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

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

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

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

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]

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]

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]

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

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

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

Non-destructive methods to estimate the actual buckling load in particularly for imperfection sensitive thin-walled structures, are of severe interest among many fields. Particular techniques for validation of structural limit state and numerical model predictions for large scale structures are getting momentum. The vibration correlation technique (VCT) allows to correlate the ultimate load our instability point with rapid decrement of self-frequency response. Nevertheless this technique is still under development for thin-walled shells and plates. The current research discusses an experimental verification of extended approach, using vibration correlation technique, for the prediction of actual buckling loads on unstiffened cylindrical shells loaded in axial compression. Validation study include two laminated composite cylinders which were manufactured and repeatedly loaded up to instability point. In order to characterize a correlation with the applied load, several initial natural frequencies and mode shapes were measured during tests by 3D laser scanner. Results demonstrate that proposed vibration correlation technique allows one to predict the experimental buckling load with high reliability, without actually reaching the instability point. Additional experimental tests and numerical models are currently under development to further validate the proposed approach to extended composite and metallic structures. [ABSTRACT FROM AUTHOR]

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

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]

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

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

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]

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]

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]

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]

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]

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]

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 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]

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]

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]

This paper focuses on the effect of member geometric imperfection on nonlinear geometrically buckling and seismic performance of a new style of space steel structure, suspen-dome, which is composed of a reticulated shell and cable-strut system. By supposing the initial curvature of members as half-wave sinusoids, a stiffness equation of imperfect truss elements is derived for the struts, while that of imperfect beam elements is derived for the reticulated shell members. The proposed imperfect elements are implanted into ANSYS finite element program. Three numerical examples are employed to validate the proposed imperfect elements and analysis method. An ellipsoidal suspen-dome of Changzhou gymnasium is taken as an example. The results show that the imperfection value has relatively great influence on the structural stiffness. With the increase of member imperfection, the critical load decreases in a basically linear way. Under different prestress states, the relation curves between the critical load and imperfection are basically parallel. The nonlinear seismic analysis results show that when imperfection is included, the initial state responses are different, namely, the seismic displacement increases while the stress in rods and cables decreases. The proposed imperfection analysis method can be widely used in not only suspen-dome structures, but also other kinds of prestressed space grid structures. In this way, the influence of member imperfection on structural buckling and seismic performance can be estimated. [ABSTRACT FROM AUTHOR]

This paper presents a method for the determination of the buckling loads of symmetrically laminated composite plates under uniaxial compressive load with explicit consideration of bending–twisting-coupling (BTC). The plates under consideration are assumed to be thin and balanced with a symmetric stacking sequence and consist of layers with ply orientations of {0°/±45°/90°}, but otherwise arbitrary lamination schemes. The characteristic laminate quantities are described in a non-dimensional notation in order to capture all combinations of material and stacking sequences that are physically possible. Plates with rectangular planforms in the framework of Classical Laminate Theory (CLT) under several different sets of boundary conditions are considered, and the buckling problem of such composite laminated plates is solved in an approximate manner by using the classical Rayleigh–Ritz method. Several combinations of the boundary conditions ‘simply supported’ and ‘clamped’ are analyzed, and the obtained results are compared with finite-element simulations for verification purposes. Based on the computed data, two different design equations for sufficiently long plates are developed which allow for a rapid and closed-form analytical assessment of the buckling behavior of symmetrically layered composite plates under explicit consideration of bending–twisting coupling. It is found that the closed-form analytical analysis equations are simple in their application and yet still work with very satisfying accuracy which makes them very suitable for use in practical engineering work. [ABSTRACT FROM AUTHOR]

Analytical buckling models are important for down-hole operations to ensure the structural integrity of the drill string. A literature survey shows that most published analytical buckling models do not address the effects of inclination angle, boundary conditions or friction. The objective of this paper is to study the effects of boundary conditions, friction and angular inclination on the helical buckling of coiled tubing in an inclined wellbore. In this paper, a new theoretical model is established to describe the buckling behavior of coiled tubing. The buckling equations are derived by applying the principles of virtual work and minimum potential energy. The proper solution for the post-buckling configuration is determined based on geometric and natural boundary conditions. The effects of angular inclination and boundary conditions on the helical buckling of coiled tubing are considered. Many significant conclusions are obtained from this study. When the dimensionless length of the coiled tubing is greater than 40, the effects of the boundary conditions can be ignored. The critical load required for helical buckling increases as the angle of inclination and the friction coefficient increase. The post-buckling behavior of coiled tubing in different configurations and for different axial loads is determined using the proposed analytical method. Practical examples are provided that illustrate the influence of the angular inclination on the axial force. The rate of change of the axial force decreases with increasing angular inclination. Moreover, the total axial friction also decreases with an increasing inclination angle. These results will help researchers to better understand helical buckling in coiled tubing. Using this knowledge, measures can be taken to prevent buckling in coiled tubing during down-hole operations. [ABSTRACT FROM AUTHOR]

Abstract: Large parabolic dish concentrators have been widely employed in solar thermal applications. The supporting structure of a solar dish concentrator consists of a circular frame, a central post, and front and rear cables connecting the frame to the post. The tensions in the cables cause compressive stresses in the circular frame and the central post, and this support structure must be designed for stability. In this paper, the nonlinear buckling behavior of the supporting structure of a cable-stayed circular frame is studied in detail. A three-dimensional finite element model of the supporting structure is developed to predict the critical cable tensions that would cause buckling of the circular frame and to determine the associated buckling mode shapes of the supporting structural system. The results show that the buckling load of a cable-stayed circular frame depends not only upon the cross-section of the frame, but also upon the number of cables and the inclinations of the cables. In all cases, in-plane buckling modes are predominant. The concentrated torques resulting from unbalanced cable tensions tend to induce the out-of-plane buckling modes. [Copyright &y& Elsevier]

The paper outlines the fundamentals of the method of solving static problems of geometrically nonlinear deformation, buckling, and postbuckling behavior of thin thermoelastic inhomogeneous shells with complex-shaped midsurface, geometrical features throughout the thickness, or multilayer structure under complex thermomechanical loading. The method is based on the geometrically nonlinear equations of three-dimensional thermoelasticity and the moment finite-element scheme. The method is justified numerically. Results of practical importance are obtained in analyzing poorely studied classes of inhomogeneous shells. These results provide an insight into the nonlinear deformation and buckling of shells under various combinations of thermomechanical loads. [ABSTRACT FROM AUTHOR]

Abstract: A new solution for analyzing of the symmetrical composite plate having two parallel edges simply supported and the remaining parallel edges being clamped (SS–C–SS–C plate) subjected to linear-varying in-plane loads is presented. Levy series are used to represent the displacement field of the plate and a numerical procedure is developed based upon finite-difference method. Convergence study is carried out as well. The proposed method has been validated for both isotropic and composite plates with various aspect ratios and load parameters through numerical examples. [Copyright &y& Elsevier]

Abstract: In the present paper, a three-dimensional elasticity approach is employed to investigate buckling of heterogeneous functionally graded plates under biaxial compression, shear, tension-compression, and shear-compression load conditions. In this regard, a formulation that employs a full compatible three-dimensional Hermitian element with 168 degrees of freedom and guarantees continuity of the strain and stress components is used. It is known that all of the available famous commercial finite element softwares and the proposed series solutions satisfy continuity conditions of the displacement rather than the stress components. Buckling occurrence is detected based on checking both the instability onset and equilibrium criteria. Results are extracted based on a Galerkin-type orthogonality. Therefore, they are more accurate than those obtained based on the traditional Ritz method. The presented three-dimensional finite element analysis and the extracted results are quite new. A vast variety of results including results of biaxial compression, compression-tension, shear, and shear-compression load cases is considered and discussed in detail. [Copyright &y& Elsevier]

Highlights: [•] Shear and torsional rigidities of trusses are theoretically derived. [•] Out-of-plane buckling loads of pin-ended circular truss arches are derived. [•] Effect of shear deformation on buckling loads of truss arches is included. [Copyright &y& Elsevier]

The conventional approach to analysis the buckling of rectangular laminates containing an embedded delamination subjected to the in-plane loading is to simplify the laminate as a beam-plate from which the predicted buckling load decreases as the length of the laminate increases. Two-dimensional analyses are employed in this paper by extending the one-dimensional model to take into consideration of the influence of the delamination width on the buckling performance of the laminates. The laminate is simply supported containing a through width delamination. A new parameter β defined as the ratio of delamination length to delamination width is introduced with an emphasis on the influence of the delamination size. It is found that (i) when the ratio β is greater than one snap-through buckling prevails, the buckling load is determined by the delamination size and depth only; (ii) as the ratio β continues to increase, the buckling load will approach to a constant value. Solutions are verified with the well established results and are found in good agreement with the latter. [ABSTRACT FROM AUTHOR]

Abstract: In the present work a model able to predict the buckling behavior of thin, orthotropic, stiffened plates and shells subject to axial compression is proposed. In the context of the Kirchhoff-Love plate theory and making use of different strain-displacement models – namely the von Kármán model, the Koiter–Sanders shell model, an enhanced von Kármán model and a spurious model commonly adopted in literature – the equilibrium equations have been solved by the Levy-type approach. The results obtained highlight the influence of each non-linear strain-displacement term and show that the von Kármán model can noticeably overestimate the buckling load when the critical mode involves significant in-plane displacements. [Copyright &y& Elsevier]

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

Abstract: The detrimental effect due to perforations on the buckling resistance of perforated hot-rolled steel L-shaped members in compression is evaluated in the current paper. FEM numerical models are used in order to carry out buckling and non linear analyses with the aim of detecting both the critical and the collapse load of the studied elements in case of one or more holes. The obtained results show that, although the critical load is not strongly influenced by the presence of holes, the load bearing capacity, when members are characterized by middle–low slenderness, could be significantly diminished when drillings of common sizes are applied on one of the two section legs, meaning that current methods given by the codes are not fully conservative. As a consequence, specific stability curves are determined and proposed as useful alternative design procedure. [Copyright &y& Elsevier]

Abstract: The paper is concerned with the buckling analysis of the composite orthotropic cylindrical shell with clamped edges subjected to inertia loading. The problem is characterised by a non-uniform pre-buckling stress state. To address this, the relevant governing system of differential equations with variable coefficients has been derived and solved using Galerkin method. As a result, the problem of determining the critical acceleration causing the buckling of shell is reduced to the solution of the corresponding generalised eigenvalue problem. Using the proposed approach, the critical accelerations are calculated for the glass-fibre reinforced shells with various dimensional and stiffness parameters. Results of calculations are compared with those based on finite-element modelling and analysis. [Copyright &y& Elsevier]

Abstract: The principal purpose of the paper is to present an efficient mathematical model for studying the buckling behaviour of geometrically perfect, elastic Reissner’s two-layer composite columns with interlayer slip and uplift between the layers. The present mathematical model is capable of predicting exact critical buckling loads and corresponding buckling modes. Thus, it is used to study the influence of the transverse interlayer stiffness in combination with the longitudinal interlayer stiffness on critical buckling loads and modes. This effect is proved to be significant. The critical buckling loads calculated by the proposed method can be up to approximately 89% smaller than those where interlayer uplift is neglected. [Copyright &y& Elsevier]

Abstract: This paper presents a detailed investigation of effect of load height on buckling resistance of steel beams. Shapes that are intended to be used primarily as a beam are generally proportioned so that moment of inertia about the principal axis is considerably larger than that about minor axis. Hence monosymmetric sections are preferable. The lateral stability of beam subjected to transverse loading is very complicated in monosymmetric sections. The distance of transverse load from shear centre axis may significantly affect the buckling resistance of a simply supported beam. When transverse concentrated load W acts at (Yq-Yo) below the shear centre and moves with the beam it acts as an additional torque W(Yq-Yo) about shear centre which opposes twist and increases resistance to buckling. Conversely, when load above shear centre, additional torque increases the twist rotation and reduces buckling resistance of beam. To verify the effect of load height on buckling resistance, a simply supported beam subjected to concentrated and uniformly distributed load is considered. The effect of load height on buckling resistance has been plotted. [Copyright &y& Elsevier]

Abstract: We study a variation on the classical problem of the buckling of an elastica. The elastica models a nanoscale sheet that interacts with a rigid substrate by intermolecular forces. We formulate a buckling problem in which the sheet is perpendicular to the substrate and a load is applied to the edge of the sheet further from the substrate. Our study is motivated by problems in nanomechanics such as the bending of a graphene sheet interacting with a rigid substrate by van der Waals forces. After identifying a trivial branch, we combine computation and analysis to determine the stability and bifurcations of solutions along this branch. We also study the boundary-layer problem that arises if the length of the sheet is large compared to the characteristic length over which the van der Waals interaction is significant. [Copyright &y& Elsevier]

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

Abstract: The paper presents a procedure for the analysis of stability and initial post-buckling behaviour of spliced columns in sway and non-sway steel frames. The main assumptions are linear elasticity and geometrically perfect columns that are loaded by a compressive force which retains its direction as the column deflects. An energy-based formulation that includes a polynomial Rayleigh–Ritz approximation into the potential energy function, in combination with the Lagrange’s method of undetermined multipliers, has been found very convenient for this type of problem. The system is thus described by a set of kinematically admissible generalized coordinates and a single loading parameter. First, the critical state is characterized by means of linear eigenvalue analysis. A parametric study is implemented to assess the critical load. The numerical results are used to develop a relatively simple yet reasonably accurate engineering method for predicting the critical behaviour of spliced columns in sway and non-sway steel frames. The energy formulation is then applied to the search of post-buckling branches of bifurcation points. The approach embraces path-following methods based on perturbation schemes built on a Newton type iterative procedure. This is illustrated in the application to post-bifurcation in columns with different splice mechanical characteristics. The findings suggest that the splice tangent stiffness has a major influence on the overall column behaviour. [Copyright &y& Elsevier]