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The so-called “plastic buckling paradox” originates from the fact that the Prandtl–Reuss’ flow theory of plasticity overestimates the plastic buckling load of plates and shells, whereas Hencky’s deformation theory of plasticity provides results that are more accurate. However, it has been shown that this problem can be overcome by introducing certain initial imperfection in accurate finite element (FE) simulations based on the flow theory of plasticity.1–4 The present study goes deeper into the problem and reveals that in the case of short cylinders under combined loading, which have long been the object of extensive research in the elastic range,5 a different modeling of the material behavior can also trigger a mode jumping from the initial imperfection, which may even reverse the reported predictions by the flow and deformation theories of plasticity. This fact must be taken in maximum consideration when performing nonlinear FE analyses for estimating the plastic buckling of thin and moderately thin short cylindrical shells. [ABSTRACT FROM AUTHOR]

Thermal buckling of functionally graded sandwich plates are presented in this article. Two common types of FGM sandwich plates, namely, homogeneous face layers with FGM core and FGM face layers with homogeneous core are considered. Material properties and thermal expansion coefficient of FGM layers are assumed to vary continuously through-the-thickness according to a simple power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FGM sandwich plate with simply supported boundary conditions are derived using the higher-order shear deformation plate theory. The influence of the plate aspect ratio, the relative thickness, the gradient index, and the thermal loading conditions on the critical buckling temperature of FGM sandwich plates are investigated. The thermal loads are assumed to be uniform, linear, and nonlinear distribution through-the-thickness. A new simple solution for thermal buckling of FGM sandwich plates under nonlinear temperature rise is presented. [ABSTRACT FROM PUBLISHER]

In this work, explicit equations to determine local buckling critical stress of thin-walled fiber reinforced polymer (FRP) profiles in pure bending or compression are proposed. Interaction between flange and web is considered and the expressions allow for different orthotropy ratios and ranges of flange-to-web widths and thicknesses. To obtain the equations, Rayleigh Quotient energy method is adopted for assumed approximate buckled shapes. As quality of selected functions affects the accuracy, different shapes are investigated and the results are compared with those obtained with Generalized Beam Theory (GBT) for typical I-section dimensions and material properties. A comparison is made to the solutions based on discrete plate with simplified support conditions as well as to a recently proposed equation for major-axis bending. Finally, a general form for the local buckling critical coefficient is also presented along with tabulated parameters for prompt assessment of critical stresses, consisting in a simple and reliable alternative for design approach. [ABSTRACT FROM AUTHOR]

In 2014 and 2015, concrete columns were tested under axial compression in the Otto-Mohr-Laboratory of Dresden University of Technology. In comparison to columns with the same volume and a constant rectangular cross section, a 25% increase in buckling resistance was attained with an optimized shape. The shape of a column can be optimized in both the longitudinal and the transverse direction. Both aforementioned possibilities were tested separately in two experimental series; the results of such tests were used to verify the accuracy of the theoretical calculations. Based on these calculations and considerations, it was determined that an even larger increase of the buckling load is possible, for example, by combining both form influences (cross section and shape in longitudinal direction). A literature review regarding the optimization of axially loaded columns was conducted in 2012 and 2013. First, the current study gives an overview of the mathematical results. Subsequently, it presents the column test results in detail. Both simply supported columns and columns with fixed ends were tested. All columns were designed with ultra-high-performance concrete. The outcomes of the experiments are provided and discussed. Additionally, the measured values are compared with the calculated values. [ABSTRACT FROM AUTHOR]

Presence of flaws or cracks may cause substantial decrease in the strength of a component or structure. This kind of structural damage will accumulate over time, leading to significant decrease in ultimate load carrying capacity of structural members and premature brittle failure. In this paper, a coupled analytical and numerical study is implemented in order to evaluate buckling load of cracked cylindrical shells which is often encountered in the fields of civil engineering, offshore engineering and mechanic engineering. In the first phase of the study, buckling load of cylindrical shells with circumferential crack is investigated by treating the symmetric model as a cracked rectangular beam-column on an elastic foundation. The cracked beam-column is modelled as two beam elements on elastic foundation connected by an equivalent rotational spring and governing characteristic equation is obtained. Finite element models are used to verify analytical results and assess their accuracy, based on which good agreement is observed between analytical and numerical results. Effect of different parameters such as the length of cylinder, radial stiffness of cylinder, crack location and crack severity is studied on the axial load carrying capacity of such members. A simplified equation is proposed in order to calculate buckling load of tall cylindrical shells with a circumferential crack. In the second phase, the buckling load of cylindrical shells with a partial crack is studied using the results of finite element analysis on models with varying crack length. Based on the results of numerical analysis, an empirical equation is proposed to interpolate buckling load of these members between two limiting values, namely the buckling loads of same uncracked cylinder and the cylinder with circumferential crack. [ABSTRACT FROM AUTHOR]

In practical engineering, the measured differential settlement can be gained by monitoring the points beneath the tank wall and it can induce the buckling of the tank even with a small amplitude. In general, Fourier series is adopted to decompose the measured differential settlement into harmonic components with various wave numbers. However, the question that which harmonic components should be considered is a main challenge for buckling investigations of the tank under measured differential settlement. In this work, a recommendation for harmonic components needed for consideration was proposed when decomposing measured differential settlement into harmonic components in terms of Fourier series. Moreover, the effects of the harmonic components considered on buckling behavior of floating roof tanks and conical roof tanks were discussed. The results presented that three monitoring points can make a first estimate of ovalling and the harmonic components considered should be smaller than and equal to [ N ]/3 ([] is the rounding function and N is the number of the monitoring points). The introduction of the harmonic component with a high wave number can cause the change of the buckling modes of the tanks under differential settlement, including floating roof tanks and conical roof tanks. Meanwhile, it can decrease the buckling strength of the floating roof tank more significantly than that of the conical roof tank. [ABSTRACT FROM AUTHOR]

This paper presents results of a numerical parametric study on elastic shear buckling of cold-formed steel channels with flat slotted webs. The study was performed on finite element models developed in ANSYS and validated against test data. The effects of perforation pattern, channel flange width, flange lip length, and aspect ratio on the elastic shear buckling load were investigated on the models with realistic and test setup boundary conditions. Equations for predicting the elastic shear buckling load of slotted channels were developed. The equations account for the effects of the studied parameters on the elastic shear buckling load of cold-formed steel channels with flat slotted webs and showed a good agreement with the finite element analysis results. [ABSTRACT FROM AUTHOR]

The design of unbraced cold-formed steel beams must consider lateral-torsional buckling due to the low torsional stiffness associated with open cross-sections. The American Iron and Steel Institute incorporated design equations for the critical elastic lateral-torsional buckling stress in the North American Specification for the Design of Cold-Formed Steel Structural Members. These equations are based on elastic theory for singly-symmetric and doubly-symmetric sections. However, the equation for point-symmetric sections is only a rough approximation. Furthermore, there are no provisions for lateral-torsional buckling of non-symmetric sections, or sections oriented to non-principal axes. This paper investigates and develops a general formulation of the lateral-torsional buckling equation to broadly cover all cold-formed steel cross-sections. [ABSTRACT FROM AUTHOR]

Classic snap-through of curved beams, plates, and shells has long been an object of attention in structural engineering. Euler buckling under axial loading is perhaps an even more entrenched part of the canon of engineering education and practice. In this paper we introduce a relationship between the two phenomena, that to our knowledge has not been directly addressed before. The relationship shows that Euler buckling configurations are connected by the force–displacement curve under transverse loading. The results are used to develop a very simple metric to estimate the number of unstable static equilibria of a buckled structure based only on its geometry with no need for static or dynamic solvers. The study is focused on beams as this allows for an unambiguous discussion of the idea on the simplest possible structure. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution for elastic buckling problems of thick rectangular transversely isotropic simply supported plates subjected to uniaxial or biaxial uniformly distributed in-plane load, one of which could also be tensile. Governing equations are simplified to two partial differential equations using displacement potential functions (DPF) which are solved using the separation of variables method with exact satisfaction of boundary conditions. The presented solution is applicable to any plate with no restriction on its thickness ratio and also to any composite plates which have the same in-plane mechanical properties in all directions of the plate. Obtained results for critical buckling loads are compared with other analytical results for thin and moderately thick, and with numerical results for thick plates which show excellent agreement between them. Then, the effects of loading conditions aspect and thickness ratios for four transversely isotropic materials and also the engineering constants on the buckling of plates are discovered. The results show that the presented method is applicable and reliable for various kinds of material properties, thickness ratios, and loading conditions. Results also show that in comparison with a uniaxially loaded plate, adding a compressive load in second direction decreases the critical buckling load and the plate buckles in lower modes, while for adding a tensile load it is vice versa. Among materials engineering constants, in-plane modulus of elasticity and transverse shear module have the most effects on the critical buckling load of plates. [ABSTRACT FROM AUTHOR]

We compute nonlinear force equilibrium solutions for a clamped thin cylindrical shell under axial compression. The equilibrium solutions are dynamically unstable and located on the stability boundary of the unbuckled state. A fully localized single dimple deformation is identified as the edge state--the attractor for the dynamics restricted to the stability boundary. Under variation of the axial load, the single dimple undergoes homoclinic snaking in the azimuthal direction, creating states with multiple dimples arranged around the central circumference. Once the circumference is completely filled with a ring of dimples, snaking in the axial direction leads to further growth of the dimple pattern. These fully nonlinear solutions embedded in the stability boundary of the unbuckled state constitute critical shape deformations. The solutions may thus be a step towards explaining when the buckling and subsequent collapse of an axially loaded cylinder shell is triggered. [ABSTRACT FROM AUTHOR]

Buckling behavior and hysteretic performance of a new type of buckling-restrained brace (BRB), namely core-separated buckling-restrained brace (CSBRB), are theoretically and experimentally investigated. The material utilization efficiency of the CSBRB is significantly improved compared with common BRB, since its cross-section spreads outwards by spacing two cores, thus improving the flexural rigidity of the restraining system. On the basis of the elastic buckling loads of pin-ended CSBRBs, a design procedure involving two design parameters, namely normalized slenderness and buckling factor, is firstly established. Then, hysteretic behavior of CSBRBs is investigated by FE nonlinear analysis to obtain the critical normalized slenderness. Finally, test results of four specimens with different normalized slenderness values are presented to reveal the hysteretic characteristics and the energy-dissipation abilities, concluding that a CSBRB with adequate restraining rigidity can provide stable hysteretic performance. The test results coincide well with the results obtained from refined FE numerical analyses. [ABSTRACT FROM AUTHOR]

Buckling behavior of nonlocal Functionally Graded Piezoelectric (FGP) beams on elastic substrate via a higher order beam model is examined. The present beam model takes into consideration the shear deformation effects needless of any shear correction factor. Employing power-law function, the gradation of material properties of the beam is described. Incorporation of small scale parameter is carried out using nonlocal elasticity theory. Implementing an analytical approach which satisfies simply-supported boundary conditions, the governing equations derived from Hamilton's principle are solved. The obtained results are compared with those provided in the literature. It is indicated that the buckling behavior of piezoelectric Nanobeams is significantly influenced by elastic foundation parameters, external voltage, scale parameter, power-law index and slenderness ratio. [ABSTRACT FROM AUTHOR]

The worst geometric imperfection is a mathematical concept which should deliver in theory a lower bound for the buckling load of unstiffened cylindrical shells. The corresponding knock-down factors could be used as base for improved shell design guidelines in order to reduce weight and cost of unstiffened shells. Commonly used worst geometric imperfections include eigenmode or axisymmetric imperfection pattern. However, experimental results show that buckling failure is induced by an isolated single dimple which can be classified as a realistic worst geometric imperfection. It is hypothesized that the interaction between single dimple motion and the deformation behavior in the pre-buckling range of cylindrical shells significantly influences the buckling load. A numerical model is proposed in order to study the before mentioned thesis. The results show that the proposed numerical model induces a physical meaningful and realistic buckling response in a cylindrical shell. It can be validated that the interaction between single dimple motion and the deformation behavior of a cylinder in the pre-buckling range significantly influences the buckling load. Based on experimental data it can also be shown that the lower bound of the buckling load is accompanied by a characteristic post-buckling pattern shortly after collapse. [ABSTRACT FROM AUTHOR]

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

This paper focuses on the buckling analysis of composite sandwich conical shells subjected to a uniform external lateral pressure based on the first-order shear deformation theory. Approximate analytical solutions are assumed to satisfy fully clamped boundary conditions and then Fourier decomposition and Galerkin method is applied to achieve closed-form relations of buckling loads. The closed analytical formula for the critical pressure has been verified by comparison with the finite-element solutions and a special case where the angle of the conical shell approaches zero, that is, a cylindrical shell. Based on this formula buckling analyses of sandwich conical shells with different types of core materials have been accomplished. The outcomes are achieved considering the effects of half-vertex cone angle, core thickness and indicating applicability, accuracy, and stability of the present method. [ABSTRACT FROM AUTHOR]

This paper presents a nonlocal nonlinear first-order shear deformable plate model for investigating the buckling and postbuckling of magneto-electro-thermo elastic (METE) nanoplates under magneto-electro-thermo-mechanical loadings. The nonlocal elasticity theory within the framework of the first-order shear deformation plate theory along with the von Kármán-type geometrical nonlinearity is used to derive the size-dependent nonlinear governing partial differential equations and associated boundary conditions, in which the effects of shear deformation, small scale parameter and thermo-electro-magneto-mechanical loadings are incorporated. The generalized differential quadrature (GDQ) method and pseudo arc-length continuation algorithm are used to determine the critical buckling loads and postbuckling equilibrium paths of the METE nanoplates with various boundary conditions. Finally, the influences of the nonlocal parameter, boundary conditions, temperature rise, external electric voltage and external magnetic potential on the critical buckling load and postbuckling response are studied. [ABSTRACT FROM AUTHOR]

Grid structures are extensively used in many engineering structures as an orthotropic layer with at most in-plane anisotropy. In this study, the laminated grids structures are considered. These structures are composed of various numbers of thin composite grid layers. This concept yields to numerous laminated grid configurations with disparate coupling effects, which can be used to tailor the stiffness, compare to conventional grids. In the present study, four known grid patterns with equal weight and thickness constitute the laminated grids. The genetic algorithm (GA) is employed to optimize the stacking sequence and pattern composition of the laminated grid. The buckling load is taken as a fitness function and the pattern and orientation of the grid layer are considered as the design variables. The first-order shear deformation and classical laminated plate theories are considered along with Ritz method to obtain the elastic buckling loads. The optimization results are presented for various boundary conditions and aspect ratios. The results show, using the laminated grid considerably improves the axial buckling load of the plates. Moreover, the plate boundary conditions and aspect ratios play an imperative role in the optimum pattern and stacking sequence of the laminated grid plates. [ABSTRACT FROM AUTHOR]

Buckling of anisotropic piezoelectric cylindrical shells subjected to axial compression and lateral pressure is investigated based on the new modified couple stress theory and using the shear deformation theory with the von Kármán geometrical nonlinearity. By applying the principle of minimum potential energy, the governing equations and boundary conditions are derived. Unlike the classical continuum model, the present model is size-dependent, and the size effects are captured using the new modified couple stress theory. The critical buckling load is obtained for simply supported, clamped-simply supported and clamped piezoelectric cylindrical shells. A detailed numerical study is carried out to discuss the effects of different parameters, such as material length scale parameter, thickness ratio, length ratio, load interaction parameter and the external electric voltage on the critical buckling load. The critical buckling load is found to be significantly size-dependent, especially for large values of thickness and small values of length ratio. Besides, the influence of load interaction parameter is found to be negligible for large values of length and small values of thickness ratio. [ABSTRACT FROM AUTHOR]

This paper presents a Ritz-type analytical solution for buckling and free vibration analysis of functionally graded (FG) sandwich beams with various boundary conditions using a quasi-3D beam theory. It accounts a hyperbolic distribution of both axial and transverse displacements. Equations of motion are derived from Lagrange’s equations. Two types of FG sandwich beams namely FG-faces ceramic-core (type A) and FG-core homogeneous-faces (type B) are considered. Numerical results are compared with earlier works and investigated effects of the power-law index, thickness ratio of layers, span-to-depth ratio and boundary conditions on the critical buckling loads and natural frequencies. [ABSTRACT FROM AUTHOR]

Buckling and post-buckling of a long, thin, inextensible tube made of graphene material acted upon by a uniform normal pressure are considered. A system of differential equations governing the equilibrium states of such a tube is derived. Perturbation solutions are provided for the cases of pressure values close to the critical buckling pressures. A Matlab numerical solver based on Newton’s and shooting methods are developed. The buckling and post-buckling shapes of the deformed tube subject to various levels of pressure are presented. [ABSTRACT FROM PUBLISHER]

Abnormal multiwalled carbon nanotubes (MWNTs) with an interlayer distance of less than 0.34 nm are proposed and optimized based on molecular dynamics simulation, in which the second-generation Tersoff-Brenner potential and Lennard-Jones (12-6) potential are used to characterize the intratube interatomic interaction and the intertube van der Waals (vdW) interaction, respectively. Then, a multishell continuum model that is combined with a refined vdW force model is used to carry out the buckling analysis of abnormal MWNTs (including two-, four-, and six-walled MWNTs) and to investigate the effect of the vdW interaction of abnormal MWNTs. The numerical results show that the effect of the vdW interaction is more significant for abnormal MWNTs than for normal MWNTs and that the vdW interaction of abnormal MWNTs cannot be neglected. The critical buckling strains of abnormal MWNTs are greatly enhanced compared with those of normal MWNTs, which suggests that abnormal MWNTs may be excellent candidates as enforced fibers of nanocomposites. [ABSTRACT FROM AUTHOR]

In this paper, under the condition of bidirectional stress, the buckling deformation of the side plate in a rectangular concrete-filled steel tube (CFST) column has been studied in detail. We have conducted a theocratical analysis, an experimental validation and a finite element simulation to investigate the influences of the height-width ratios and Nominal Poisson's ratios on the buckling form of the side plate, and we also try to explain the change of buckling form between unidirectional and bidirectional stress, both of them can provide a good reference and basis for design and application of the CFST column. The specific work can be summarized as follows: Firstly, a theoretical analysis has been conducted to study the buckling coefficient solution method of the thin plate under the conditions of axial compress and transverse tension. Then, under the conditions of the unidirectional and the bidirectional stress, a comparative study is carried out to investigate the changing relationship of the buckling coefficient (k) of the side plate; the results indicate that the buckling characteristic is changed due to the bidirectional stress, meanwhile, the buckling coefficient and the number of buckling half-wave will increase. Furthermore, the existing outcomes and the numerical simulations are adopted to study the relevance between the number of the elastic buckling half-wave in the side plate and the corresponding height-width ratio of the component; the results indicate that the former is larger than the latter. Finally, based on the obtained, the buckling relationship curve, the conclusion can be drawn as follows: when the bidirectional stress has been applied to the side plate, there is an equal interval between the different buckling half-waves; meanwhile, the interval shows a quadratic function reduce trend with the increase of nominal Poisson's ratio. [ABSTRACT FROM AUTHOR]

This paper presents an analytical approach to study nonlinear response and buckling analysis of FGM toroidal shell segments reinforced by FGM stiffeners surrounded by elastic foundations in thermal environment and under external pressure. The formulations are based on Reddy's third-order shear deformation shell theory (TSDT) with von Karman nonlinearity, Pasternak type elastic foundations and smeared stiffener technique. By applying Galerkin's method and using stress function, closed-form expressions for determining the static critical external pressure load and postbuckling load–deflection curves are determined. Finally, the influences of geometrical parameters, volume fraction index, elastic foundations, and the effectiveness of stiffeners on the stability of shells are considered. [ABSTRACT FROM AUTHOR]

During the fabrication of lightweight ship panel, thin plates are usually employed and welding induced buckling may be generated, which will significantly influence the manufacturing integrity and performance. Computational approach based on inherent deformation was proposed, and its framework and application were introduced in this study. In detail, typical fillet welded joint was experimentally conducted and its solid elements FE model was numerically examined with experimental validation. Then, welding inherent deformation was evaluated based on computational results; elastic FE analysis with welding inherent deformations as input parameters was implemented to predict out-of-plane welding distortion and critical welding buckling condition. As the practical technique, intermittent welding procedure was employed to decrease the magnitude of welding inherent deformation, and sequentially avoid the occurrence of welding induced buckling. With this holistic investigation, welding induced buckling during thin plate section assembly was represented; critical welding buckling condition and mitigation technique were also demonstrated. [ABSTRACT FROM AUTHOR]

Atomic defects can be generated relatively easily in phosphorene due to their low formation energies. How these defects affect the buckling behavior of phosphorene nanotubes (PNTs) remains unexplored. Using molecular dynamics simulations, we investigate the effect of vacancies on the buckling properties of PNTs. We show that compared to a pristine PNT, the defective one exhibits a much lower buckling strength and strain. Remarkably, 1% concentration of vacancies in a PNT is able to cause a 30% reduction in buckling strength. Interestingly, for long PNTs, the buckling occurs via column or global buckling. As a result, the buckling strength decreases significantly with the increase (decrease) in the tube length (diameter) for both the pristine and defective PNTs, consistent with the Euler buckling theory. For short PNTs with small slenderness ratio (L/D), however, buckling occurs via shell or local buckling. As a result, the buckling strength increases with decreasing the tube diameter, consistent with shell buckling theory. Finally, with the increase in temperature, the buckling strength and strain can be reduced significantly for both the pristine and defective PNTs. These findings may provide important guidelines for the design and applications of PNTs-based nanodevices. [ABSTRACT FROM AUTHOR]

The present paper deals with the interactive buckling of thin-walled C-beams with imperfections, subjected to the bending moment in the web plane when the shear lag phenomenon and distortional deformations are taken into account. A plate model (2D) was adopted for the C-beams. The structures were assumed to be simply supported at the ends. Two kinds of cross-sections in the C-beams were considered: channels and lip channels. A method of the modal solution to the coupled buckling problem within Koiter's asymptotic theory, using the semi-analytical method (SAM) and the transition matrix method, was applied. The calculations were carried out for C-beams of different lengths – from short through medium-long to long beams. [ABSTRACT FROM AUTHOR]

This paper presents a finite element analysis of flexural-torsional and buckling behaviour of a thin-walled frame with a special focus on the joint warping behaviour. Four different joint types and two different cross-sections are analysed in order to investigate the influence of warping transmission on the overall behaviour of the structure. External loads are assumed to be static and conservative. The material is assumed to be homogenous, isotropic and linear elastic. The analysis is performed using the MSC Nastran shell model consisting of parabolic shell elements. The results obtained in the analysis together with some typical examples are discussed. [ABSTRACT FROM AUTHOR]

Sandwich structures are often used in space and aviation industry as energy absorption elements due to their load carrying capacity and light weight features. In experiments, it has been found that sandwich hemispherical structures have two different deformation modes referred as dimpling and flat mode under axial compression load. Deformation modes exercise a great influence on load carrying capacity of sandwich hemispherical structure. In this paper, theoretical models for two deformation modes of sandwich hemispherical structures under axial compression have been proposed. The reason for two different deformation modes observed in the compression tests has been explained. A finite element model has been set up and validated by the experimental results. Based on the numerical simulation results, buckling behaviors, load carrying capacities and displacements of top points of two different deformation modes have been compared. It is found that the load carrying capacity of the sandwich hemispherical structure under dimpling mode is about half of that under flat mode with very similar configurations. The deformation mode can be changed from dimpling to flat by adjusting the thicknesses of the out and inner metal sheets. This is a feasible and efficient way to improve the load carrying performance of the sandwich hemispherical structure. The optimal thickness ratio range of out and inner metal sheets are proposed. The methods can help improve the design of sandwich hemispherical structures to obtain better load carrying capacity with reasonable configuration. [ABSTRACT FROM AUTHOR]

In this paper the discrete-Kirchhoff Mindlin quadrilateral (DKMQ) element was developed for buckling analysis of plate bending including the shear deformation. In this development the potential energy corresponding to membrane stresses was incorporated in the Hu-Washizu functional. The bilinear approximations for the deflection and normal rotations were used for the membrane stress term in the functional, while the approximations for the remaining terms remain the same as in static analysis. Numerical tests showed that the element has good predictive capability both for thin and thick plates. [ABSTRACT FROM AUTHOR]

This work aims to reveal the in-plane-compressive characteristics of Glass Fibre based single face corrugated Structure Sheet (GFSS) by developing a loading holder of the both ends of the panel of GFSS in the direction of the cross machine direction. A grooved end-support device was developed and exmined. In order to set stably and quickly a straight panel of GFSS on the compressive-testing apparatus, the width and the depth of the holder's groove were varied against the geometrical size of the panel, and the stability and reproducibility of compressive deformation of the panel was experimentally investigated. When changing the height of the panel and reinforcing the both ends of the panel by dipping instant adhesives, the deformation behavior and the buckling strength was characterized in three modes: a short height crushing without lateral deflection, a small lateral deflection mode as the intermediate state, and a triangle-like folding as a long height crushing. [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]

Abstract This paper is dedicated to study the elastic buckling behavior of isotropic, laminated composite and sandwich beams subjected to various axially varying in-plane loads and boundary conditions (BCs). The formulation of the problem is derived by using the Ritz method with the displacement field based on a shear and normal deformable beam theory (SNDBT). Polynomial functions are employed to present the displacement field. The convergence studies are performed and then obtained results are compared with those of reported works. Results from extensive analysis are presented for different BCs, aspect ratios, orthotropy ratios, fiber angles and loading conditions. It is observed that the type of the axially variable in-plane load significantly affects the critical buckling loads and mode shapes of the beams depending on the BCs. The normal deformation effect depends on not only the aspect ratio but also BCs and the fiber orientation angles. [ABSTRACT FROM AUTHOR]

Abstract The result of an experimental programme investigating a novel technique to strengthen web plates of steel plate girders against breathing fatigue due to shear buckling deformations is presented. An experimental test series is present in which six specimens were manufactured to simulate the end panel of a plate girder; these were strengthened with an optimized FRP retrofit panel that was developed in an earlier phase of the research project, and tested for plate girder web shear buckling deformation mitigation under repeated cyclic loading, as well as ultimate load capacity enhancement. Test results and non-linear finite element modelling demonstrated the efficiency of this technique for stiffening the web against these deformation and thus reducing the critical stresses, consequently increasing the fatigue life of the girders by a factor ranging between three and seven, depending on the applied stress range and the fatigue resistance assessment method. The research demonstrates the applicability of this novel FRP strengthening technique to prolong and extend the fatigue life of existing plate girder bridges. [ABSTRACT FROM AUTHOR]

An elastic continuum mechanics model is presented to study the elastic buckling of single- and double-walled carbon nanotubes (CNTs) subjected to hydrostatic pressure. It is shown that a pressure-induced instability can occur in CNTs when a circle cross-section of the CNTs is destroyed. In this paper, we investigate the effects of deformation modes and dimension of CNTs on their mechanical stability. The results show that the critical pressure depends largely on the buckling mode, the diameter and aspect ratio of CNTs. The critical pressure of the single-walled CNTs (SWCNTs) with a diameter 1.3 nm is about 1.6 GPa, which is in excellent agreement the results reported in the relative literatures. The critical pressure of the double-walled nanotubes (DWCNTs) with a diameter of 2.2 nm will increase by 26%, compared with that of an identical diameter SWCNT. [ABSTRACT FROM AUTHOR]

This paper compiles the experimental and finite-element parametric study on member distortional buckling behaviour of new built-up metal hybrid double-I-box beams (HDIBBs). The cross-section of this built-up beam is unique and looks similar to the shape of a double-I-box fabricated using four channel sections. The flange plates were provided with an intermediate stiffener. In these built-up beams there is more material in the flange portions far away from the horizontal centroidal axis of their cross-section. Hence, there is an increase in the flexural rigidity that enhances the moment capacity of the beam, under major axis bending. The geometry consists of torsionally rigid closed-box web portion that provides high resistance to minor axis lateral-buckling. The varying parameters considered were the ratio of yield stresses of the flange to the web steel plates, the ratio of breadth to the depth of the section, and the flange plate thickness. In the experimental programme, all the HDIBB members failed due to kinds of distortional buckling which was identified by web buckling and flange twist along edges. The results revealed that when flange plate slenderness increases there is a drop in the moment resistance capacity of the beams. The numerical study was performed using ABAQUS software. In comparison, there was good agreement between experimental and numerical results. The validated finite element models were further extended to perform parametric studies on ideal HDIBB models. Both the experimental and parametric study results were compared with the predicted strengths using effective width method equations specified in the Euro code standards EN 3-1-3. It was found that the current Euro code design rules slightly over-estimate the distortional buckling resistance capacity of closed form built-up cold-formed steel members. A new design equation was formulated and recommended for estimating the reduction in distortional buckling moment resistance capacity for HDIBBs. [ABSTRACT FROM AUTHOR]

The thermal post-buckling responses of Functionally Graded Material shell structures are reported in this paper. Geometrically nonlinear analysis based on a modified First order Shear Deformation Theory are proposed. The modified theory takes into account the shear strains with a parabolic shape function and it verifies a zero shear stresses condition at the top and bottom surfaces. For the numerical computation, four nodes shell elements are implemented. The large displacement is described by Green–Lagrange nonlinear strains. Moreover, it is assumed that the shell structures are exposed to uniform, linear and nonlinear temperature distributions through the thickness direction. The thermal and the mechanical properties are described according to a power law distribution and either temperature-independent or temperature-dependent material properties are considered. Two numerical examples of functionally graded plates and cylindrical shells are presented to highlight the effectiveness and the accuracy of the present finite element procedure. The effect the geometrical parameters, the volume fraction index and boundary conditions on nonlinear responses are performed. [ABSTRACT FROM AUTHOR]

This paper is devoted to analytical and numerical studies of global buckling of a sandwich circular plate. The mechanical properties of the plate core vary along its thickness, remaining constant in the facings. The middle surface of the plate is its symmetrical plane. The mathematical model of the plate is presented. The field of displacements is formulated using the proposed nonlinear hypothesis that generalizes the classical hypotheses. The equations of equilibrium are formulated based on the principle of stationary total potential energy. The proposed mathematical model of the displacements considers the shear effect. The numerical model of the plate is also formulated with a view to verify the analytical one. Numerical calculations are carried out for the chosen family of plates. The values of the critical load obtained by the analytical and numerical methods are compared. The effects of the material properties of the core and the change of the plate radius on the critical load intensity are presented. [ABSTRACT FROM AUTHOR]

This work presents an analytical approach to investigate the mechanical and thermal buckling of functionally graded material truncated conical shells resting on Pasternak elastic foundations, subjected to thermal load and axial compressive load. The shells are reinforced by closely spaced stringers and rings. The change in spacing between the stringers in the meridional direction is also taken into account. Two cases on uniform temperature rise and linear temperature distribution through the thickness of the shell are considered. Using the first-order shear deformation theory, Lekhnitskii smeared stiffener technique and the adjacent equilibrium criterion, the linearization stability equations are established. An approximate solution satisfies simply supported boundary conditions, and the Galerkin method is applied to obtain a closed-form expression for determining the critical compression buckling load and thermal buckling load in cases of uniform temperature rise and linear temperature distribution across the shell thickness. The effects of temperature, foundation, stiffeners, material properties, dimensional parameters and semi-vertex angle on the buckling behaviors of shell are shown. [ABSTRACT FROM AUTHOR]

The elastic buckling of square and skew thin functionally graded material (FGM) plates with cutout resting on an elastic foundation is investigated using the isoparametric spline finite strip method. It is assumed that the material properties of FGM plates vary smoothly through the thickness according to the power law model. The elastic foundation is simulated by the Winkler and two-parameter Pasternak models. The isoparametric spline finite strip method is also applied to investigate initial inelastic local buckling loads of skew homogenous plates with cutout based on the Ramberg-Osgood representation of the stress-strain curve using the deformation theory of plasticity. The critical buckling load of the plate is achieved by minimizing its total potential energy and solving the corresponding eigenvalue problem. In addition, the effects of elastic foundation coefficients and hole size on the local buckling of plates with different boundary conditions are determined and discussed. [ABSTRACT FROM AUTHOR]

In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances. [ABSTRACT FROM AUTHOR]

This paper presents a stiffened-plate buckling model for calculating the critical stress of distortional buckling of cold-form steel (CFS) channel-section columns. The model is the further extending of the buckling model we developed recently for beams (International Journal of Mechanical Sciences 2016, 115/116: 457–464) to columns. In the present buckling model, the web is treated as a plate which has both in-plane and out of plane bending deformations, whereas the flange and lip are modelled as the angle stiffener applied at the two ends of the web, which is subjected to asymmetric bending and torsion. The critical buckling stress of the stiffened plate is calculated using the classical principle of minimum potential energy. To validate the present stiffened plate buckling model, finite strip analysis is also carried out to the CFS channel-section columns. Good agreement is demonstrated between the critical stress calculated from the present stiffened plate buckling model and that obtained from the finite strip analysis. [ABSTRACT FROM AUTHOR]

A nonlinear analytical model for investigating localized interactive buckling in simply supported thin-face plate sandwich struts with weak cores is extended to account for local deformations in both face plates, which have been observed in experiments and finite element simulations. The original model is based on potential energy principles with large displacement assumptions. It assumes Timoshenko shear deformable theory for the core and approximates the overall mode as a half-sine wave along the length of the strut while the local face plate displacements are initially unknown and are found as solutions of the governing equations. The extended model is able to capture measurable local face plate displacements in the less compressed face plate, beyond the secondary bifurcation which leads to localized interactive buckling, for the case where overall buckling is critical. Moreover, the allowance of local displacements in both face plates allows the extended model to predict the post-buckling behavior better in cases where local buckling is critical. The results from this model compare very well with nonlinear finite element simulations with respect to both the equilibrium paths and panel deformations. [ABSTRACT FROM AUTHOR]

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

In this paper, an anti-buckling fixture was proposed to assess the deformation characteristics of DP500 and DP980 dual-phase steels, and AZ31B magnesium composite under tension–compression cyclic loading. The advantage of the device lies in the possibility of monitoring friction between the specimen and supporting blocks during the test. In consequence, it allows to avoid an error during stress determination. The full cyclic loading capacity for each material can be executed at the displacement amplitude within the range ± 2.5 mm which corresponds to the maximum strain amplitude of ± 0.2 for the specimen with the gauge length of 21.5 mm. It is concluded, that the technique proposed is promising since the thin sheet material can be tested under tension–compression in a wide range of deformation without the buckling effect. Furthermore, useful data for modelling cyclic deformation behaviour for shell structures can be obtained. [Display omitted] • Proposed fixture enables to avoid buckling during thin metal sheet compression. • The friction force is continuously registered during the test. • Complex characteristics could be successfully and precisely determined. • Useful data for modelling cyclic deformation can be obtained. [ABSTRACT FROM AUTHOR]

Buckling deformation of pipe in actual bore hole will limit the maximum running depth and is likely to further damage the drilling pipe, causing huge losses. Therefore, the buckling analysis of the pipe is necessary. In order to investigate the mechanical behaviour of coiled tubing (CT), a test bench including a vertical, a bending and a horizontal segments and an end-loading unit is designed. In this paper, the method of combined numerical calculation and experimental validation is used to study the inside-pipeline CT buckling. Based on the experimental investigation, the influence of induced torque on the helical buckling equation is analysed. In addition, by comparing the theoretical result and experimental result, the helical reverse phenomenon is carefully analysed. In the end, the maximum running depth for different CTs in different diameters and friction environments are also investigated, having an instructive significance to the actual operation and the choice of CT. [ABSTRACT FROM AUTHOR]

The compressive buckling behaviour of extruded aluminium alloy I-section columns with fixed-pinned end conditions has been experimentally and numerically investigated in this study. A total of 11 column tests, involving two heat-treated aluminium alloys – 6061-T6 and 6063-T5, were carried out to acquire the compressive buckling strengths. Prior to the column tests, material properties of the two aluminium alloys were determined from tensile coupon tests, while the initial local and global geometric imperfections were separately measured by means of experimental techniques. By using the ABAQUS software package, finite element (FE) models that could account for material non-linearity and initial geometric imperfections were developed. The FE models were further validated against the test results, enabling reliable simulation of the compressive buckling behaviour of the tested columns with fixed-pinned end conditions. Based on the obtained test and numerical results, the calculation methods in the current design standards, including the European, Chinese, American and Australian/New Zealand specifications, were all assessed. It was shown that the design provisions in all the four standards provided relatively conservative strength predictions, especially for the aluminium alloys with more pronounced strain hardening capacity. [ABSTRACT FROM AUTHOR]

Lateral buckling is an important issue in unburied high-temperature and high-pressure (HT/HP) subsea pipelines systems. The imperfection–sleeper method is one of the most well-known methods used to control lateral buckling of HT/HP pipelines. Pipelines–sleeper–seabed numerical models are established and verified to analyze the buckling behavior of pipelines using the imperfection–sleeper method. The influence of six main factors on lateral buckling behavior is investigated in details based on the numerical results. Equations of buckling displacement (buckling displacement is defined by the final displacement of the middle point of the pipelines), critical buckling force, and buckling stress (Mises stress) are proposed using the gene expression programming technique. These equations show good accuracy and can be used to assist in the design of sleepers and assess the compressive and stress levels of pipelines. [ABSTRACT FROM AUTHOR]

Based on von Karman's plate theory, the axisymmetric thermal buckling and post-buckling of the functionally graded material (FGM) circular plates with inplane elastic restraints under transversely non-uniform temperature rise are studied. The properties of the FGM media are varied through the thickness based on a simple power law. The governing equations are numerically solved by a shooting method. The results of the critical buckling temperature, post-buckling equilibrium paths, and configurations for the in-plane elastically restrained plates are presented. The effects of the in-plane elastic restraints, material property gradient, and temperature variation on the responses of thermal buckling and post-buckling are examined in detail. [ABSTRACT FROM AUTHOR]

The present paper describes a theoretical study on the effect of pre-buckling displacements on the elastic instability of U-shaped members. Expressions for the elastic critical bending moments under mono-axial bending and the elastic critical load amplification factor for the case of bi-axial bending are derived and validated through elastic geometrically non-linear analysis including a geometric imperfection. It will be shown that pre-buckling displacements have a non-negligible influence on the behaviour of U-shaped members, especially when subjected to minor-axis and bi-axial bending. It will be shown that, contrariwise to the natural feeling, U-shaped members under minor-axis bending may, in some cases, be sensitive to elastic instability (lateral-torsional buckling). Moreover, the validated analytical expressions show that shorter members are more sensitive to elastic instability under minor-axis bending than their longer counterparts! [ABSTRACT FROM AUTHOR]