed approach was validated by comparing the calculations from the theoretical model and Finite Element Method (FEM): the load history and deformation shape of extruded Al6061-T6 corrugated core sandwich columns and bending/brazed SS304 corrugated core sandwich columns. The model successfully yielded the imperfection-sensitive, velocity-dependent dynamic response and appearance of higher buckling modes. In addition, it has been demonstrated that the sandwich columns with periodic cellular metals outperform their weight-equivalents, monolithic solid columns, under dynamic conditions. The proposed approach as an efficient tool to explore the dynamic global buckling response in design space can make preliminary studies of weight minimization for dynamic applications. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of geometric nonlinearity and temperature field on the in-plane elastic behaviour and buckling of crown-pinned circular steel arches that is subjected to a uniform radial load. Differential equations of equilibrium are derived based on the principle of stationary potential energy, and analytic solutions for the linear and nonlinear behaviour and buckling loads are derived. It is found that the nonlinearities have significant influences on the in-plane behaviour and buckling of crown-pinned arches. The nonlinear bending actions produced by the uniform radial load in crown-pinned arches are substantial, while the linear bending actions are equal to zero for three-pinned arches and are small for one-pinned arches. The nonlinear buckling loads are much lower than their linear counterparts. It is also found that the uniform temperature field influences the nonlinear elastic behaviour and buckling of crown-pinned arches, while it has no effects on the linear internal actions of three-pinned arches and small effects on those of one-pinned arches. As temperature increases, radial displacements decrease while the nonlinear buckling loads increases. It is further found that crown-pinned arches can buckle only in a symmetric mode, but not in an antisymmetric mode. Comparisons with the finite element results show that the analytical solutions derived in this paper are quite accurate. [ABSTRACT FROM AUTHOR]

In this paper, a Levy-type solution based on the modified couple stress theory is developed to study the buckling behaviors of micro-plates. Based on this theory, length scale parameter is considered to capture the size effect of rectangular micro-plates. Minimum potential energy and adjacent-equilibrium criteria are exploited to obtain the stability equations and corresponding boundary conditions. Different boundary conditions with two opposite edges simply supported and arbitrary boundary conditions along the other edges are considered. To illustrate the new model, both uniaxial and biaxial loads are applied and the critical buckling loads are defined for over a wide range of thickness, different length scale parameters and various boundary conditions. To show the accuracy of the formulations, present results are compared with available results in literature for specific cases and a very good agreement is observed. Results reveal that the critical buckling load increases as the length scale parameter increases especially when the thickness of the micro-plates becomes in order of length scale parameter and this effect is more significant for free boundary condition. [ABSTRACT FROM AUTHOR]

Abstract: Presented in this paper is analysis of buckling of double-orthotropic nanoplates based on nonlocal elasticity theory. It is assumed that two nanoplates are bonded by an internal elastic medium and surrounded by external elastic foundation. Three characteristic types of buckling are considered. Governing equations are derived based on nonlocal theory, while the expressions for the buckling load are given in explicit form for a nanoplate with all edges simply supported. Explained in detail is the influence of small scale coefficient, aspect ratio, and stiffness of internal elastic media and external elastic foundation, on the nondimensional buckling load. [Copyright &y& Elsevier]

Abstract: This paper presents an investigation into the effect of cutout and flange reinforcement on the buckling and post-buckling behaviour of a carbon/epoxy composite C-section structure. The C-section having a cutout in the web is clamped at one end and subjected to a shear load at the other free end. Three different stiffener reinforcements were investigated in finite element analysis by using MSC Nastran. Buckling load was predicted by using both linear and nonlinear FE analysis. Experiments were carried out to validate the numerical model and results. Subsequently post-buckling analysis was carried out by predicting the load–deflection response of the C-section beam in nonlinear analysis. Tsai-Wu failure criterion was used to detect the first-play-failure load. The effect of circular and diamond cutout shape and effective flange reinforcements were investigated. The results show that the cutout and reinforcement have little effect on the buckling stability. However an L-shape stiffener to reinforce the C-section flange can improve the critical failure load by 20.9%. [Copyright &y& Elsevier]