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This technical note presents the optimal shape of an arch carrying a central point load to two pinned supports for maximum in-plane bifurcation buckling load. The arch shapes considered are triangular, parabolic, circular, catenary, and ogival. It is assumed that the arches are elastic and inextensible and their flexural rigidity is uniform throughout the arch length. The Hencky bar-chain model was used for elastic buckling analysis. It is found that the optimal arch shape depends on the arch apex height to length (h/L) ratio. The optimal arch shape changes from circular to catenary to parabolic and finally to triangular from h/L=0.1 to 1. This shows that the funicular triangular arch shape for the central point load is not the optimal arch shape against in-plane buckling when h/L is less than 0.528. For maximum buckling load, one may use either the circular, catenary, or parabolic arch with h/L approximately equal to 0.3. [ABSTRACT FROM AUTHOR]

An accurate nonlinear hygrothermal-electro-elastic (HTEE) buckling analysis of piezoelectric fiber-reinforced composite cylindrical shells subjected to the coupled loading effects of axial compression and hydrostatic pressure was established by considering the nonuniform prebuckling effect. Nonlinear governing equations were derived based on higher-order shear deformation theory and Novozhilov's nonlinear shell theory. Accurate critical buckling stresses and pressures and explicit buckling modes for both axisymmetric and nonaxisymmetric buckling were obtained by the Galerkin method. A comparison between the new prediction and existing results is presented and excellent agreement is reported. A comprehensive parametric study of geometric parameters, end conditions, distribution patterns, and hygrothermal-electric multiphysical fields on the buckling behavior of HTEE composite cylindrical shell is also analyzed and discussed. [ABSTRACT FROM AUTHOR]

Arches are important components in nanostructures and systems. Because of the remarkable strength of nanomaterials, nanoarches are slender, thus enhancing their vulnerability to geometric instability, such as buckling. Although molecular simulations are often employed to analyze nanostructures, their use in routine analysis/design is formidable due to prohibitively exhaustive computation. Equivalent continuum models were developed as alternatives. The buckling and postcritical phenomena of the classical arch also form an important benchmark problem in nonlinear mechanics. This study investigates the buckling and the postcritical behavior of nanoarch subjected to inward pressure using nonlocal (NL), strain gradient (SG) continuum theory. The governing equations are derived in the form of a sixth-order nonlinear integrodifferential equation, unlike the fourth-order for a classical arch. The equation is then solved numerically using a differential quadrature (DQ) with appropriate boundary conditions. An incremental-iterative arc-length continuation is employed for the solution of the resulting algebraic system of equations. The equilibrium paths are traced for the possible instability modes, such as symmetric/antisymmetric bifurcations, snap-through and limit point instability, ascertained with the internal-external force diagrams. A particular instability mode is triggered at a certain threshold/range of the slenderness ratio of the arch, which is significantly influenced by the NL and SG interactions. These interactions not only cause quantitative changes in the instability behavior but also lead to qualitative changes, such as cessation, shift, and conversion of modes, more prominently for SG arches. Similar to classical arches, the prebuckling nonlinearity is shown to be significant. [ABSTRACT FROM AUTHOR]

The N -segment circular arch with rigid members and semirigid joints under external pressure is studied. The problem is formulated in coupled difference equations. An efficient initial value method is presented to solve the stability problem. The product of buckling pressure and N tends to be that of the continuous elastic arch as N→∞. Critical buckling is mostly antisymmetric but may be symmetric at larger opening angles. Optimum shapes (for maximum critical pressure) are determined for both segmented and continuous circular arches. [ABSTRACT FROM AUTHOR]

Hybrid simulation is a tool for investigating the dynamic response of a structural prototype subjected to realistic loading. Hybrid simulation is conducted using a hybrid model that combines physical and numerical substructures interacting with each other in a feedback loop. As a result, the tested substructure interacts with a realistic assembly subjected to a credible loading scenario. In the current practice, experimental results obtained via hybrid simulation support conceptualization and calibration of computational models for structural analysis. Instead, this paper extends the scope of hybrid simulation in constructing a safe/failure state classifier for the tested substructure by adaptively designing a sequence of parametrized hybrid simulations. Such a classifier is intended to compute the state of any physical-substructure-like component within system-level numerical simulations. It follows that the main contribution of this paper lies in the way experimental results are aggregated and integrated with structural analysis. The proposed procedure is experimentally validated for a three-degrees-of-freedom hybrid model subjected to Euler buckling. [ABSTRACT FROM AUTHOR]

This paper considers the case of a relatively large number of parallel columns that buckle simultaneously. The close proximity between columns results in the possibility of contact between adjacent columns as buckling proceeds, and this brings with it some interesting observations on load-carrying capacity. Some experimental results verify the theoretical development based on the versatility of high-fidelity 3D printing, but also highlights the difficulty of applying purely axial loading. The sensitive nature of initial geometric imperfections (slight lack of straightness) and load eccentricity strongly influence postbuckled contact, load-carrying capacity, and, as the number of columns is increased, a statistically based evaluation of anticipated behavior is explored and ultimately found to be unrealistic. [ABSTRACT FROM AUTHOR]

The concept of vacuum lighter-than-air vehicles is a generalization of the idea behind floating vehicles, which enclose a volume of gas that is lighter than air. In particular, the enclosed volume is completely evacuated. From a pure geometrical perspective, the sphere is appealing because of the symmetry properties and the best surface-area-to-volume ratio. However, the pressure differential between the external fluid and the internal vacuum imposes significant compressive forces, which put the structure at risk of instability due to buckling. At the present technology level, no available material can be used to create a shelled sphere with a relatively large radius-to-thickness ratio and an internal vacuum without buckling. This work explored the concept of a star polyhedron obtained from the pentakis icosidodecahedron by adding pockets on the triangular surfaces. Under the assumption of elastic linear isotropic material and using commercial software ABAQUS version 2016, it was demonstrated that the stability performance, postbuckling response, type of buckling and its location, and mesh convergence properties are significantly affected by the ratio of the radius of the circumscribed sphere to the shell thickness. The structure exhibits sensitivity to the geometric imperfections, as assessed by using different amplitudes and types of imperfections. However, it was demonstrated that the proposed shape presents a true buckling load approximately twice that of a sphere, indicating that the adopted geometry is less sensitive to manufacturing imperfections than is a circumscribed sphere. Using the Buckingham Π theorem, an empirical formula predicting the buckling load (eigenvalue analysis of the perfect structure) was derived and related to the corresponding relationship valid for spherical shells. [ABSTRACT FROM AUTHOR]

The aim of this work is to explore the potential of two hierarchic sets, one polynomial and the other trigonometric, in the construction of versatile Ritz bases to accurately solve the linear buckling of anisotropic Kirchhoff plates. Focus is placed on reporting the basis ability to surmount numerical degrading effects associated with anisotropy. Several examples are presented to illustrate the merits and demerits of each set in terms of accuracy and rate of convergence, mainly by comparing their results with those obtained from traditional Ritz bases and finite-element models. [ABSTRACT FROM AUTHOR]

This article investigates the structural stability of prismatic columns with elastically restrained ends under axial compressive force. An emphasis is placed on the analysis of the effect of Engesser's and Haringx's hypotheses on buckling. Based on the Timoshenko beam theory and a higher-order shear-deformable beam theory, simple characteristic equations were derived for buckling of an axially loaded elastic column with two ends linked to translational and rotational springs. By introducing orientation factor α , a buckling load falls between those corresponding to Engesser's (α=0) and Haringx's (α=1) models. For freely standing, simply supported, and clamped columns, explicit expressions for each critical load were obtained. The effects of Engesser's and Haringx's hypotheses as well as of the translational and rotational spring stiffnesses at the elastically restrained end on buckling loads are analyzed in detail. Obtained results indicate that Engesser's and Haringx's hypotheses hardly affect buckling loads for a column with strong shear rigidity, and they have a significant influence on buckling loads for a column with weak shear rigidity. The effect of translational spring stiffness on buckling loads is more pronounced than that of rotational spring stiffness. [ABSTRACT FROM AUTHOR]

Multistable structural members are extensively used in various fields, including microelectromechanical systems (MEMS) actuation, sensing, and energy harvesting. The multistable configuration of elements can be obtained through their elastic postbuckling response. Under quasi-static excitations, the snap-through transitions of buckled elements constitute a useful tool to generate high-rate excitations for piezoelectric transducers. Yet, more efficient energy harvesting and accurate sensing requires that buckling events happen at specific loading levels. This paper investigates the control of snap-through events by using beam assemblies. Multiple bilaterally constrained beams were arranged in parallel and subjected to axial displacement–controlled loading. Experimental studies show that snap-buckling transitions can be controlled by changing the geometry of the assembled beams. An analytical model was developed to investigate the effect of system parameters on its postbuckling response. Results show that transitions are mainly controlled by the beams' thicknesses and lengths. By tuning both parameters, the system can be designed to snap at a desired axial displacement. In this paper, the assemblies were designed to transition at equally spaced axial displacements. However, other displacement combinations can be achieved. [ABSTRACT FROM AUTHOR]

In this paper the influence of bimoment, induced by external axial loads, on the global buckling of thin-walled Z-section beams, subjected to different boundary conditions, is studied. Since bimoment varies along the beam axis, the problem of torsional and torsionalflexural buckling of thin-walled beams is defined by linear homogeneous differential equations of the second-order theory with a variable coefficient. To obtain the buckling load numerically, a finite-difference method is employed for discretizing the governing differential equations. To verify the validity and the accuracy of this study, numerical solutions are presented and compared with those calculated by simulation software. [ABSTRACT FROM AUTHOR]

The equilibrium governing equations of nonlocal anisotropic thin-walled circular cylindrical shell under combined axial compressive force, torsional load, and external pressure are explicitly derived. This is accomplished by appropriately combining the equilibrium equations and the strain-displacement relations according to Flügge’s shell theory and the stress-stain equations of Eringen’s nonlocal elasticity theory. An analytical solution for the buckling of the shells is presented by using the complex method. This model is validated by a good agreement between the results given by the present model and available data in the literature. Furthermore, the model is utilized to elucidate the buckling properties for different load combinations. [ABSTRACT FROM AUTHOR]

The problem of dynamic instability of rectangular plates with complex constraints at the edges is here solved starting from a theory in the literature; the suggested approach allows for the definition of generic, nonperfect constraint configurations for the regions of instability due to in-plane compression loads as diagrams that are expressed in function of the applied dynamic force and its frequency. The novelty of the work stands in (1) the study of viscoelasticity, combined with damage, at the constraints, which allows for the discussion of the performance of a rectangular plate with regards to dynamic instability at varying degrees of damping and damage, and (2) the analytical approach developed to solve the associated eigenvalue problem for rectangular plates with generic viscoelasto-damaged constraints at two opposite edges and simply supported at the other edges. Regarding the second point, the differential equation of motion of such a system is derived and, via the variable separation method, a solution for the transverse displacements is sought among those satisfying the generic boundary conditions at the four edges. Namely, the constraints are assigned in a homogeneous way, which has particularly convenient results for computational purposes. By imposing that the determinant of the resulting system vanishes, a closed-form solution is found for the freevibration problem. The associated boundaries of the unstable regions for specific constraint configurations are discussed. [ABSTRACT FROM AUTHOR]

This paper revisits the nonlinear in-plane analysis of a shallow pin-ended circular arch under a central concentrated load. It is found that the arch may have multiple equilibrium branches and limit points, and a modified slenderness of the arch defined in the paper plays an important role in the number of the limit points and equilibrium branches. The analytical solution for the specific modified slendernesses that switch the number of equilibrium branches and limit points is derived. The analytical solutions for the load, axial force, and radial displacements corresponding to the specific modified slendernesses are also derived. This paper deepens the understanding for the geometric nonlinear analysis of circular arches and their geometric softening and stiffening behavior and provides useful benchmarks for the analyses of shallow arches. In addition, this paper extends the current solutions of nonlinear equilibrium of arches associated with axial compression to those associated with axial tension caused by large deformations. [ABSTRACT FROM AUTHOR]

This paper presented new analytical solutions for the elastic buckling of Eringen's nonlocal columns with allowance for self-weight. A discrete column model on the basis of the central finite difference formulation and the equivalent Hencky bar-chain model also were presented for this buckling problem. The discrete column model allows one to determine the buckling solutions of columns constructed from repetitive cells. In addition, one may use the discrete buckling solutions to calibrate the small-length scale coefficient e0 in the Eringen's nonlocal column model. It was found that e0 values varied from 0.289 to 0.373 with respect to increasing selfweight for clamped-free column case, from 0.289 to 0.276 for the pinned-pinned column case, and from 0.289 to 0.281 for the clamped-clamped column case. [ABSTRACT FROM AUTHOR]

This paper presents an exact solution for the boundary-value problem which describes the linear buckling of axially compressed circular cylindrical panels with stringers attached to the straight edges. The boundary conditions differ from the classical simply supported ones, often assumed for design purposes, in the sense that the torsion resisted by the stringers are also taken into account. The presence of the stringers makes the results reported herein of practical interest and valuable as benchmark data. [ABSTRACT FROM AUTHOR]

When a beam is subjected to an in-plane linear temperature gradient field, the thermal effects of the temperature gradient field tend to change the curvature of the beam in the transverse direction and to expand the beam in the axial direction. The rotation and expansion of the ends of the beam may be restrained elastically by its supports or by adjacent members such as columns. The restrained thermal actions will produce bending moments and compressive forces in the beam, and when these actions reach critical values the elastically restrained beam may bifurcate from its primary in-plane equilibrium configuration to an out-of-plane buckled equilibrium configuration. This paper investigates the thermoelastic out-of-plane buckling of an elastically restrained beam with a doubly symmetric cross section that is subjected to an in-plane linear temperature gradient field. The analytical solution for the critical temperature gradient for thermoelastic out-of-plane buckling of the beam is derived. It is found that the positions of the effective centroid and shear center of a cross section subjected to a linear temperature field are different from those under mechanical loads. Beams having a doubly symmetric cross section under a linear temperature gradient field behave as beam-columns with a monosymmetric cross section, thereby rendering the thermoelastic out-of-plane buckling of an elastically restrained beam under a linear temperature gradient field more complicated than its counterpart under mechanical loading. [ABSTRACT FROM AUTHOR]

For exposed subsea pipelines, lateral buckles are usually artificially triggered as an accommodation technique to release thermal expansion by providing temporary flotation with controlled spacing. With the given buoyancy load, the pipeline will be uplifted initially and will then buckle laterally under a certain thermally induced axial load, which is called the bifurcation load. Previous studies have analyzed this problem and modeled the uplifted pipeline as a fixed-fixed end beam, assuming the lateral seabed stiffness is infinite. However, the lateral seabed stiffness is usually low because the seabed is formed from soft soils. Using analytical methods, this paper investigates the buoyancy load required to trigger lateral buckles along a pipeline, considering a seabed with finite elastic stiffness, and provides suggestions for the buoyancy design with an elastic-plastic seabed model using an example of finite-element analysis. It was found that the seabed condition significantly influenced the flotation design. [ABSTRACT FROM AUTHOR]

This paper considers the minimum buckling load and mode shape of a simply supported beam on an elastic foundation. Solutions are obtained by solving the eigenvalue problem delivered by a finite-element formulation and by using the analytical solutions involving (1) trials and (2) rounding of real numbers to integers as described by Hetényi [Hetényi, M. (1946). Beams on Elastic Foundations, University of Michigan Press, Ann Arbor, MI]. The comparison shows that the solution by rounding can lead to overestimation of the buckling load close to the transition zone between mode shapes. The paper explains the reason for the overestimation and offers a simple direct algorithm that always leads to the correct mode shape and minimum buckling load. [ABSTRACT FROM AUTHOR]

Buckling and vibration characteristics of thin, symmetrically laminated, elliptical composite plates under initial in-plane edge loads and resting on Winkler-type elastic foundation are presented based on the classical laminated-plate theory. The governing equations were obtained from the variational approach and solved by the Ritz method. Extensive numerical data are provided for the first three natural frequencies as a function of in-plane load, and critical buckling loads as a function of aspect ratio for various classical edge conditions (free, clamped, and simply supported). Moreover, the effects of fiber orientation on the natural frequencies and buckling loads of laminated angle-ply plates, with stacking sequence of , were studied for chosen foundation parameter. Selected deformation buckling mode shapes are illustrated. The accuracy of calculations was checked by performing good convergence studies, and the correctness of results is established by comparison to existing results in the literature and FEM data. [ABSTRACT FROM AUTHOR]

A crack in a steel structure will cause a local change in its stiffness. The change in stiffness will lead to a change in buckling loads and a discontinuity in the associated buckling modes. The changes in the buckling characteristics of columns cause a change in the buckling stability of the structure. The effect of cracks on the buckling load of structural systems can be investigated through numerical methods. The FEM is a well-known method for this work. In this paper, a new and innovative finite-element (FE) formulation for the buckling analysis of cracked columns is presented. The method presented is simpler and, at the same time, more accurate and practical than those available in the literature. The proposed FE formulation for cracked columns has the same format as that for intact columns. The formulation is used successfully in efficient and accurate buckling analysis of cracked frames. [ABSTRACT FROM AUTHOR]

Solving the buckling problem for a battened column as a statically indeterminate structure yields a Euler critical load that is significantly higher than the buckling load being obtained on the basis of Engesser's assumption. The stability problem is reduced to numerically solving a two-point boundary value problem for a system of recurrence relations between deformation parameters of adjacent joint cross sections of the column. The expression of deformation parameters for each further joint cross section of the column as a linear function of deformation parameters for the preceding joint cross section is possible using the initial-value method. For columns with any degree of static indeterminacy, the critical force is determined as the smallest eigenvalue of the fourth-order system of homogeneous linear algebraic equations. A computer realization of the present method requires implementing reorthogonalization of the vectors of particular solutions for the system of recurrence relations. Plots of the buckling load for columns with any number of panels can be constructed as a function of the batten rigidity parameter. Applying these plots can be useful in selecting a cross section of the columns being designed. [ABSTRACT FROM AUTHOR]

This study presents the buckling analysis of a radially loaded, solid, circular plate made of porous material. Properties of the plate vary across the thickness. The edge of the plate is either simply supported or clamped and the plate is assumed to be geometrically perfect. The geometrical nonlinearities are considered in the Love-Kirchhoff hypothesis sense. The equilibrium and stability equations, derived through the variational formulation, are used to determine the prebuckling forces and critical buckling loads. The equations are based on the Sanders nonlinear strain-displacement relation. The porous plate is assumed to be of the form where pores are saturated with fluid. The results obtained for porous plates are compared with the homogeneous and porous/nonlinear, symmetric distribution, circular plates. [ABSTRACT FROM AUTHOR]

In this paper, buckling delamination around interface inner cracks contained within the simply supported elastic and viscoelastic rectangular sandwich plate under biaxial loading is studied. It is assumed that the materials of the face layers are viscoelastic and the material of the core layer is pure elastic. Moreover, it is assumed that the material of the core layer is stiffer than the materials of the face layers. Within these assumptions it is supposed that between the face and core layers there are rectangular inner cracks, the locations of which are symmetric with respect to the plate geometry. The edge surfaces of the cracks have insignificant initial imperfections before the loading. The evolution of these initial imperfections with the flow of time is investigated within the scope of the three-dimensional (3D) geometrically nonlinear field equations of the theory of viscoelasticity. For determination of the values of the critical parameters (buckling force, time, and buckling mode), the initial imperfection criterion (i.e., the case where the size of the initial imperfection starts to increase and grows indefinitely) is used. Mathematical modeling of the corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model. To solve the corresponding boundary-value problems, boundary form perturbation techniques, the Laplace transform, 3D FEM modeling and the Schapery method are used. The numerical results related to the influence of the materials or geometrical parameters of the plate on the critical parameters and critical time are presented and analyzed. [ABSTRACT FROM AUTHOR]

A nonlinear theoretical model is developed in this paper for investigating the time-dependent behavior of one-way high-strength RC panels, with particular emphasis on the combined effects of creep and shrinkage on the buckling capacity and its degradation with time. A rheological generalized Maxwell chain model is used for modeling the creep of the concrete including its cracking, tension stiffening, and aging through strain- and time-dependent springs and dashpots. The incremental governing equations of the panel are derived and solved through a step-by-step time analysis that takes into account the variation of the internal stresses and deformations with time. A smeared cracking model is adopted, and an iterative procedure is conducted at each time step for the determination of the unknown rigidities of the cracked section, as well as the length of the cracked region. The capabilities of the proposed model are demonstrated through numerical and parametric studies, which show the important roles of creep and shrinkage in the buckling of high-strength concrete panels and which reveal the sensitivity of the nonlinear response to the magnitude and eccentricity of the sustained load and to the reinforcement ratio. [ABSTRACT FROM AUTHOR]

In many cases, an arch may have in-plane elastic end restraints provided by the connected structures or elastic foundations, which may influence the elastic lateral-torsional buckling of the arch. However, little research of the lateral-torsional buckling of arches with elastic end restraints has been reported in the open literature. This paper analytically investigates the lateral-torsional buckling of pin-ended circular arches having in-plane elastic rotational end restraints under a uniform radial load. The analytical solutions for the prebuckling behavior of such an arch show that the uniform radial load produces combined axial compressive and bending actions in the arch and that the axial compressive force produced by the uniform radial load is approximately uniform along the arch axis. It is found that the stiffness of elastic rotational end restraints has significant effects on the magnitude and distribution of the axial compressive forces and bending moments. The axial compressive force decreases with an increase of the stiffness of rotational end restraints. The analytical solution for the lateral-torsional buckling load of the arch is derived, which accounts for the effects of rotational end restraints. It is found that the effects of the stiffness of rotational end restraints on the lateral-torsional buckling load are profound. The buckling load increases with an increase of the stiffness of the end restraints. It is demonstrated by comparisons with the finite-element results that the analytical solution provides good predictions for the lateral-torsional buckling load of both shallow and deep arches having in-plane rotational end restraints. [ABSTRACT FROM AUTHOR]

In this study, critical buckling load of an impacted composite laminate is predicted, using the structural similitude method. Because of impact loading, damaged regions have formed in the laminate. To establish similarity conditions between impacted laminates for buckling loading, the idea of sequential similitude method is introduced. According to the sequential similitude method, similarity conditions can be established for a structure subjected to different loading situations, provided that each loading event is simulated independently. On the basis of this method, to develop similarity conditions for buckling loading of impacted composite laminates, similarity conditions are developed first for impact loading and then for buckling loading separately. Afterward, the obtained conditions are implemented in the commercial finite-element software, ABAQUS, to obtain the critical buckling load. Results show that sequential similitude method can be used as a simple and accurate method for prediction of buckling load of impacted laminates. [ABSTRACT FROM AUTHOR]

Many civil-engineering materials and novel materials developed in recent years exhibit a property of different elastic moduli in tension and compression. One such material is graphene, a wonder material, which has the highest strength yet measured. However, the dominant failure of structures composed of this high-strength material is often attributed to buckling problems. Investigations on buckling problems for structures with different moduli are scarce. To address this new problem, the present paper develops a semianalytical method for the critical buckling loads of variable-cross section slender rods with different moduli. Based on the variational principle, a differential equation of the deflection of these structures is derived for the first time. By developing a nonlinear iterative program and using the variational iteration method, the critical buckling loads are obtained. Then, buckling tests and numerical simulation were conducted for slender rods made from graphite with different moduli. By comparing the semianalytical results with the laboratory tests and finite-element analysis results, the semianalytical model proposed in this paper was demonstrated to be accurate and reliable. The conclusion can be drawn that the characteristics of different moduli of materials have a significant influence on the buckling stability of structures. Therefore, it may lead to unsafe results if the classic theory is still adopted to determine the buckling loads of those rods composed of a material having different moduli. The proposed model could provide a novel approach for further investigation of nonlinear mechanical behavior for structures with different moduli. [ABSTRACT FROM AUTHOR]

Wood I-joists are efficient and lightweight structural members that are well suited for long-span floor and rafter applications. However, because of the thin-wall nature of the web and relatively low stiffness, local web buckling of the joist is an issue that must be considered. To increase the buckling capacity of these joists, investigators at West Virginia Univ. and Univ. of Idaho developed web panels with a sinusoidal geometry, instead of the flat web panels commonly used for prefabricated I-joists. This study presents analytical modeling, experimental testing, and finite-element (FE) analysis of the local buckling capacities of these sinusoidal web panels under compression. The flanges and web are not rigidly connected; thus, this problem can be described as the instability of a sinusoidal shell with two rotationally restrained loaded edges under compression. Using an energy method, the critical compression buckling stresses were obtained in terms of the elastic rotational restraint stiffness. The analytical solution was verified by FE analysis. Compression tests were performed for joists with both flat and sinusoidal webs, each at two different heights, to evaluate the elastic rotational restraining effect and illustrate the increase of the buckling capacities for sinusoidal webs compared with flat webs. Finally, a parametric study was conducted to study the core aspect ratio effect on the buckling load. The method described in this paper can be further extended to determine local buckling capacities of other structural shapes with elastic restraints along the loaded edges. [ABSTRACT FROM AUTHOR]

This paper presents an efficient stochastic buckling model for studying the structural reliability of layered composite columns with interlayer slip between the layers and random material and loading parameters. The model is based on the exact buckling model, response surface method, and Monte Carlo simulations. The probability of failure is investigated for a different number of random variables, sample points, and various degrees of response surfaces. The results show that the probability of failure is considerably affected by the type (deterministic or probabilistic) of the loading and its distribution. [ABSTRACT FROM AUTHOR]

This paper presents analytical approximate solutions for the initial postbuckling deformation of sandwich beams including transverse shear. The approximate procedure is based on the nonlinear beam equation (with transverse shear included) by coupling the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials; the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-nonlinear equation. Analytical approximations to the resulting boundary condition problem are established by combining the methods of Newton linearization and harmonic balance. Unlike the classical method of harmonic balance, the linearization is performed prior to proceeding with harmonic balancing thus resulting in a set of linear algebraic equations instead of one of nonlinear algebraic equations, thereby establishing analytical approximate solutions. Illustrative examples are presented for a few typical sandwich construction configurations, and it is shown that the proposed approximate solutions are in excellent agreement with the numerical solution obtained via the shooting method for both small and large angles of rotation. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analytical and numerical modeling of the lateral-torsional stability of horizontally layered composite beams. Composite beams are classified as horizontally layered beams with interlayer slip or sandwich beams with a weak shear core. The governing differential equations of the out-of-plane behavior of horizontally layered composite beams are supported by variational arguments. In the theoretical analysis, a distinction is made between the influence of the shear connection at the interface with respect to the in-plane or transversal deformations and to the out-of-plane or lateral deformations, respectively. Some engineering results are presented for a partially composite beam under pure bending moment. In the case of noncomposite in-plane action (orthotropic connection), a simple closed-form solution is derived for the lateral-torsional buckling moment, and it is shown that the exact dimensionless buckling moment depends only on two structural parameters for beams composed of two identical subelements. The results are analogous to those obtained for the in-plane buckling of partially composite or sandwich-type beams, where the buckling moment increases with the stiffness of the shear connection. Prandtl's valid solution for lateral-torsional buckling of ordinary beams is also found for composite beams in the case of noncomposite action in both the transversal and lateral directions. A generalization of Prandtl's valid solution for composite beams with partial composite action in the lateral direction and noncomposite action in the transversal direction is derived. It is shown that the lateral-torsional buckling formulas are strongly affected by the kinematics of the connected shear layer. Also, the lateral-torsional buckling of partially composite beams with both in-plane and out-of-plane slip behavior is analyzed using the Rayleigh-Ritz method. This mathematical problem leads to a system of differential equations with nonuniform coefficients. An approximated solution is derived for the isotropic connection with isotropic noncomposite actions, whereas an exact solution is presented for the orthotropic connection with noncomposite in-plane action. Finally, the Rayleigh-Ritz approach is compared with some numerical results associated with the exact resolution of the differential equations with nonuniform coefficients. The Rayleigh-Ritz approach appears to be efficient to capture the main phenomena, including the nonmonotonic dependence of the buckling load to the connection parameter. [ABSTRACT FROM AUTHOR]

The analytical solution of a buckling force of a pretwisted delaminated composite column with a proper consideration of the extensional and bending stiffness coupling and transverse shear effect is presented. The system of homogenous linearized differential equations with nonconstant coefficients obtained for this problem is solved with the help of the mathematical theory of analytic differential systems. The parametric studies are presented considering the effect of slenderness, the length of delamination, the asymmetrical position of delamination, and the transverse shear on the critical buckling force. [ABSTRACT FROM AUTHOR]

This paper deals with the lateral-torsional buckling of elastic microstructured beams. A linear gradient elasticity approach is presented. The elastic constitutive law is linear for the generalized beam model, expressed with first- and second-order moment variables in a sixth-order dimensional stress-strain space. The boundary conditions (including the higher-order boundary conditions) are derived from application of the variational principle applied to second-grade elastic models. The effect of prebuckling deformation is taken into consideration based on the Kirchhoff-Clebsch theory. Some analytical solutions are presented for a hinged-hinged strip beam. The lateral-torsional buckling moment is sensitive to small length terms inherent in the microstructured constitutive law. It is shown that the gradient parameter tends to increase the critical lateral-torsional buckling moment, a conclusion different from the one obtained with an Eringen-based nonlocal model. This tendency is consistent with that observed for the in-plane stability analysis (based on a second-grade model), for the lateral buckling of a hinged-hinged axially loaded column. The effect of higher-order boundary conditions is also studied with the vanishing of the couple stress components. It is numerically shown, through the resolution of a sixth-order differential equation, that the lateral-torsional buckling moment is not significantly affected by the choice of higher-boundary conditions for sufficiently small ratio between the characteristic length and the total length of the structure. We finally notice that the introduction of the warping effect can be understood as a special case of gradient elasticity theory. [ABSTRACT FROM AUTHOR]

An analytical pilot model for interactive buckling in sandwich struts with cores made from a functionally graded material based on total potential energy principles is presented. Using a Timoshenko beam approach, a system of nonlinear differential and integral equations is derived that predicts critical and secondary instabilities. These are validated against numerical simulations performed within the commercial finite-element package Abaqus. Good agreement is found, and this offers encouragement for more elaborate models to be devised that can account for face-core delamination-a feature where functionally graded materials are known to offer distinct advantages. [ABSTRACT FROM AUTHOR]

The analytical strip method (ASM) is extended in this paper to the buckling analysis of antisymmetric laminated composite plates with bending-extension coupling. A system of three equations of equilibrium governing the buckling response of antisymmetric laminated composite plates is reduced to a single eighth-order partial differential equation, expressed in terms of a displacement function. This equation is then solved analytically to generate the critical value of the in-plane forces (, ) for antisymmetric cross-ply and angle-ply laminated and stiffened composite plates. The effects of various parameters, including plate aspect ratio, plate orthotropicity ratio, beam rigidity, and plate bending-extension coupling on the critical values of and on antisymmetric laminated composite plates are discussed. The results derived using the ASM are presented in tabular and graphical forms and compare very well with ones derived using finite-element analysis. [ABSTRACT FROM AUTHOR]

The buckling response of symmetric laminates that possess strong flexural-twist coupling is studied using different methodologies. Such plates are difficult to analyze because of localized gradients in the mode shape. Initially, the energy method (Rayleigh-Ritz) using Legendre polynomials is employed, and the difficulty of achieving reliable solutions for some extreme cases is discussed. To overcome the convergence problems, the concept of Lagrangian multiplier is introduced into the Rayleigh-Ritz formulation. The Lagrangian multiplier approach is able to provide the upper and lower bounds of critical buckling load results. In addition, mixed variational principles are used to gain a better understanding of the mechanics behind the strong flexural-twist anisotropy effect on buckling solutions. Specifically, the Hellinger-Reissner variational principle is used to study the effect of flexural-twist coupling on buckling and also to explore the potential for developing closed-form solutions for these problems. Finally, solutions using the differential quadrature method are obtained. Numerical results of buckling coefficients for highly anisotropic plates with different boundary conditions are studied using the proposed approaches and compared with finite-element results. The advantages of both the Lagrangian multiplier theory and the variational principle in evaluating buckling loads are discussed. In addition, a new simple closed-form solution is shown for the case of a flexurally anisotropic plate with three sides simply supported and one long edge free. [ABSTRACT FROM AUTHOR]

This paper presents a study on the thermal postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium. The surrounding elastic medium is modeled as a Pasternak foundation. Two kinds of micromechanics models, namely the Voigt model and Mori-Tanaka model, are considered. The governing equations are based on a higher-order shear deformation shell theory that includes shell-foundation interaction. The thermal effects are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature dependent. The governing equations are solved by a singular perturbation technique. The numerical results show that in some cases the FGM cylindrical shell with intermediate volume fraction index does not have intermediate buckling temperature and thermal postbuckling strength. The results reveal that Voigt model and Mori-Tanaka model have the same accuracy for predicting the thermal buckling and postbuckling behavior of FGM shells. The results confirm that for the case of heat conduction, the postbuckling equilibrium path for geometrically perfect FGM cylindrical shells with simply supported boundary conditions is no longer of the bifurcation type. [ABSTRACT FROM AUTHOR]

In this paper, the buckling behavior of generic higher-order shear beam models is investigated in a unified framework. This paper shows that most higher-order shear beam models developed in the literature (polynomial, sinusoidal, exponential shear strain distribution assumptions over the cross section) can be classified in a common gradient elasticity Timoshenko theory, whatever the shear strain distribution assumptions over the cross section. The governing equations of the bending/buckling problem are obtained from a variational approach, leading to a generic sixth-order differential equation. Buckling solutions are presented for usual archetypal boundary conditions such as pinned-pinned, clamped-free, clamped-hinge, and clamped-clamped boundary conditions. The results are then extended to general boundary conditions based on generalized linear elastic connection law including vertical and rotational stiffness boundary conditions. Engineering analytical solutions are derived in a dimensionless format. The model valid for macrostructures is generalized for micro- or nanostructures using the nonlocal integral Eringen's model. The nonlocal framework is also developed in a variational consistent framework. Buckling solutions are finally presented for the nonlocal higher-order beam/colum models. [ABSTRACT FROM AUTHOR]

The effect of fiber orientation is studied on the failure load of a laminated curved panel subjected to uniaxial compression for a combination of simply supported and clamped boundary conditions. The failure modes are specified as buckling and first-ply failure, with the failure load defined as the minimum of these two loads. The panel is taken as a shear-deformable symmetrically laminated angle-ply laminate, and the effect of fiber orientation on the failure load is investigated by considering several laminations consisting of 0, 90, and ply angles and by determining the failure load for different aspect ratios and panel thicknesses. The best ply angles for each stacking sequence are determined to maximize the failure load and the stacking sequence giving the highest failure load. The numerical results are obtained using an eight-noded shell finite element that avoids the parasitic shear or shear locking problem. It is observed that the rotational restraints at the curved edges have a major effect on the failure load. [ABSTRACT FROM AUTHOR]

An analytical study of local buckling of discrete laminated plates or panels of fiber-reinforced plastic structural shapes is presented. Two cases of composite plate analyses with two opposite edges simply supported and the other two opposite edges either both rotationally restrained or one rotationally restrained and the other free, are studied. Generic loading cases with combined linearly varying axial and in-plane shear loading are considered. A variational formulation of the Ritz method is used to establish the eigenvalue problem for the local buckling behavior, and explicit expressions for predictions of the plate buckling stress resultants, in terms of the rotationally restrained stiffness, the plate aspect ratio, and the ratios of applied stress resultants, are developed. Based on different boundary and loading conditions, simple and explicit local buckling solutions for several special cases are further reduced. Validity of the explicit solutions presented is demonstrated by a good agreement of comparisons between the present predictions and available solutions in the literature. Parametric studies are further conducted, and the influences of several parameters such as the rotationally restrained stiffness, biaxial loading stress ratio, material flexural orthotropy, and linearly varying axial loading stress gradient on the local buckling stress resultants are discussed. [ABSTRACT FROM AUTHOR]

This paper presents finite-element (FE) analysis to study the axial load capacity of pretwisted steel bars of rectangular cross sections. The FE simulations are conducted using the commercial software ABAQUS. The FE simulations include bars of 20- and 30-mm width, 3- and 6-mm thicknesses, and three different lengths of 300, 400, and 500 mm. The bar ends are gripped and embedded in cylindrical slips. A set of twisting angles, ranging between 0 and 270° with an increment of 15°, is considered for each length. Geometric imperfections as well as actual elastic-plastic behaviors have been implemented in nonlinear FE models. The column strengths, load-shortening curves as well as failure modes, were predicted. The FE model is initially verified by comparing the buckling capacity and mode of the simulated straight bars with the experiments and the AISC code. The bars are then twisted beyond their elastic limit, unloaded to remove elastic recovery, and subjected to axial displacement. FE simulations showed that the permanent twists have influenced the axial strength and the static performance of the pretwisted bars. This improvement is supported by the considerable increase in the critical buckling loads of the bars, particularly at twisting angles ranged between 15 and 90°. Two analytical models capable of predicting the critical elastic and inelastic loads were developed using the FE results and utilizing multiple regression analysis for permanent angles of twist up to 90°. Multiple regression analysis models were shown to accurately predict the buckling loads within a 90% or more confidence interval. [ABSTRACT FROM AUTHOR]

Eccentric discharge in slender metal silos is known to be one of the most critical load conditions, responsible for many silo buckling disasters in the past. The high failure rate may be significantly attributed to difficulties in devising a suitable wall pressure representation for this condition. Where the flow of stored solids is eccentric and has partial contact with the wall in a slender silo, the solid exerts much lower pressures than the adjacent stationary solid. This pressure drop leads to very high local axial compression and causes buckling failure. Experimentally measured pressures indicate that a significant rise in pressure may occur just outside the flow channel, but its form and magnitude are not yet well understood because very detailed and expensive instrumentation is needed to obtain data that can define it. This paper explores the nonlinear structural behavior and buckling of a slender metal silo with and without specific inclusion of an adjacent rise in pressure, to determine whether it is a necessary part of any design pressure representation. To assist this investigation, the mechanics of the nonlinear behavior of a cylindrical silo under this load condition is explored using the analogy of a propped cantilever slice beam. Advantage is taken of a particular load condition that leads, by chance, to buckling at the same load factor for both linear and geometrically nonlinear analyses. This special case permits the detrimental effect of wall flattening and the beneficial effect of the changing prebuckling stress pattern to be explored to give a deeper insight into the behavior. The slice-beam analogy may also be generalized to describe the nonlinear behavior of any thin-walled cylindrical shell under meridional strip-like loads acting on part of the circumference. [ABSTRACT FROM AUTHOR]

This paper deals with the buckling analysis of Timoshenko beams of finite length in frictionless contact with an elastic substrate in a generalized plane stress or plane strain regime. The proposed FEM makes use of a mixed variational formulation based on the boundary integral equation commonly referred to as the Flamant solution. The corresponding finite-element model for the soil-structure interaction system adopts two-node locking-free finite elements for the Timoshenko beam and a constant soil reaction underlying each foundation element. Significant cases are thoroughly discussed, and a classical two-dimensional finite-element model is developed to have reference solutions. Numerical examples show that the proposed model is very simple and effective, and the Timoshenko beam model appears to be very useful in determining buckling loads in good agreement with reference solutions. Conversely, the Euler-Bernoulli beam model provides satisfactory results for long beams on soft soil only. [ABSTRACT FROM AUTHOR]

The static and dynamic analysis of functionally graded material (FGM) skew plates under mechanical load is studied. The FEM formulation based on a third-order shear deformation (TOSD) theory that does not require any shear correction factor is used in the analysis. The continuity requirement of the higher-order theory has been overcome in this study by adopting a continuous isoparametric Lagrangian element with seven degrees of freedom at each node. The Mori-Tanaka homogenization scheme is used to estimate the effective properties of the constituents, and it is assumed that mechanical properties vary according to a power-law distribution of the volume fraction of the constituents. The efficiency of the present model has been validated by comparing the results obtained with those available in the literature. The effects of skew angle, boundary conditions, volume-fraction exponent, loading conditions, aspect ratio, thickness ratio, and other parameters on deflection, natural frequency, and critical buckling load of functionally graded skew plates are reported for the first time based on TOSD that can serve as the benchmark for future research. [ABSTRACT FROM AUTHOR]

In the current study, a semianalytical closed-form solution is presented for the first time for buckling analysis of two-directional, functionally graded (FG) circular plates with variable thickness supported by both constrained edges and two-parameter elastic foundations. It is assumed that the material properties of the functionally graded material (FGM) vary in the transverse and radial directions, simultaneously. While variations of the elasticity modulus in the transverse direction is described by a power-law, variations of the material properties and the thickness in the radial direction are assumed to obey exponential laws. Mindlin's shear deformation plate theory and the differential transform technique are employed to develop the governing equations. A sensitivity analysis including evaluation of effects of various edge conditions, geometric parameters, coefficients of the elastic foundation, and material heterogeneity is performed. Results reveal that the strength degradation caused by the radial thickness reduction may be compensated by an appropriate increasing of the elasticity modulus in the radial direction. Furthermore, the elastic foundation may significantly affect the buckling load in some circumstances. [ABSTRACT FROM AUTHOR]

A finite-element formulation is developed for the lateral torsional buckling analysis of plane frames with moment connections consisting of two pairs of welded plate stiffeners. The finite element provides a realistic representation of the partial warping restraint provided by the joint to the adjoining members. The element consists of two nodes with four generalized buckling degrees of freedom per node and is thus devised to interface with two classical beam buckling elements connected at right angles. The new finite element extends the functionality of the classical beam finite element to predict the lateral buckling load for noncollinear structures, such as portal frames. A comparison with results based on shell finite-element analysis demonstrates the ability of the new formulation to reliably predict the lateral buckling resistance of plane frames at a fraction of the computational and modeling cost of shell-based finite-element solutions. [ABSTRACT FROM AUTHOR]