Search

A new size-dependent beam model is introduced on the basis of hyperbolic shear deformation beam and modified strain gradient theory. The governing differential equations and corresponding boundary conditions are obtained with the aid of minimum total potential energy principle. The static bending and buckling behaviors of simply supported microbeams embedded in an elastic medium are investigated. The interactions between the microbeam and elastic medium are simulated by Winkler foundation model. Navier solution procedure is employed to obtain analytical solutions for deflections under sinusoidal load and critical buckling loads. The effects of material length scale parameter, length-to-thickness ratio, shear correction factors and Winkler modulus on the bending and buckling responses of microbeams are discussed in detail. The results are comparatively presented with the results of other beam theories. It is observed that the new results predicted by the present model and the results evaluated by sinusoidal shear deformation beam model are in good agreement. [ABSTRACT FROM AUTHOR]

Computer simulations are becoming increasingly important for the optimisation of various processes since they can significantly reduce the development time and costs. The discrete element method (DEM) offers a powerful tool for simulating the interactions of large numbers of particles. The method has proven its usefulness for many applications where granular and spherical particles are handled. Very recently DEM, was used to simulate the interactions of tubular particles. While the existing linear elastic models could describe the reversible bending and denting of these particles in a realistic way for small deformations, they are inadequate for describing the bending and compression behaviour at higher forces. In this region, buckling phenomena become important. Therefore, new phenomenological models, inspired by the collapse of steel tubes due to ovalisation of the cross section and the formation of plastic hinges, have been implemented for metal and synthetic plastic tubes. Using these models virtual, bendable tubes were created in the DEMeter++ software. The DEM parameters were calibrated for copper and PVC tubes based on combined bending and denting tests conducted using an Universal Testing System. The simulations were in good agreement with the measurements ( R 2 > 0.91 ). This realistic DEM model of bending can, in future research, be used to simulate the processing of large numbers of tubular particles (e.g. the processing of crop stems). [ABSTRACT FROM AUTHOR]

In this work a finite element model is presented for buckling and nonlinear analysis of multilayer sandwich plates and shells, with a soft core sandwiched between stiff elastic layers. The finite element is obtained by assembling all element-layers through the thickness using specific assumptions on the displacement continuity at the interfaces between layers, but allowing for different behaviors of the layers. The stiff elastic layers are modelled using the classic plate theory and the core is modelled using Reddy׳s third order shear deformation theory. The present finite element model is a non-conforming triangular plate/shell element with 24 degrees of freedom for the generalized displacements. This model is applied in the solution of illustrative examples and the results are presented and discussed. [ABSTRACT FROM AUTHOR]

Buckling of cracked functionally graded plates resting on Pasternak foundation under tension has been studied. Classical plate theory in framework of the finite element method has been used. Shape functions for elements surrounding crack tips have been derived using previous solutions of displacement fields around crack tips. In-plane loads have been obtained by a pre-buckling solution using quarter-point elements around crack tips. Results show that an increase of foundation stiffness, leads to greater values of buckling loads. For longer cracks the effect of foundation stiffness on buckling load diminishes. For bi-axial loading such stiffness has less effect on buckling compared to uni-axial case. [ABSTRACT FROM AUTHOR]

Abstract: In the present work, the buckling and vibration of rectangular single-layered graphene sheets is analyzed based on the nonlocal theory of elasticity which takes the small scale effects into account. The graphene sheet is assumed as a thin plate, and the classical plate theory is applied to obtain the differential equation of the sheet. For the first time, the complex finite strip method is employed to study the vibration and buckling behavior of graphene sheets. The weighted residual method is employed to obtain the stiffness, stability and the mass matrices of the graphene sheet which is assumed to be an isotropic nanoplate. A sinusoidal displacement function is used for the longitudinal direction, which satisfies the simply supported boundary condition, while piecewise interpolation polynomials including the Hermitian and bubble functions are assumed for the other direction. A matrix eigenvalue problem is solved to find the vibration frequency and buckling load of graphene sheets subjected to different types of in-plane loadings including the uniform and non-uniform uniaxial and biaxial compressions as well as shear loading. The accuracy of the proposed model is validated by comparing the results with those reported by the available references. Furthermore, a number of examples are presented to investigate the effects of various parameters (e.g., boundary conditions, nonlocal parameter, aspect ratio, and type of loading) on the results. [Copyright &y& Elsevier]

Abstract: An analytical solution of the buckling problem formulated for a rectangular orthotropic plate with two opposite edges clamped and another two edges free of load and support (CCFF) loaded by linearly distributed in-plane loads is presented. The Kantorovich procedure is employed to derive a governing equation and boundary conditions for the buckling problem which is subsequently solved using the generalised Galerkin method. The plate deflection is approximated by certain combinations of beam functions. The analytical formula for the critical load has been obtained and verified by comparison with a finite-element solution. Applications of this formula to the solutions of design problems have been demonstrated for the CCFF plates with various elastic characteristics and geometric parameters. [Copyright &y& Elsevier]

Abstract: The divergence and flutter behavior of Beck׳s type of laminated box beams are investigated based on the finite element model. Mechanics of laminated box beam with non-symmetric lay-up is presented based on kinematic assumptions consistent with Vlasov beam theory. To obtain mass-, elastic stiffness-, geometric stiffness-, damping-, and load correction matrices, the extended Hamilton׳s principle is employed. Evaluation procedures for critical values of divergence and flutter with and without damping effects are briefly introduced. Through numerical examples, influences of fiber angle change, non-conservative parameter, external (viscous fluid) and internal (material) damping on divergence and flutter loads of laminated box beams subjected to a subtangential force are newly presented. [Copyright &y& Elsevier]

Abstract: This paper deals with the large amplitude vibration, nonlinear bending and thermal postbuckling of functionally graded material (FGM) beams resting on an elastic foundation in thermal environments. Two kinds of micromechanics models, namely, Voigt model and Mori-Tanaka model, are considered. The motion equations are based on a higher order shear deformation beam theory that includes beam–foundation interaction. The thermal effects are also included and the material properties of FGMs are assumed to be temperature-dependent. The numerical illustrations concern the nonlinear vibration, nonlinear bending and thermal postbuckling of FGM beams resting on Pasternak elastic foundations under different thermal environmental conditions. It is found that the FGM beam with intermediate material properties does not necessarily have intermediate nonlinear frequencies. The thermal postbuckling path of simply supported FGM beams is no longer of the bifurcation type for both uniform and non-uniform temperature fields. [Copyright &y& Elsevier]

Abstract: In this paper, a new microstructure-dependent sinusoidal beam model for buckling of microbeams is presented using modified strain gradient theory. This microbeam model can take into consideration microstructural and shear deformation effects. The equilibrium equations and corresponding boundary conditions in buckling are derived with the minimum total potential energy principle. Buckling problem of a simply supported microbeam subjected to an axial compressive force is analytically solved by Navier solution procedure. Influences of thickness-to-length scale parameter and slenderness ratios on buckling behavior are discussed in detail. It is observed that the size dependency becomes more important when the thickness of the microbeam is closer to material length scale parameter. Also, it can be said that the effects of shear deformation are more considerable for short and thick beams with lower slenderness ratios. [Copyright &y& Elsevier]

Abstract: This paper presents an analytical solution for the linear elastic buckling analysis of simply supported battened columns subjected to axial compressed loading. The critical buckling load is derived by using the classical energy method. Unlike most of existing work, the present approach considers not only the shear effect but also the discrete effect of battens on the global buckling behaviour of the columns. The present analytical solution is validated using the data obtained from the finite element analysis. The results show that the number of battens has significant influence on the critical buckling load of battened columns, particularly when the relative rigidity of the batten to the main member is small. It is shown that the critical buckling load increases with the number of battens, the combined bending and shear rigidity of battens, but decreases with the increased membrane stiffness of the two main members, and the increased distance between the centroids of the two main members. [Copyright &y& Elsevier]

Abstract: In this paper, instability of a thick through-the-thickness functionally graded material (FGM) rectangular plates under the practical cases of thermal and mechanical loading conditions is analyzed. Uniform shear, uniform uni-axial or biaxial compression/tension, uniform temperature rise, heat conduction across the thickness, and combined cases are considered. For thermal buckling and combined cases in thermal field, temperature dependency of the properties is also taken into account. The four-variable refined plate theory with parabolic distribution of shear strains through-the-thickness is implemented to establish the governing equilibrium and stability equations. Only the clamped type of boundary conditions is considered after the proof of bifurcation type buckling existence. The resulted equations are uncoupled in a reasonable manner. The multi-term Galerkin method is used to derive the critical buckling loads/temperatures and buckled shapes of the plate under various loading conditions. [Copyright &y& Elsevier]

The couplings of unsymmetric laminated structures and the comparatively low transverse shear stiffnesses significantly influence their stability behaviour. The aim of this work is to improve the purely analytical stability analysis of unsymmetric laminated structures. This problem can be reduced to one single plate with the use of the discrete plate theory. In this study, laminates under uniaxial compressive load are considered that are simply supported at all edges and have rotational restraints on the unloaded edges (SRSR) or have a free edge (SFSR). Therefore, the present study provides explicit solutions for the buckling load in two ways. Firstly, the first explicit solution for the buckling load of unsymmetric laminates with the mentioned boundary conditions is developed, which takes the bending–extension couplings into account in a direct way. The method is an energy-based method in the form of the Rayleigh-quotient for classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and third order shear deformation theory (TSDT). Secondly, the reduced bending (RBS) method is investigated for the first time in the framework of TSDT. The comparison of unsymmetric cross-ply and angle-ply laminates shows a good agreement with finite element analysis (FEA). Due to the high computational efficiency of the presented methods, they are excellently suited for pre-design and optimization of composite structures, with simultaneous high usability in practical application. [Display omitted] • First explicit buckling load for unsymmetric rotationally restrained laminates. • First reduced bending stiffness (RBS) method in the framework of TSDT. • Bending–extension couplings are taken into account in CLPT, FSDT and TSDT. • Pronounced transverse shear deformation in closed-form stability analysis. • High computational efficiency: very suitable for pre-design and optimization. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the instability behavior of thin elastic circular disks subjected to two concentrated edge loads arranged along a diameter. Despite the determination of critical load intensities for disks, made of conventional, linear elastic material, under some specific boundary conditions has been published in the past, we show some new and quite interesting findings. Particularly new are the investigations of tensile buckling of completely free disks as well as the post-buckling behavior of such disks under tension and compression, respectively. Comparisons with already existing results are presented, too. As far as the buckling load is concerned, all results are expressed in terms of a non-dimensional buckling factor. It is well known that the use of auxetic materials provides some potential for improving the behavior of lightweight structures. This fact has motivated us to consider, in which way the variation of the Poisson's ratio ν influences the stability behavior of the disks both under compression and under tension not just for the so far not investigated completely free stretched disks but also for the already published configurations. The Poisson's ratio is varied in the full thermodynamically admissible range [ − 1.0, 0.5] and some quite peculiar results are found and explained, especially for disks made of auxetic materials, i.e. for ν < 0. Although the stress fields are independent of the value of ν , the dependency of the critical load intensities is not simply proportional to the dependency of the plate's bending stiffness on ν , and the buckling modes show significant changes when ν is varied. The buckling factors for disks under tensile loading are by an order of magnitude larger than those for the compressed disks. Of course, also the buckling modes differ completely between compression and tension. Furthermore, the post-buckling behavior is qualitatively and quantitatively significantly different, too. The considerations and the achieved results are interesting for scientists working in the field of structural stability and for engineers in lightweight design of structures. Furthermore, there are applications in the design of sensors and actors as well as of flexible electronics. Since similar thin membrane structures appear in biological tissues, the paper might be interesting also for biologists. [Display omitted] • New results for buckling factors determined for completely free circular disks under tension along a diameter. • Considering completely free and simply supported disks under tension and compression; comparisons with existing results. • Unexpected findings regarding the dependency of buckling factors on Poisson's ratio; extensions to disks made of auxetic materials. • Deep post-buckling analyses show how bottle pourer disks behave and that under tension mode jumping can be observed. [ABSTRACT FROM AUTHOR]

Abstract: A simple refined shear deformation theory is proposed for bending, buckling, and vibration of thick plates resting on elastic foundation. The theory accounts for parabolic distribution of transverse shear stress, and satisfies the free transverse shear stress conditions on the top and bottom surfaces of the plate without using shear correction factor. The number of unknowns of present theory is two as against three in the case of other shear deformation theories. The elastic foundation is modeled as two-parameter Pasternak foundation. Equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are presented to verify the validity of present solutions. It can be concluded that the proposed theory is accurate and efficient in predicting the bending, buckling, and vibration responses of thick plates resting on elastic foundation. [Copyright &y& Elsevier]

Abstract: Three-dimensional reinforced sandwich structures are generally designed in order to provide optimal out-of-plane mechanical properties, beside traditional sandwiches which generally display satisfactory specific flexural properties but fatally insubstantial stiffnesses in the through-thickness direction. This paper deals with sandwich structures manufactured with polymeric foam core reinforced thanks to the technology (which is based on transverse needling) and specially investigates the compression behavior through the thickness direction. The compressive longitudinal moduli of such sandwiches are shown to be significantly improved in the presence of fibrous orthogonal reinforcements but the experimental estimations rather differ from analytical predictions that can be easily obtained using classical mixture laws. These discrepancies are mainly due to the buckling phenomenon, inherent in the geometry of the reinforcements, and the associated imperfection sensitivity. This work is thus devoted to the prediction of the critical loading of such a sandwich structure under through-thickness compression. A closed-form analytical expression is first derived from a general 3D elastic bifurcation analysis, then compared to finite element numerical solutions (obtained by both linearized buckling and incremental post-buckling analyses) for validation purposes, and finally confronted to experimental results. The buckling phenomenon is actually proved to be mainly responsible for the final collapse of the through-thickness reinforced sandwich. [Copyright &y& Elsevier]

Abstract: Problems of dynamics and stability of a moving web, travelling between two rollers at a constant velocity, are studied using analytical approaches. Transverse vibrations of the web are described by a partial differential equation that includes the centrifugal force, in-plane tension, elastic reaction and nonstationary inertial terms. The model of a thin elastic plate subjected to bending and non-homogeneous tension is used to describe the bending moment and the distribution of membrane forces. The stability of the plate is investigated with the help of studies of small out-of-plane vibrations. The influence of linearly distributed in-plane tension on the characteristics of the web vibrations is studied. The static forms of instability are investigated using numerical methods. It can be concluded that inhomogeneities in the applied tension may significantly decrease the critical web velocities and even small inhomogeneities in the tension may have a large effect on the divergence forms. [Copyright &y& Elsevier]

Abstract: This paper investigates computationally the buckling of simply supported sandwich columns constructed using elastic cores reinforced by skin-sheets of triaxial weave fabric (TWF) composites. A novel computationally cheap volume segmentation based thin plate model for the elastic properties of TWF is first developed. The predicted elastic properties of TWF exhibit quasi-isotropic behavior and correlate well with published numerical and measured results. Having demonstrated strong agreement with established results, these properties are then employed in the use of a plate on elastic foundation concept to study the stability of sandwich columns under a uniaxially compressed load environment. The parametric study comprises the effects of thickness, aspect ratio, and modulus of the sandwich core (treated as an elastic foundation), as well as the inclusion of the effects of the initial in-plane and out-of-plane imperfections of the skin-sheets on the critical buckling load. Remarkable dependencies of the critical buckling load on these parameters are demonstrated, due to both independent and wedding actions, noting that a perturbation due to out-of-plane imperfections has been observed to be the most significant contributor to reduction in compressive resistance. [Copyright &y& Elsevier]

Abstract: This paper is a theoretical and numerical study of the uniform growth of a repeating sinusoidal imperfection in the line of a strut on a nonlinear elastic Winkler-type foundation. The imperfection is introduced by considering an initially deformed shape which is a sine function with an half wavelength. The restoring force is either a bi-linear or an exponential profile. Periodic solutions of the equilibrium problem are found using three different approaches: a semi-analytical method, an explicit solution of a Galerkin method and a direct numerical resolution. These methods are found in very good agreement and show the existence of a maximum imperfection size which leads to a limit point in the equilibrium curve of the system. The existence of this limit point is very important since it governs the appearance of localization phenomena. Using the Galerkin method, we then establish an exact formula for this maximum imperfection size and we show that it does not depend on the choice of the restoring force. We also show that this method provides a better estimate with respect to previous publications. The decrease in the maximum compressive force supported by the beam as a function of the imperfection magnitude is also determined. We show that the leading term of the development has a different exponent than in subcritical buckling of elastic systems, and that the exponent values depend on the choice of the restoring force. [Copyright &y& Elsevier]

Abstract: This paper presents an analytical study on the influence of in-plane forces on the dynamic characteristics of a plate with grooves in different sizes. A sub-structuring approach, the reverse receptance method, is applied to solve the eigenvalues of an in-plane forces loaded plate with two parallel grooves and two orthogonal grooves, respectively. On considering coupling and interaction between two orthogonally connected grooves, the point receptance arrays are employed. Accuracy is evaluated by comparing the analytical solutions with numerical results obtained from the finite element model. Parametric study reveals, the deeper the groove, the lower the natural frequencies and buckling loads of the grooved plate will be. With in-plane tensions applied and increased linearly, the grooved plate is stiffened gradually and its natural frequencies increase accordingly. With equal bi-axial tensions, the natural frequencies of the grooved plates increase twice as much as those with uni-axial tension do. With in-plane compressive forces on the plate, the situations are reversed. The lowest natural frequency of a grooved plate with sufficient tensions can be higher than that of a non-grooved unloaded plate. When the groove size and the loading condition are the same, the orthogonal grooves decrease the natural frequencies and the buckling loads of a plate more than the parallel grooves do. The in-plane forces do not affect the mode shapes of the grooved plate; but the grooves do. The analytical evaluation demonstrates the accuracy and applicability of the proposed approach. [Copyright &y& Elsevier]

Abstract: A mathematical model for a slip-buckling problem has been proposed and its exact solution has been found for the analysis of materially inelastic two-layer composite columns with non-linear interface compliance. The mathematical model has been carried out to evaluate exact critical buckling loads. It has been demonstrated mathematically exactly, that exact critical buckling loads are influenced by the initial stiffness, and hence on linear portion of the interface force-slip relationship. Besides, it has been shown that material inelasticity can reduce the critical buckling loads significantly and that the interlayer stiffness has an important effect on the transition between the elastic and inelastic buckling. [Copyright &y& Elsevier]

Abstract: The paper presents a predictive model of the flatness defects, which appear during rolling of thin plates, the origin of which is the roll stack thermo-elastic deformation. The combination of the elastic deflection, the thermal crown and the roll grinding crown results in a non-parallel bite, and if the deformed roll transverse profile is not an affinity of the incoming strip profile, differential elongation results and induces high stresses in the outgoing strip. The latter, combined with the imposed strip tension force, result in a net post-bite stress field which may be sufficiently compressive locally to promote buckling. A variety of non-developable shapes may result, generally occurring as waviness (centre waves, wavy edges, quarter-buckles, etc.). This problem is most of the time addressed in a decoupled way, i.e. as a post-processing of the residual stresses computed by a strip rolling model; the present paper on the contrary describes a fully coupled approach of in-bite plastic deformation and post-bite buckling. For this purpose, a simple buckling criterion has been introduced in a FEM model of strip and roll deformation, Lam3/Tec3; its implementation is documented in details. The capabilities and limits of the present approach are described and discussed. Characterised by its coupled approach, it is primarily devoted to cases where on-line (under tension) manifested defects occur. It is shown that the impact of the post-bite, post-buckled stress field on the in-bite stress and strain fields is quite small in the cases investigated; however, subtle changes appear in the velocity field at bite exit, and this is sufficient to transform completely the post-bite stress field, which is found in much better agreement with measurements if such a coupled treatment is used. [Copyright &y& Elsevier]

Abstract: A new hyperbolic shear deformation theory taking into account transverse shear deformation effects is presented for the buckling and free vibration analysis of thick functionally graded sandwich plates. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. Equations of motion are derived from Hamilton''s principle. The closed-form solutions of functionally graded sandwich plates are obtained using the Navier solution. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the classical plate theory, but are almost comparable to those obtained using higher order theories with more number of unknown functions. [Copyright &y& Elsevier]

Abstract: Buckling analysis of symmetrically laminated rectangular plates with parabolic distributed in-plane compressive loadings along two opposite edges is performed using the Rayleigh–Ritz method. Classical laminated plate theory is adopted. Stress functions satisfying all stress boundary conditions are constructed based on the Chebyshev polynomials. Displacement functions for buckling analysis are constructed by Chebyshev polynomials multiplying with functions that satisfy either simply supported or clamped boundary condition along four edges. Methodology and procedures are worked out in detail. Buckling loads for symmetrically laminated plates with four combinations of boundary conditions are obtained. The proposed method is verified by comparing results to data obtained by the differential quadrature method (DQM) and the finite element method (FEM). Numerical example also shows that the double sine series displacement for simply supported symmetrically laminated plates having bending–twisting coupling may overestimate the stiffness, thus providing higher buckling loads. [ABSTRACT FROM AUTHOR]

Abstract: Wire-woven bulk Kagome (WBK) has recently been used to fabricate multi-layered truss-type cellular metals. A tube WBK structure is fabricated of tubes instead of solid wires. In this work, tube WBK specimens with various combinations of slenderness ratio and inner-to-outer diameter ratio of the tubular struts were tested under compression to investigate the effects of geometric factors on peak strength, equivalent Young′s modulus and energy absorption capability. To aid in the physical interpretation of the results and the development of a design methodology, numerical simulations of single tubular struts were performed with a wide range of slenderness ratio and inner-to-outer diameter ratio. The tube WBKs outperformed most cellular metals, but they were inferior to hollow trusses, especially those with a diamond configuration. However, energy absorption of the tube WBKs was comparable to that of hollow trusses because of stable deformation of the tube WBKs after initial yielding or maximum strength. [Copyright &y& Elsevier]

Abstract: A point receptance array is proposed to study behaviors of panel structures with stiffeners. Although the overall objective is intended to develop a general algorithm for large structural members with stiffeners of arbitrary arrangements, the present study focus on an analytical evaluation of the accuracy of the approximation. To simplify the formulations, a thin plate with two diagonally connected beam stiffeners is selected. By solving governing differential equations for the plate and beam, point receptances that represent the interaction and compatibility conditions at the plate–beam interfaces are analytically obtained. Buckling modes of the stiffened plate are obtained by solving an eigenvalue problem. Accuracy of the approach is verified by a comparison of the analytical solution with data obtained from a direct finite element model. A parametric study was also performed. Good agreement indicates that the point receptance is a viable approach for general applications. [ABSTRACT FROM AUTHOR]

Abstract: In the present paper, buckling loads of rectangular composite plates having nine sets of different boundary conditions and subjected to non-uniform inplane loading are presented considering higher order shear deformation theory (HSDT). As the applied inplane load is non-uniform, the buckling load is evaluated in two steps. In the first step the plane elasticity problem is solved to evaluate the stress distribution within the prebuckling range. Using the above stress distribution the plate buckling equations are derived from the principle of minimum total potential energy. Adopting Galerkin''s approximation, the governing partial differential equations are converted into a set of homogeneous linear algebraic equations. The critical buckling load is obtained from the solution of the associated linear eigenvalue problem. The present buckling loads are compared with the published results wherever available. The buckling loads obtained from the present method for plate with various boundary conditions and subjected to non-uniform inplane loading are found to be in excellent agreement with those obtained from commercial software ANSYS. Buckling mode shapes of plate for different boundary conditions with non-uniform inplane loadings are also presented. [Copyright &y& Elsevier]

Abstract: This paper discusses the buckling behaviour of orthotropic composite plates under uniform uniaxial compression with one free reinforced unloaded edge. A typical application example for use of such a mechanical model is the web of stiffeners and frames attached to the fuselage skin of an aircraft. The considered plates are rectangular and simply supported at the loaded transverse edges. One of the longitudinal unloaded edges is also simply supported, while the second unloaded edge is not supported at all but is reinforced by a flange of arbitrary cross-section. At first, an exact solution for the elastic buckling problem is derived from the governing differential equation by imposing the underlying boundary conditions. Thereafter, two approximate closed-form solutions for the buckling load are derived, which can be conveniently used for practical application purposes. Generic buckling curves using characteristic non-dimensional quantities are also presented. Finally, the question of the required bending stiffness of the flange is treated, to ensure that the flange withstands buckling and provides simply supported boundary conditions to the free reinforced plate edge. [Copyright &y& Elsevier]

Abstract: This paper presents a nonlinear in-plane elastic buckling analysis of circular shallow arches that are subjected both to a uniform temperature field and to a uniform radial load field. A virtual work method is used to establish nonlinear equilibrium equations and buckling equilibrium equations, and analytical solutions for the limit instability and bifurcation buckling loads are obtained. It is found that the temperature influences the limit instability, bifurcation buckling and postbuckling behaviour of shallow arches significantly. The limit instability and bifurcation buckling loads increase with an increase of the temperature. A maximum temperature is shown to exist for the occurrence of bifurcation buckling of shallow arches, and when the temperature is higher than this value, bifurcation buckling of an arch is not possible. An arch geometric parameter is introduced to define switches between the limit instability and bifurcation buckling modes, and between buckling and no buckling. Formulae and methods for the calculation of the limiting values of the arch geometric parameter are developed. It is also found that the limiting values of the arch geometric parameter decrease with an increase of the temperature. [Copyright &y& Elsevier]

Abstract: This paper discusses the results of a finite element (FE)-based study of the compressive instabilities of axial fiber tows in 2D triaxial braided carbon fiber composites (2DTBC). A 3D FE model of an axial tow is used in conjunction with the ABAQUS commercial FE code. To accommodate unstable snap-back post-peak behavior, an arc-length solution technique is adopted to solve the FE equations. Explicit account of the braid microstructure (geometry and packing) and the measured inelastic properties of the matrix (the in-situ properties) are accounted for via the use of the FE method. This type of detailed modeling is necessary for developing a mechanism-based failure prediction capability. The computational model provides a means to assess the compressive strength of the axial fiber tow and its dependence on various microstructural parameters. It also serves as a tool to assess the most significant parameters that affect compressive strength of a 2DTBC. [Copyright &y& Elsevier]

Abstract: Thermal post-buckling analysis of uniform, isotropic, slender and shear flexible columns is presented using a rigorous finite element formulation and a much simpler intuitive formulation. The ends of the columns are axially restrained to move and consequently any temperature rise above the stress free condition of the column produces an equivalent constant compressive mechanical load that causes the column to buckle at a critical temperature. Further increase in temperature beyond critical temperature results in the thermal post-buckling phenomenon. As a result of constraints imposed on the axial displacement at the ends of the column, the post-buckling phenomenon is governed by the von-Karman strain displacement relation applicable to one dimensional problems. Empirical formula for ratio of nonlinear axial load to critical load (equivalent constant mechanical load for a given temperature rise) as a function of the central deflection are obtained using both the rigorous finite element and intuitive formulations for various boundary conditions. The boundary conditions considered are the classical such as hinged–hinged, clamped–clamped and clamped–hinged conditions and nonclassical boundary conditions like the hinged–guided or the clamped–guided conditions. Post-buckling analysis results pertaining to nonclassical boundary conditions are meagre in the literature. It is observed that results obtained from both the formulations are in excellent agreement for all boundary conditions considered. Also the accuracy and simplicity of the intuitive formulation is aptly demonstrated to slender and shear flexible columns. [Copyright &y& Elsevier]

Abstract: Over the last years, a better comprehension of hydraulic cylinder performance is observed to be a prime objective of many owing to demanding applications. By observing these hydraulic cylinder applications, we see currently proposed models and design criteria do not take into account real factors, and further there are misalignment and boundary conditions in the end supports, mechanism interaction, dust, clearance and imperfections. Since these boundary conditions can develop progressive moments, the ideal simple supported bi-articulated configuration of the actuator is no longer valid, and virtual clamped configuration appears with friction moments that substantially modify the buckling analysis. In a previous work, misalignment effects were studied and discussed. In the present work a study of the influence of friction moments when misalignment effects are deliberately left aside is carried out. In order to separate these two phenomena (friction and misalignment) boundary conditions in a column are analysed. From this analysis, a theoretical and experimental work has been carried out for columns and an actuator characterizing the critical factors that cause the collapse. The aim of this paper is to describe the behaviour of actuators under load capacity with experimental validation when friction moment is taken into account and becomes an unknown variable. Experimental and theoretical results point out the importance and influence of the friction effects in columns and hydraulic cylinders. Then, it is recommended that knowledge of the hydraulic cylinder application to predict its load capacity owing to that direct extrapolation of results from current theories and criterions could lead to incorrect estimations. [Copyright &y& Elsevier]

Abstract: Analytical and experimental investigations of typical hydraulic cylinders have indicated that their load capacities are significantly different from those obtained from simple buckling analysis of idealized systems. In any case, an increase in the friction coefficient at the restrained ends changes the actuator''s limit load, while an increase in the initial maximum deflection (initial misalignment) decreases the limit load. A common practice of most cylinder manufacturers is to use a safety factor (between 2.5 and 4) to determine the service load after the critical load (buckling) is obtained by simple analytical procedures treating the cylinder as a perfect stepped column. The intricate aspects of friction effects have been deliberately left aside in this present work. Nevertheless, friction and interaction between mechanism and actuator in the buckling characteristics will be presented in the ongoing paper, which will follow this work. Authors know that, in a real system, the cylinder tube–rod interface is not rigid. Due to the flexibility of guide rings and clearances between components, misalignment (an angular deflection which increases with increasing axial load) exits at the interface. When initial imperfection angle exists, there is no sudden buckling. Then, stresses and deflections increase with increasing load. After repetitive use, the tolerance between the parts will become larger, consequently increasing the initial deflection, which has been proved to considerably decrease the load capacities of the power cylinders. From this analysis, a theoretical and experimental work has been carried out in order to show the advantages and disadvantages of the current design methods, characterizing the critical factors that cause the collapse and proposing useful design criterions. The present work aims to describe the behaviour of actuators under load capacity with experimental validation. [Copyright &y& Elsevier]

Abstract: The present paper investigates the structural stability of thin-walled steel cylinders surrounded by an elastic medium, subjected to uniform external pressure. A two-dimensional model is developed, assuming no variation of load and deformation along the cylinder axis. The cylinder and the surrounding medium are simulated with nonlinear finite elements that account for both geometric and material nonlinearities. Cylinders of elastic material within a rigid boundary are considered first, and the numerical results are compared successfully with available closed-form analytical predictions. Subsequently, the external pressure response of confined thin-walled steel cylinders is examined, in terms of the initial out-of-roundness of the cylinder, the initial gap between the cylinder and the medium, and the stiffness of the surrounding medium. Numerical results are presented in the form of pressure-deformation equilibrium paths, and show a rapid drop of pressure after reaching the maximum pressure level, as well as a significant imperfection sensitivity. A plastic-hinge mechanism is developed that results in a closed-form expression and illustrates the post-buckling response of the cylinder in an approximate manner. The distributions of plastic deformation, as well as the variation of cylinder-medium contact pressure around the cylinder cross-section are also depicted and discussed. Furthermore, the effects of uniform vertical preloading on the maximum pressure sustained by the cylinder are examined. Finally, the numerical results show good comparison with a simplified closed-form expression, proposed elsewhere, which could be used for design purposes. [Copyright &y& Elsevier]

Abstract: An approach to analytical solution is presented for vibration and buckling of thin-walled tubular beam shells typical of automotive structures, which are fabricated by joining sheet metal stampings along the two longitudinal edges with periodic spot welds, adhesive bonding, or combination of spot welds and bonding, known as weld bonding. Solutions are obtained for such beam shells of rectangular cross-section with two opposite ends simply supported. The beam shell is modeled as an assembly of the constituent walls and Levy-type formulation is used to obtain a series solution for the transverse displacement of each of the walls. The challenge of expressing the discrete point support conditions at the spot welds by a continuous function is addressed using the flexibility function approach used in literature. The flexibility function, used earlier to represent the flexibility distribution along weld-bonded edges of rectangular plates with periodic spot welds, is used here. The characteristic equations are obtained by satisfying the displacement, slope, shear, and moment equilibrium at the mating edges of the walls including the two weld-bonded edges and the compatibility conditions at the spot-weld locations. This approach to analytical solution, described here for thin-walled beam shells of rectangular cross-section, can be suitably adopted for more general cross-sections and joints along non-symmetric edges. A parametric study is undertaken to show the effect of aspect ratio of the beam shell, adhesive joint parameters, and the number of spot welds on the elastic buckling loads and the natural frequencies. Such parametric studies can be of use to designers in arriving at an optimal joint configuration of weld-bonded beam shells from buckling and vibration considerations. [Copyright &y& Elsevier]

• Buckling and postbuckling performance of panels with cutouts is studied using streamline fibres. • Streamlines around a given body are adopted to define the fibre trajectories. • Optimum stacking sequence of laminates is obtained for maximum buckling capacity. • The residual postbuckling stiffness of the optimum designs is evaluated. • Using continuous streamline fibres improves the buckling and postbuckling performance. In this paper the buckling and postbuckling behaviour of variable-stiffness composite fuselage panels with window openings based on streamline fibres is addressed. Streamlines of a fluid flow around a given body that represents the cutout are adopted to define the fibre trajectories that curve around the cutout in a continuous fashion. Plates and shells with circular and elliptical cutouts subjected to compressive and shear loads are investigated. Various design scenarios using different laminate layups are considered. As a first step, an optimum stacking sequence is obtained for maximum buckling capacity. Then, a postbuckling analysis is performed to evaluate the initial postbuckling stiffness that represents the strength of the laminates beyond buckling. The buckling and postbuckling performance of panels with streamline fibres is compared with that obtained for traditional panels with straight fibres. It is shown that significant improvements in the buckling capacity can be achieved using streamline fibres instead of straight ones. Moreover, laminates with streamline fibres optimized for maximum buckling loads exhibit a higher postbuckling strength than do the laminates with straight fibres. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] • The attempt of building FEA model dedicated to damage prediction. • Comparison of PFA and experimental damage evaluation in 1:1 macro- and microscale. • Analysis of ply stacking sequence effect on damage initiation and propagation. • Ply clusters reduce delamination range at the expense of intense crack development. • PFA model predicts well the localization of damage onset but not the damage types. Fibre reinforced polymers are widely used materials in terms of their mechanical properties. The application of proper stacking-sequence of layers allows to obtain desirable properties of composite structure, and affect its failure mechanisms. The aim of this work was to evaluate the stacking sequence influence in the axially compressed glass-fibre reinforced epoxy thin-walled columns. To highlight the differences, the comparative failure analysis was performed. The macroscopic observation and the analysis of X-ray µCT images presented numerous damage types for particular stacking sequences. Also, the progressive failure analysis model, which takes the manufacturing conditions into account, was implemented. The novelty of the analysis approach lies in direct comparison of experimental and numerical results in scale 1:1 – both in macroscale and microscale. The analysis indicated the most sensitive points of the studied columns in terms of damage initiation. The most dominant failure mode was delamination. It was noted ply clustering allows one to limit the damaged area in cost of increased matrix failure. It was also noticed that symmetric and asymmetric stacking sequences possess insignificant differences in the damaged area. The changes of stacking sequences have the effect on the development of translaminar, interlaminar and intralaminar cracks likewise. The comparison of experimental failure analysis and finite element method showed that the PFA model predicts the approximate localization of the failures. [ABSTRACT FROM AUTHOR]

• Computer simulations using both the standard and structural versions of molecular mechanics lead to close post-buckling stable equilibrium configurations of a compressed single layer graphene sheet (SLGS). • Column-like post-buckling deformation modes of a compressed SLGS obtained without the inclusion of van der Waals (vdW) interatomic forces are similar to those known for the planar Euler elastica. • Compressed SLGSs can have post-buckling out-of-plane equilibrium configurations whose stability is provided by attractive vdW forces. [Display omitted] The standard molecular mechanics (MM) method with the DREIDING force field (see Mayo et al. The Journal of Physical Chemistry, 1990, 94: 8897–8909) and the molecular structural mechanics (MSM) method with Bernoulli–Euler beam elements are used to study the quasi-static nonlinear buckling and post-buckling behavior of a compressed nearly square single layer graphene sheet (SLGS) for different types of boundary conditions. The novelty of this study is the finding that well-calibrated parameter sets provide similar values of buckling forces/modes and similar post-buckling deformations for stable equilibrium configurations of SLGSs in simulations using the standard MM and MSM methods. In addition, the effect of accounting for non-bonded van der Waals (vdW) forces on the advanced post-buckling deformation modes of compressed SLGSs was studied for the first time. It is shown that the column-like post-buckling deformation modes of compressed SLGSs obtained without the inclusion of vdW interatomic forces are similar to the well-known ones for the planar Euler elastica , and the advanced post-buckling modes obtained with the inclusion of interatomic vdW forces are qualitatively different from the corresponding modes for the planar Euler elastica. In addition, the study shows the theoretical possibility of the existence of post-buckling out-of-plane equilibrium configurations whose stability is provided by attractive vdW forces. [ABSTRACT FROM AUTHOR]

• Local buckling behavior of omega-stringer-stiffened panels under shear load. • Simple closed-form analytical solution for the eigenvalue problem. • Laminated composite plates with bending-twisting coupling. • Results in good agreement with finite element analyses. The local shear-buckling behaviour of omega-stringer-stiffened composite panels is analysed introducing a novel approximate analytical computational model. This type of stability analysis is critical for thin-walled structures like the proposed panel, which is applied, among other things, mainly in aerospace structures and marine vessels. In this context, computationally efficient methods are especially necessary for preliminary design phases that often involve optimization and extensive parameter studies. In the present work, a simple analytical model for the critical shear-buckling load is developed and evaluated taking bending-twisting coupling and different load directions into account. The modelling approach is based on energy methods and employs the principle of the stationary value of the total elastic potential. Hereby, the buckling shape functions are based on a combination of a polynomial term and a trigonometric Timoshenko-type term, where the latter is commonly used for closed-form analytical shear-buckling analysis. The approximate computational model is evaluated for four different laminate configurations and a wide range of different panel dimensions in comparison to finite element analyses. The parameter studies yield promising results with errors very acceptable in the context of preliminary design. [ABSTRACT FROM AUTHOR]

Abstract: The post-buckling solutions of non-uniform linearly and non-linearly elastic rods are constructed via a higher-order perturbation approach. For rods with continuously varying flexural stiffness, the onset of buckling and the post-buckling branches are determined employing a suitable set of admissible functions within the context of Galerkin''s method combined with a regular perturbation approach. On the other hand, for piece-wise continuous rods, closed-form eigenvalue solutions are exploited as a basis for the non-linear post-buckling description. Closed-form conditions on the non-linearly elastic constitutive function for the bending moment are obtained ensuring supercritical or subcritical divergence bifurcations. Several illustrative examples are discussed highlighting the effects of the stiffness non-uniformity on the onset of buckling and the post-buckling non-linear regime as well as the influence of the non-linear elasticity on the latter. [Copyright &y& Elsevier]

Abstract: The paper presents finite element free vibration and buckling analysis of laminated hat-stiffened shallow and deep shells using arbitrarily oriented stiffener formulation. Modified approach for modelling the curved stiffener is implemented using necessary transformations. A simplified stiffener formulation is presented to accommodate various shapes of stiffener shapes in developing the rigidity matrix for the finite element formulation. Investigation has been carried out on free vibration and buckling analyses of laminated composite stiffened shell structures with laminated open section (rectangular or ‘T’ shaped) and closed section (‘hat’ shaped) stiffeners. Parametric study on the hat-stiffened panels for the free vibration and buckling analyses confirms that the closed section stiffener being torsionally rigid is found to show better performance over open section stiffeners. [Copyright &y& Elsevier]

Abstract: The thermal expansions and rotations that result from a linear in-plane temperature gradient field are fully restrained at the ends of a fixed beam. These restrained expansions and rotations will produce internal bending and compressive actions in the beam, and these actions increase with an increase of the temperature differential and average temperature of the linear temperature gradient field. When these actions reach critical values, the fixed beam may bifurcate from its primary equilibrium state to a buckled equilibrium configuration. This paper presents a systematic treatment of classical buckling analysis for thermoelastic lateral-torsional buckling and for in-plane thermoelastic flexural buckling of a fixed beam of doubly symmetric open thin-walled cross-section that is subjected to a linear temperature gradient field over its cross-section. It is shown that the effective centroid and shear centre, rather than the geometric centroid and shear centre, should be used in formulating the thermoelastic prebuckling and buckling analysis and that the effects of temperature on the buckling resistance need to be considered. The thermoelastic lateral-torsional buckling of a fixed beam under a linear temperature gradient field is more complicated than its mechanical counterpart for uniform bending or for uniform compression, and iterative methods are needed to obtain accurate solutions. [Copyright &y& Elsevier]

Abstract: In this research, mechanical buckling of circular plates composed of functionally graded materials (FGMs) is considered. Equilibrium and stability equations of a FGM circular plate under uniform radial compression are derived, based on the higher order shear deformation plate theory (HSDT). Assuming that the material properties vary as a power form of the thickness coordinate variable z and using the variational method, the system of fundamental partial differential equations are established. A buckling analysis of a functionally graded circular plate (FGCP) under uniform radial compression is carried out and the results are given in closed-form solutions. The results are compared with the buckling loads of plates obtained for FGCP based on the first order shear deformation plate theory (FSDT) and classical plate theory (CPT) given in the literature. The study concludes that HSDT accurately predicts the behavior of FGCP, whereas the FSDT and CPT overestimates buckling loads. [Copyright &y& Elsevier]

Abstract: This paper presents a finite element model for the static and dynamic stability of a rotating pretwisted aerofoil cross-section two-bladed packet subjected to uniform radial periodic force. The effects of various parameters such as shroud dimensions, pretwist angle, stagger angle, rotational speed and distance of shear center from the centroid on the stability of the blade packets are presented. The numerical results show that pretwist angle and the coupling effect are important in high-frequency modes depending on shear center distance from the centroid on dynamic stability regions. The increase in stagger angle makes the pretwisted two-bladed packet less stable. However, the increase in rotational speed makes the pretwisted two-bladed packet more stable. [Copyright &y& Elsevier]

Abstract: The objective of this work is to examine the effect of a non-uniform distribution of the applied edge loads on their net critical value with reference to the title problem. This forms a sequel to an earlier work on uniaxial compression of plates without any in-plane restraint at lateral edges to suppress the Poisson effect. A rigorous superposition approach is employed for plane stress analysis of the loaded plate, and the resulting non-uniform in-plane stress field is fully accounted for in the subsequent stability analysis which is based on Galerkin''s approach with a complete set of admissible functions. Pertinent results are presented to highlight the influence of various non-uniform distributions as well as an in-plane restraint at the lateral edges. [Copyright &y& Elsevier]

Abstract: In this paper, the initial buckling loads and the corresponding buckling modes of symmetric rectangular laminated plates are investigated. The considered laminates are supposed to have a uniform thickness, are subjected to a linearly distributed inplane compressive normal load and are simply supported at the two loaded edges with one free unloaded plate edge and with one simply supported unloaded edge where elastic rotational restraints are considered. Unlike in many other investigations, the composite laminates presently under consideration may have arbitrary yet symmetric lamination schemes with bending–torsion coupling. The initial buckling loads of such plates are calculated using the RITZ-method for which some especially adjusted displacement shape functions are employed. Since a series expansion of the buckling shape is performed in the load direction only while in the perpendicular direction one single displacement function can be shown to be sufficient, the present approach is numerically very efficient when compared to approaches in which a series representation is chosen with respect to both inplane directions. Comparison with reference results and with finite element computations leads to an excellent agreement. Some new findings on the general stability behaviour of this class of laminated plates are presented as a closure. [Copyright &y& Elsevier]

Abstract: In this paper, lower and upper bounds of the buckling load of a composite beam with two non-overlapping delaminations are obtained by developing analytical models. The characteristic equation governing the delamination buckling is derived by using Euler–Bernoulli beam theory, performing proper linearization and by imposing the appropriate continuity and boundary conditions. The effects of the differential stretching and the bending–extension coupling are considered. The accuracy of the approach is verified by comparing results with previously published data and a separately carried out finite element analysis. The effects of the dimensions of the delaminations, their thicknesswise and spanwise locations on the lower and upper bounds of the buckling load are investigated in detail. The longer of the two non-overlapping delaminations dominates the buckling behavior. Composite beams with anti-symmetric non-overlapping delaminations withstand lower buckling loads than the composite beams with symmetric non-overlapping delaminations. The lower and upper bounds of the buckling load will be useful to gauge the working range of bridging and give guidelines for practical applications. [Copyright &y& Elsevier]

Abstract: The main objective of this study is to give a numerical solution of three-dimensional analysis of thick rectangular plates. The analysis uses discrete singular convolution (DSC) method. Free vibration, bending and buckling of rectangular plates have been studied in this paper. Regularized Shannon''s delta (RSD) kernel is selected as singular convolution to illustrate the present algorithm. In the proposed approach, the derivatives in both the governing equations and the boundary conditions are discretized by the method of DSC. The obtanied results are compared with those of other numerical methods. It is found that the convergence of the DSC approach is very good and the results agree well with those obtained by other researchers. [Copyright &y& Elsevier]

Abstract: The buckling of thin rectangular plates with nonlinearly distributed loadings along two opposite plate edges is analyzed by using the differential quadrature (DQ) method. The problem is considerably more complicated since it requires that first the plane elasticity problem be solved to obtain the distribution of in-plane stresses, and then the buckling problem be solved. Thus, very few analytical solutions (the only one available in the literature is for rectangular plates with all edges simply supported) have been available in the literature thus far. Detailed formulations and solution procedures are given herein. Nine combinations of boundary conditions and various aspect ratios are considered. Comparisons are made with a few existing analytical and/or finite element data. It has been found that a fast convergent rate can be achieved by the DQ method with non-uniform grids and very accurate results are obtained for the first time. It has also been found that the DQ results, verified by the finite element method with NASTRAN, are not quite close to the newly reported analytical solution. A possible reason is given to explain the difference. [Copyright &y& Elsevier]

Abstract: The closed-form heating response of a thin uniform circular wafer is obtained, in view of a new processing method for semiconductor materials. A strain energy formulation is obtained expeditiously using Gaussian curvature and associated structural concepts. The method is developed for generally curved wafers, which accounts for flat, spherical, cylindrical and twisted shapes. Solutions for the first two types become available in closed form, and the deformation can exhibit a sudden change in axi-symmetrical response or a snap-through buckling, or both: for the latter two types, a numerical solution points to progressive deformation in both without buckling. All results are shown to compare rather well with finite element analysis. [Copyright &y& Elsevier]

Abstract: Engineering approach for computation of stringer stiffened cylindrical shells is realized mainly using the structurally orthotropic theory with momentless pre-buckling state. On the other hand, experimental results suggest that in many cases the mentioned theory provides excessive values of buckling load. The influence of imperfections for stringer stiffened shells seems to be less important than in an isotropic case. Considering axially symmetric momentous components of pre-buckling state cannot essentially improve theoretical results. Specific experiments showed a significant influence of stringer discreteness on the buckling loads of reinforced shells. The mentioned influence can be divided into two parts: excitation of essentially non-axially symmetric pre-buckling and buckling states. Usually, only the latter phenomenon is taken into account. In this paper we show that the first factor dominates. We propose simple analytical expressions governing non-axially symmetric pre-buckling state components. We also propose an asymptotic simplification of the buckling boundary value problem. Results obtained are compared numerically with the known theoretical and experimental data. [Copyright &y& Elsevier]