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Owing to the excellent performance of microstructures or nanomaterials with well-designed topological configuration, the characteristic scale of structural design is gradually shifting from macroscopic to nanoscale or microscale structural design. However, the size effect that emerges from the small-scale structures may not be explained effectively with the hypothesis of classical mechanics owing to the lack of microscopic parameters in the classical constitutive model. In addition, slender beams within such small-scale structures are prone to buckling failure, which puts forward additional requirements for the stability design of the structure except for the overall compliance of the structure. Therefore, a topology optimization framework combining the modified couple stress theory with the solid isotropic material penalization (SIMP) model is constructed to illustrate the size effect on topology optimization. Numerical results show that the size effect affects the compliance, buckling performance, and topological configurations of the evolutionary structures. [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 deals with the large deflections and buckling loads of tapered cantilever columns with a constant volume. The column member has a solid regular polygonal cross-section. The depth of this cross-section is functionally varied along the column axis. Geometrical nonlinear differential equations, which govern the buckled shape of the column, are derived using the large deflection theory, considering the effect of shear deformation. The buckling load of the column is approximately equivalent to the load under which a very small tip deflection occurs. In regard to the numerical results, both the elastica and buckling loads with varying column parameters are discussed. The configurations of the strongest column are also presented. [ABSTRACT FROM AUTHOR]

Dynamic buckling of viscoelastic sandwich truncated nanocomposite conical shell subjected to moisture, temperature and magnetic field is presented in this paper. This class of structures is of great interest due to its extensive use in aerospace applications. The layers of the structure are made from a multiphase nanocomposite consist of polymer-carbon nanotubes (CNT)-carbon fibers. The micromechanics and Halpin–Tsai equations in hierarchy are applied for calculating the effective material properties of the multiphase nanocomposite layers. The structural damping effects are considered based on Kelvin–Voigt theory. The surrounding medium is simulated using visco-Pasternak model. Utilizing the first order shear deformation theory (FSDT), energy method and Hamilton's principle, the motion equations are derived. Differential quadrature method (DQM) and Bolotin's method are applied for solution of the motion equations to obtain the dynamic instability region (DIR) of the structure. The effects of various parameters such as structural damping, viscoelastic medium, magnetic field, number of layers, volume fraction of CNTs, temperature and moisture changes as well as boundary conditions on the DIR of the structure are studied. The results reveal that by increasing the moisture and temperature changes, the DIR will be happened at lower excitation frequencies. [ABSTRACT FROM AUTHOR]

The buckling behavior and failure mode of a composite panel stiffened by J-shaped stringers under in-plane shear is studied by experiments and numerical analysis. Digital fringe projection profilometry was applied to monitor and measure the buckling morphology changes of the stiffened composite panel during in-plane shearing, which was verified by strain gauge measurement. Numerical simulation was performed using the finite element method to predict the failure load and buckling modes of the stiffened composite panel under in-plane shear. Numerical results showed good agreement with the full-field optical buckling measurement. The combination of experimental and numerical prediction can be effective in revealing the deformation process and failure mechanism of the stiffened composite panel. [ABSTRACT FROM AUTHOR]

In the current work, an innovative fixture was designed and made to test local buckling of the notched plates under tensile loading. The conducted experimental measurements include the symmetric and for the first time the anti-symmetric modes of the buckling. Both monotonic and cyclic loading were applied on the specimens and the effect of the buckling on the fracture capacity and fatigue life of the specimens were investigated. The main interest of the paper is to describe the fixture and some experimental techniques. The buckling load was obtained from the tests as well as fracture capacity and fatigue life. Based on the obtained results, the buckling can reduce the fracture capacity as well as the fatigue life by 35% and 59%, respectively. Due to the mix mode of I-III, the anti-symmetric buckling shows a greater effect on the fracture capacity, however, the sliding crack closure due to mode III prevents the crack growth in the case of anti-symmetric buckling. [ABSTRACT FROM AUTHOR]

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]

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]

An analytical model describing the nonlinear interaction between global and local buckling modes in long thin-walled rectangular hollow section struts under pure compression founded on variational principles is presented. A system of nonlinear differential and integral equations subject to boundary conditions is formulated and solved using numerical continuation techniques. For the first time, the equilibrium behaviour of such struts with different cross-section joint rigidities is highlighted with characteristically unstable interactive buckling paths and a progressive change in the local buckling wavelength. With increasing joint rigidity within the cross-section, the severity of the unstable post-buckling behaviour is shown to be mollified. The results from the analytical model are validated using a nonlinear finite element model developed within the commercial package Abaqus and show excellent comparisons. A simplified method to calculate the local buckling load of the more compressed web undergoing global buckling and the corresponding global mode amplitude at the secondary bifurcation is also developed. Parametric studies on the effect of varying the length and cross-section aspect ratio are also presented that demonstrate the effectiveness of the currently developed models. [ABSTRACT FROM AUTHOR]

Analytical and numerical study of buckling of imperfect cylindrical shells made by functionally graded materials (FGM) are presented. Critical bending moment is determined in presence of internal pressure. In the analytical solution, the eigenvalue method is used and the buckling equation of defective shell is derived based on the generalized Donnell shallow shell theory. Three types of geometrical imperfections in longitudinal and circumferential directions and also their combinations are considered. The effects of some parameters such as internal pressure, shell dimensions, amplitude and shape of the imperfections and degree of the material grading are investigated. Results show that the defects greatly decrease the critical bending moment and change the buckling mode. Increasing the percentage of ceramic content, radius and thickness increase the buckling load while the cylinder length has not considerable effects in perfect shells. Symmetric defect reduces considerably the buckling moment versus skew-symmetric one. Small skew-symmetric defects (in size of the thickness) have little effects on the shells with small radii. For imperfect shells, the buckling moment increases versus radius and length less than the thickness. [ABSTRACT FROM AUTHOR]

The perforated stiffened panel is generally found as a sub-component of sophisticated structures. The fundamental purpose of this panel is to withstand against buckling under complicated loading and environmental conditions. Hence, an accurate knowledge of critical buckling behaviour of stiffened panels is very much essential for a reliable and lightweight structural design. In this paper, the focus is on quasi-laminated panels with different cutout shapes of various sizes and their responses to hygrothermal environments under nonlinearly varying edge loads and is compared with the locally stiffened panels. Towards this, the modelling of the panel and stiffener is done by adopting nine-noded heterosis plate elements and three noded beam elements respectively. The stiffener formulation is suitably modified in order to take the torsional effect also into consideration along with the effect of shear deformation. Initially, the plate and the stiffener elements are treated separately, and then the displacement compatibility is maintained between them by using the transformation matrix. For a given loading and geometric discontinuity, the stress distribution within the perforated panel is highly non-uniform in nature and hence a dynamic approach has been used to calculate buckling loads by adopting two sets of boundary conditions, one set for pre-buckling stress analysis and the second set for buckling analysis. Four different quasi-isotropic stacking sequences are deliberated in this work by varying different plyorientation in each scheme. The study also addresses the effect of various parameters such as nonlinear loads, hygro-thermal loads, cutout size and shapes, position of cutout, stiffener parameters, stacking sequences, thickness of plate and boundary conditions. [ABSTRACT FROM AUTHOR]

With the exploitation of offshore oil and gas gradually moving to deep water, higher temperature differences and pressure differences are applied to the pipeline system, making the global buckling of the pipeline more serious. For unburied deep-water pipelines, the lateral buckling is the major buckling form. The initial imperfections widely exist in the pipeline system due to manufacture defects or the influence of uneven seabed, and the distribution and geometry features of initial imperfections are random. They can be divided into two kinds based on shape: single-arch imperfections and double-arch imperfections. This paper analyzed the global buckling process of a pipeline with 2 initial imperfections by using a numerical simulation method and revealed how the ratio of the initial imperfection’s space length to the imperfection’s wavelength and the combination of imperfections affects the buckling process. The results show that a pipeline with 2 initial imperfections may suffer the superposition of global buckling. The growth ratios of buckling displacement, axial force and bending moment in the superposition zone are several times larger than no buckling superposition pipeline. The ratio of the initial imperfection’s space length to the imperfection’s wavelength decides whether a pipeline suffers buckling superposition. The potential failure point of pipeline exhibiting buckling superposition is as same as the no buckling superposition pipeline, but the failure risk of pipeline exhibiting buckling superposition is much higher. The shape and direction of two nearby imperfections also affects the failure risk of pipeline exhibiting global buckling superposition. The failure risk of pipeline with two double-arch imperfections is higher than pipeline with two single-arch imperfections. [ABSTRACT FROM AUTHOR]

The paper is devoted to the effect of some geometrical imperfections on the critical buckling load of axially compressed thin-walled I-columns. The analytical formulas for the critical torsional and flexural buckling loads accounting for the initial curvature of the column axis or the twist angle respectively are derived. The classical assumptions of theory of thin-walled beams with non-deformable cross-sections are adopted. The non-linear differential equations are derived and the critical buckling loads are approximated by means of the Galerkin’s method. Comparison of analytical results to numerical analysis of simply supported I-columns by means of finite element method (FEM) is provided. Moreover the analytical formulas is adapted to I-columns with lipped flanges and satisfactory agreement of analytical and numerical results of stability analysis is observed. [ABSTRACT FROM AUTHOR]

The Hencky bar-net model, developed from a finite difference plate model, is proposed for buckling and vibration analyses of rectangular plates with non-uniform thickness. The Hencky bar net comprises rigid bars joined by elastic rotational springs to allow for bending flexibility and diagonal springs in each panel to simulate the twisting effect. The non-uniform plate thickness can be readily handled by adjusting the spring stiffnesses. For generality, the edges of the plate are elastically restrained where the special cases are the classical boundary conditions of simply supported edge, clamped edge and free edge. The plate is subjected to uniaxial load or biaxial loads. In order to demonstrate the versatility and the accuracy of the Hencky bar model, some plate problems are analysed and the obtained results compared with existing results reported in the open literature. [ABSTRACT FROM AUTHOR]

Behaviour of designs after buckling is need to be analysed. In this paper supercritical behaviour of rod systems was studied. Numerical methods used in popular computing programs to analyse designs after buckling were considered and new methodology was proposed, which successfully used in program STK. [ABSTRACT FROM AUTHOR]

The local buckling of steel plates in rectangular concrete-filled steel tubular (CFT) columns subjected to eccentric compression is investigated based on the energy method. The formulas for elastic local buckling stress of the steel plates in rectangular CFT columns under eccentric compression are derived, assuming that the unloaded edges of the steel plate are elastically restrained against rotation, whereas the loaded edges are clamped. Subsequently, the formulas are calibrated with the experimental results and compared with calculated results by the empirical method, which exhibit good agreement. Then, these formulas are applied to investigate the local buckling behavior of steel plates in eccentrically loaded rectangular CFT columns. It is found that the local buckling stress of steel plates in eccentrically loaded rectangular CFT columns is significantly influenced by the stress gradient coefficients and width–thickness ratios while it is slightly influenced by cross-sectional aspect ratios (D/B). Finally, the reasonable ranges for width–thickness ratios (B/t) and depth–thickness ratios (D/t) at various stress gradient coefficients corresponding to different cross-sectional aspect ratios are suggested for the steel plates in eccentrically loaded rectangular CFT columns. Furthermore, the appropriate relationship for the thickness of the steel plates at various stress gradient coefficients is suggested for the design of rectangular CFT columns under eccentric compression. [ABSTRACT FROM AUTHOR]

The nonlinear buckling and post-buckling of ceramic–metal–ceramic layers (S-FGM) toroidal shell segment surrounded by elastic foundation under thermo-mechanical loads are investigated with an analytical approach in this paper. Based on the classical thin shell theory with geometrical nonlinearity in von Karman–Donnell sense, Stein and McElman assumption and Pasternak foundation model, the governing equations of nonlinear buckling of S-FGM toroidal shell segment are analyzed. The static critical buckling loads and the post-buckling analyses in two cases – movable and immovable boundary conditions including temperature effects are obtained. Furthermore, the effects of geometry ratios, characteristic of materials, elastic foundation and thermal environment on the nonlinear buckling of shells are presented. [ABSTRACT FROM AUTHOR]

Buckling and free vibration behavior of functionally graded carbon nanotube reinforced polymer composite plate subjected to nonuniform temperature fields have been investigated using finite element approach. The effective material constants of the plate are obtained using the extended rule of mixture along with efficiency parameters of the carbon nanotube (to include geometry-dependent material properties). Influence of boundary conditions, aspect ratio, functional grading of the carbon nanotube, nonuniform thermal loading on thermal buckling and free vibration behavior of the heated plate are analyzed. It is observed that temperature fields and functional grading are influenced on the critical buckling temperature of the plates. Further, nature of functional grading showed significant change in buckling mode shapes irrespective of the boundary conditions. The first few natural frequencies of the plate under thermal load decreases as the temperature increases and they are influenced significantly by the nature of temperature field. Variations in free vibration mode shapes of the square plates found with not significant change as temperature increases. However, free vibration modes of the rectangular plates are sensitive to the nature of temperature field whenever there is a free edge associated with the boundary condition. Influence of functional grading on the free vibration mode shapes is not significant in contrast with the free vibration natural frequencies. The magnitude of free vibration natural frequencies of functional grade-X type carbon nanotube reinforcement showed higher in comparison with other two types of reinforcements considered here. [ABSTRACT FROM AUTHOR]

Evaluation of the lateral-torsional buckling resistance of bisymmetrical I-section beams using finite element method was widely discussed in the paper. Numerous FEM simulations with regard to the stability behavior of steel structural elements subjected to bending about the major principal axis were performed. The use of different finite element modeling techniques and their influence on obtained results were presented by the authors. The ultimate state of both perfect and imperfect elements was assessed. Considerations were concerned with hot-rolled wide flange HEB and narrow flange IPE section beams. Idealization of boundary conditions of FEM models complies with the assumptions used in the analytical formulation of stability problems of thin-walled beams. Geometrically and materially nonlinear analyses GMNA and GMNIA preceded by LBA analyses were carried out. Numerical simulations were conducted with use of ABAQUS/ Standard program. [ABSTRACT FROM AUTHOR]

This paper is concerned with an analytical study of the nonlinear in-plane equilibrium and buckling of fixed shallow circular arches that are subjected to an arbitrary radial concentrated load. The structural behavior of an arch under an arbitrary radial concentrated load is quite different from that of an arch under a central concentrated load. It is shown that a fixed arch under an arbitrary radial concentrated load can buckle in a limit point instability mode, but cannot buckle in a bifurcation mode, which is different from that of a fixed arch under a central concentrated load that can buckle in a bifurcation mode or in a limit point instability mode. Analytical solutions for the nonlinear equilibrium path and limit point buckling load of shallow circular arches under an arbitrary radial concentrated load are derived. It is found that the load position influences the buckling load significantly and the influence is much related to the modified slenderness of the arch defined in the paper. It is also found that when the modified slenderness of an arch is smaller than a specific value, the arch has no typical buckling behavior. The analytical solution for the relationship of the specific modified slenderness with the load position is also derived. Comparisons with finite element (FE) results show that the analytical solutions can accurately predict the nonlinear equilibrium and buckling load of shallow fixed arches under an arbitrary radial concentrated load. [ABSTRACT FROM AUTHOR]

Abstract: A single-wall carbon nanocone (SWCNC) is treated as a tailored graphite sheet rolled up into a seamless hollow tapered form where its two sides are connected together. As either the top radius or height increases, the difference between the potential of a SWCNC and a graphite sheet becomes increasingly smaller. A quasi-continuum approach is adopted to investigate buckling and post-buckling behaviors of the formed SWCNCs, upon bending. It is found that both the height and top radius result in a decreasing critical bending angle. Only one pit develops at the top-centre of the SWCNC, irrespective of its height, and moves towards the bottom as the bending angle continues to increase. At the stage of post-buckling, two tiny symmetrical fins arise near the bottom, accompanying a slight jump in the average strain energy. [Copyright &y& Elsevier]

At the nano scale, the effect of surface stress becomes prominent as well as the so-called small scale effect. Furthermore due to difficulties in making accurate measurements at nano-scale as well as due to due to molecular defects and manufacturing tolerances, there exists a certain degree of uncertainty in the determination of the material properties of nano structures This, in turn, introduces some degree of uncertainty in the computation of the mechanical response of the nano-scale components. In the present study a convex model is employed to take surface tension, small scale parameter and the elastic constants as uncertain-but-bounded quantities in the buckling analysis of rectangular nanoplates. The objective is to determine the lowest buckling load for a given level of uncertainty to obtain a conservative estimate by taking the worst-case variations of material properties. Moreover the sensitivity of the buckling load to material uncertainties is also investigated. [ABSTRACT FROM AUTHOR]

Highlights • Introducing a buckling-monitoring member. • Studying static behaviors of the buckling-monitoring member. • Performance of finite element analyses to explain the failure mechanism of the buckling-monitoring member. • Performance of parametric studies for design suggestions of the buckling-monitoring member. • Monitoring the ultimate bearing capacity of a space truss preventing or postponing the potential progressive collapse. Abstract Buckling of compression members may lead to progressive collapses of space grid structures. On the basis of the sleeved compression member, a buckling-monitoring member is introduced to raise the alert of and control buckling of the compression member by sensing the contact between the core and sleeve. Simplified theoretical analyses are conducted indicating that the contact opportunity between the core and sleeve is affected by three factors, namely protrusion length of the core above sleeve, slenderness ratio of the core and gap between the core and sleeve. Finite element analyses are performed with the finite element models calibrated identifying that the buckling-monitoring member has an improved resistance to buckling and the failure of buckling-monitoring member is attributed to local buckling of the core segment near the end. Parametric studies are performed to investigate the effects of the three factors on the improvement of ultimate and post-ultimate bearing capacities of the sleeved compression members for design suggestions of the buckling-monitoring members. Short protrusion length of the core above sleeve is proposed and the post-ultimate bearing capacities of the buckling-monitoring members are improved significantly. The buckling-monitoring member is applied in a space truss with the ultimate bearing capacity of the space truss monitored, which is considered as a positive supplement of the structural health monitoring system. [ABSTRACT FROM AUTHOR]

The size-dependent effect on the biaxial and shear nonlinear buckling analysis of an isotropic and orthotropic micro-plate based on the surface stress, the modified couple stress theory (MCST), and the nonlocal elasticity theories using the differential quadrature method (DQM) is presented. Main advantages of the MCST over the classical theory (CT) are the inclusion of the asymmetric couple stress tensor and the consideration of only one material length scale parameter. Based on the nonlinear von Kármán assumption, the governing equations of equilibrium for the micro-classical plate considering midplane displacements are derived based on the minimum principle of potential energy. Using the DQM, the biaxial and shear critical buckling loads of the micro-plate for various boundary conditions are obtained. Accuracy of the obtained results is validated by comparing the solutions with those reported in the literature. A parametric study is conducted to show the effects of the aspect ratio, the side-to-thickness ratio, Eringen's nonlocal parameter, the material length scale parameter, Young's modulus of the surface layer, the surface residual stress, the polymer matrix coefficients, and various boundary conditions on the dimensionless uniaxial, biaxial, and shear critical buckling loads. The results indicate that the critical buckling loads are strongly sensitive to Eringen's nonlocal parameter, the material length scale parameter, and the surface residual stress effects, while the effect of Young's modulus of the surface layer on the critical buckling load is negligible. Also, considering the size dependent effect causes the increase in the stiffness of the orthotropic micro-plate. The results show that the critical biaxial buckling load increases with an increase in G/ E and vice versa for E/ E. It is shown that the nonlinear biaxial buckling ratio decreases as the aspect ratio increases and vice versa for the buckling amplitude. Because of the most lightweight micro-composite materials with high strength/weight and stiffness/weight ratios, it is anticipated that the results of the present work are useful in experimental characterization of the mechanical properties of micro-composite plates in the aircraft industry and other engineering applications. [ABSTRACT FROM AUTHOR]

After introducing the Eurocode standards several theses have been published on the now much-discussed phenomenon of lateral-torsional buckling of steel structural elements under pure bending. According that, researchers are working on the development of such new design methods which can solve the problems of the design formulae given by the EN 1993-1-1. This paper gives a detailed review on the proposals for novel hand calculation procedures for the prediction of LT buckling resistance of beams. Nowadays, the application of structural design softwares in practical engineering becomes more common and widespread. Recognizing this growing interest, the main objective of our research work is the development of a novel, computer-aided design method. In this paper the details of a general type stability design procedure for the determination of the LT buckling resistance of members under pure bending are introduced. Here, the theoretical basis of the proposed method is clarified, the calculation procedure is detailed and some results for the evaluation of the appropriateness of the method is also presented. Based on the evaluations it can be stated that the new, general type design method is properly accurate and has several advantages on the stability check of beams under bending. [ABSTRACT FROM AUTHOR]

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

Large compression deformation causes micro-springs buckling and loss of load capacity. We analyzed the impact of structural parameters and boundary conditions for planar micro-springs, and obtained the change rules for the two factors that affect buckling. A formula for critical buckling deformation of micro-springs under compressive load was derived based on elastic thin plate theory. Results from this formula were compared with finite element analysis results but these did not always correlate. Therefore, finite element analysis is necessary for micro-spring buckling analysis. We studied the variation of micro-spring critical buckling deformation caused by four structural parameters using ANSYS software under two constraint conditions. The simulation results show that when an x-direction constraint is added, the critical buckling deformation increases by 32.3-297.9%. The critical buckling deformation decreases with increase in micro-spring arc radius or section width and increases with increase in micro-spring thickness or straight beam width. We conducted experiments to confirm the simulation results, and the experimental and simulation trends were found to agree. Buckling analysis of the micro-spring establishes a theoretical foundation for optimizing micro-spring structural parameters and constraint conditions to maximize the critical buckling load. [ABSTRACT FROM AUTHOR]

Thermal buckling analysis of rectangular sigmoid functionally graded plates (S-FGPs) is investigated using first-order shear deformation theory. The sigmoid functionally graded material (S-FGM) system consists of ceramic (Al2O3) and metal (Al) phases varying through the thickness of plate according to a two power-law distribution. Material properties and thermal expansion coefficient of the plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The thermal loads are assumed to be uniform and sinusoidal distribution through-the-thickness. Numerical examples cover the effects of the gradient index, plate aspect ratio, side-to-thickness ratio and loading type on the critical buckling for S-FGM plates. [ABSTRACT FROM AUTHOR]

Experiments have been conducted to investigate the buckling and postbuckling behavior of aluminum alloy 7050-T7651 integrally stiffened panel under a combined compression-shear load. A new combined-load test fixture was designed and used in these experiments. There were a total of six large rectangular stiffened panels in the size of960 by 850 mm, which were classified in two groups according to the cross section and layout of their stiffeners. Three panels, named J panels, were designed in four parallel J-shaped stiffeners. Another three panels, named X panels, were designed in eight orthogonal blade-shaped stiffeners. Strain rosettes bonded back-to-back on the skin were used to measure the strains of skin at their locations in three directions (0,45, and 90 deg), whereas the strain gauges installed on the stiffeners were used to measure the strains of stiffeners in a single direction. The integrally stiffened panels were loaded up to a sudden drop of the applied load and an accompanying harsh noise caused by the stringers splitting from skins. All the test panels failed in the same modes of global flexural buckling and the spitting of the stiffeners from skins. The mean value of the first buckling loads of X panels is 11.6% higher than that of the J panels. The mean value of the failure loads of X panels is 1.5% less than that of the J panels. All experimental results will be employed for the validation of finite element models and optimization method on the buckling and postbuckling analyses of integrally stiffened aluminum panel in further studies. [ABSTRACT FROM AUTHOR]