Search

In this paper, the bending, buckling, and free vibration of functionally graded porous (FGP) beams are studied based on two beam theories (with or without considering thickness stretching, respectively). The effect of thickness stretching is obtained by comparing the results of the two theories. Two symmetrical distributions and one asymmetrical distribution of pores are considered. Both Young’s modulus and mass density of the FGP beams are in gradient variation in the thickness direction. The governing equations are constructed using Hamilton’s principle. The analytical solutions are obtained by Navier’s method. The effects of slenderness ratios, pore distribution, porosity and thickness stretching on FGP beams have been investigated. The results show that the inhomogeneity of FGP beams in the thickness direction is positively correlated with the effect of thickness stretching. [ABSTRACT FROM AUTHOR]

This paper reports a detailed numerical investigation on the buckling aspects of laminated composite shell panels of three forms (cylindrical, spherical and hyperbolic paraboloid) with five support conditions exposed to linearly varying in-plane edge load employing eight nodded isoparametric finite element formulation. The impacts of different parameters including ply orientation, load factor, shell forms, aspect ratio, modulus ratio, curvature ratio, width-to-thickness ratio and angle of lamination on the buckling load of shell panels are examined. It is found that the various parameters addressed in this study have a remarkable impact on the buckling phenomena of laminated composite shell panels. Further, a comparison is made showing the effects of five types of compressive edge loads like uniform, triangular, parabolic, partial edge load and point load on the buckling phenomena of laminated shell panels with respect to five support conditions. [ABSTRACT FROM AUTHOR]

This work presents a thermoelectric vibration and buckling behavior of a bidirectional functionally graded piezoelectric porous (BD-FGPP) plate resting on the elastic foundation with arbitrary boundary conditions. The variation of the material properties in the FGPP plate is bidirectional, i.e. along longitudinal and thickness directions, using the modified power law distributions. Also, the BD-FGPP plate carries various porosity distributions, i.e. even, uneven and symmetric center types. The governing equation of the FGPP plate has been obtained through Hamilton's principle and solved through a higher-order finite element approach. The correctness and usefulness of the current technique are confirmed and compared with existing model outcomes available in the literature. A comprehensive parametric study has investigated the effect of the elastic foundations, porous exponent with various porosity distributions, bidirectional material exponent, temperature change, electrical loading and boundary conditions. The attained results are more valuable for designing functionally graded piezoelectric-based smart structures by considering the porosity distribution in a thermoelectric environment. [ABSTRACT FROM AUTHOR]

This paper conducts the analytical investigation on the buckling of cylindrical shells with axially variable elastic modulus subjected to axial compressive load for the first time. First, it proves that the axially distributed elastic modulus can be expressed as the combination of constant and variable component. Then, governing differential equations for buckling analysis are derived and exactly solved by the combined perturbation method and Fourier analysis. Accordingly, the closed analytical solutions for the cylinder with arbitrarily variable elastic modulus are obtained, which reveal the explicit relations among buckling load, shell sizes and elastic modulus functions. Based on the presented analytical formulas, four types of elastic modulus variations for shell material which are uniform, periodic, linear and combined are studied in detail, and the results are also well verified. The derived analytical solutions in this paper can serve as benchmarks for buckling analyses of thin-walled cylinders with elastic modulus variations resulted from design, material manufacturing process, material imperfections and so on. [ABSTRACT FROM AUTHOR]

The woven structure made of naturally curved (in-plane) ribbons has smooth geometry and fewer geometric imperfections, but there is no study of its buckling mechanical properties under vertical loads. The aim of this paper is to investigate buckling mechanical properties of spherical woven structures. Three spherical woven structures with different ribbon types and six new spherical woven structures with different ribbon widths and thicknesses were designed and the quasi-static vertical compression tests were carried out. The buckling load of spherical woven structures were studied by nonlinear finite element and ring buckling theory. Results indicate that the failure mode of the spherical weave structure under vertical loading can be divided into two stages, where a flat contact region forms between the spherical weave structure and the rigid plate and inward dimple of ribbons. Spherical weave structures using naturally curved (in-plane) ribbon weaving have better buckling stability than those woven with straight ribbon. Based on theoretical and finite element analysis, we propose a buckling load equation and buckling correction factor equation for the new spherical weave structure under vertical compression load. The formula is validated and has good agreement with the test results, which could help to design the stability of spherical weave structures with in-plane ribbons. [ABSTRACT FROM AUTHOR]

The buckling and postbuckling behaviors of functionally graded graphene platelets-reinforced composite (FG-GPLRC) circular plates are studied based on the classical nonlinear von Karman plate theory. The effective Young's modulus of the composite is estimated using the modified Halpin–Tsai micromechanical model, and the effective Poisson's ratio is estimated by the rule of mixtures. Governing equations of the problem are derived based on the Hamilton principle and the numerical solutions of critical loads and postbuckling deflection–load relationships are calculated using the shooting method. Different from the existing linear buckling analysis based on the Terriftz criterion, the study with considering the global deformation of the plates, we analyze the influencing factors of the critical buckling loads and postbuckling paths of the FG-GPLRC circular plates subjected to uniformly distributed radial pressure. The results show that the content, geometric parameters and distribution pattern of GPL have great influences on the critical buckling loads and the post-buckling bearing capacities of the circular FG-GPLRC plates. [ABSTRACT FROM AUTHOR]

Eccentrically stiffened plates are widely used as a structural component in many engineering applications. However, these structures are exposed to complex loading conditions, resulting in strength reduction leading to failure. This research aims to examine the stability performance of the perforated stiffened laminated composite plate subjected to non-uniform edge load under the influence of environmental conditions. Towards this, a robust and computationally efficient finite element (FE) formulation has been developed, where the plate is modeled using a 9-noded heterosis element to avoid the shear locking of the plate element and a 3-noded isoparametric beam element is adopted to model the stiffener by applying a displacement compatibility condition at the skin-stringer interface. A torsion correction factor is introduced in the beam formulation to account for the twisting of the stiffener. A unique dynamic technique is utilized to obtain the buckling load by employing two types of boundary conditions due to the non-uniform stress distribution in the perforated plate under environmental and operational loading conditions. An analysis is performed on the unstiffened plate to determine a suitable cutout shape, loading pattern and lamina scheme based on its improved stability performance. Unlike previous studies, several stiffener configurations are considered to comprehend the influence of temperature and moisture on the stability behavior of centrally placed cutout plates and obtain a stiffener configuration with improved performance. It is noticed that when the perforated stiffened plate is exposed to thermal or hygroscopic load close to a critical temperature or moisture, the buckling capacity drops suddenly in the plate attached to a stiffener of greater depth. Moreover, it is observed that when the stiffened plate is exposed to higher intensity of hygrothermal load, the plate's buckling capacity drops significantly as the thickness of the plate reduces. [ABSTRACT FROM AUTHOR]

This study explored the disparities in bending, buckling, and vibration results of ideal and non-ideal functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) beams. The smooth and continuous profiles of material distributions of ideal FG-GPLRC beams were modified for making the controlling tracks to produce two different forms of non-ideal FG-GPLRC beams which had in-and out-stepwise distributions of material constituents across the beam's thickness. The Halpin–Tsai model and the rule of mixture were used to predict the effective material properties of the nanocomposite beams. The closed-form solution possessing less time of computation was provided for predicting the mechanical behavior of the beams, and it was validated for accuracy by comparing with the results of the Ritz method. The study's results suggest that non-ideal beams with an out-stepwise distribution of material constituents have a better dispersion of reinforcing nanomaterials than in-stepwise distribution. Therefore, the results of the beams with an out-stepwise distribution are closer to those of ideal beams than with in-stepwise distribution. [ABSTRACT FROM AUTHOR]

In this paper, buckling of a nanowire column subjected to self-weight and tip load is investigated. One end of the nanowire is free, while the other end is attached to a rotational spring support. Considering the equilibrium equations together with the Euler–Bernoulli beam theory, the governing differential equation describing the behavior of the column can be obtained. Effect of surface stress is also incorporated into the formulations in terms of transverse distributed loading. The differential equation has been solved analytically and the general solution can be presented in the terms of Bessel function of the first kind. Applying the boundary conditions, the characteristic equations influenced by surface stress and stiffness of the rotational spring at the support can be expressed and then the critical load can be determined using the Newton–Raphson iterative scheme. From the results, they reveal that the positive surface stress could strengthen the nanowire against the buckling. Fixity at the base is also influenced to the critical load where the increase of the stiffness of the spring results in the increase of critical load as well. [ABSTRACT FROM AUTHOR]

This paper proposes a modified segmented rod method (MSRM) in order to facilitate the introduction of boundary conditions in the analysis of free vibrations and buckling of Euler–Bernoulli beams. First, the basic idea of proposed modifications is presented in the case of elementary length beam, and then the idea is generalized to the full-length beam. In addition to facilitating the introduction of boundary conditions, by comparing the results of MSRM with segmented rod method (SRM) and Hencky bar-chain method (HBM), a faster convergence of MSRM results to the exact ones was observed. Although the case of uniform beam is considered in this paper, proposed MSRM may contribute to greater use of segmented beam approach in solving of various static, free vibration or buckling problems of non-uniform beams. Also, it was shown that MSRM can be easily adapted for the analysis of beams that resting on partial elastic foundation. [ABSTRACT FROM AUTHOR]

The aim of this work is to investigate the free vibration and buckling characteristics of sigmoid functionally graded (FG) nanoplate with the influence of porosity. The modified rule of the mixture is utilized to calculate the effective material properties of porous sigmoid functionally graded (P-SFGM) nanoplate. Three schemes of porosity distribution, including uniform, symmetric and nonsymmetric are investigated. The first-order shear deformation theory is utilized to simulate the displacement fields of P-SFGM nanoplate. Eringen's nonlocal elastic theory and isogeometric analysis (IGA) are used to establish the governing equations for free vibration and buckling analysis of nanoplate structure with small size effect. By using NURBS as a basic function, IGA can fulfill the higher-order derivative requirement of governing equations. The accuracy of the presented solution is verified. By taking the nonlocal parameter into account, the stiffness of the plate is softened. Also, the effects of porosity distribution across the plate's thickness, porosity parameter, material power index, boundary conditions (BCs) and aspect ratio on the frequency response of P-SFGM nanoplate are presented. [ABSTRACT FROM AUTHOR]

This presents a mathematical model proposed by the author for description of deformation process of a shell structure under the action of a load that depends linearly on time. Material orthotropy, geometric nonlinearity, transverse shifts are taken into account. A distinctive feature of the model is the use of a refined discrete method for taking into account stiffeners, proposed by the author earlier. Prior to this, the method was used only in static or isotropic dynamic problems. It is proposed to add correction normalizing factors, which makes it possible to obtain the most accurate values of critical loads. The methodology of the calculation algorithm under dynamic loading is based on the Kantorovich method and the Rosenbrock method, which allows solving rigid ordinary differential equation (ODE) systems. New numerical results for cylindrical panels are obtained. The influence of the number of stiffening elements on the values of the critical load is shown. A comparison with the classical discrete method of taking into account stiffeners is carried out. For the problems considered in this paper, the phase portraits of the system are shown. [ABSTRACT FROM AUTHOR]

The structural response and design of normal strength and high strength steel I-sections at elevated temperatures are investigated in this paper. The shell finite element models of steel I-section elements capable of replicating their behavior in fire are developed and validated against experimental results from the literature. The validated shell finite element models are then utilized to generate extensive structural performance data for steel I-sections, considering a broad range of plate slenderness values for cross-section elements, elevated temperature levels, cross-section aspect ratios as well as different loading conditions and normal strength and high strength steel grades. The accuracy of the existing methods provided in the European structural steel fire design standard EN 1993-1-2 and its upcoming version prEN 1993-1-2 for the ultimate strength predictions of normal strength and high strength steel cross-sections in fire is assessed. Scope for improvement is observed. Considering this, a new method for the ultimate strength predictions of normal strength and high strength steel sections at elevated temperatures is put forward. It is shown that the proposed method leads to more accurate ultimate strength predictions for normal strength and high strength steel I-sections in fire with a higher level of reliability relative to the existing design methods provided in EN 1993-1-2 and prEN 1993-1-2. [ABSTRACT FROM AUTHOR]

This paper analytically studies the buckling of a cylindrical shell having varying thickness under non-uniform axial compressive loads for the first time, which widely exists in engineering practice. A novel quadratic perturbation technique is developed to establish general buckling load formulas for the shell. This method overcomes the difficulties of traditional energy methods in solving high order determinants and deriving direct expressions for buckling loads when shell thickness and axial load are unknown. Applying presented formulas, various shell thicknesses and axial loads are analyzed, and a series of new results for buckling loads are obtained and validated. Even for classical cosine thickness variation under uniform axial compression, we also give general conclusions compared with Koiter's results by the energy method. The effects of thickness variations and load distribution parameters on buckling loads are analyzed in detail. The presented study in this paper fills the gap and establishes a foundation of buckling analysis for non-uniformly loading cylindrical shells with variable thickness. Certainly, the established formulas are general and available for buckling resistance capacity evaluation for the shells under all circumstances involving thickness variations or/and non-uniform axial compressive loads. [ABSTRACT FROM AUTHOR]

Buckling design of axially compressed cylindrical shells is still a challenging subject considering the high imperfection-sensitive characteristic in this kind of structure. With the development of various design methods, the energy barrier concept dealing with buckling of imperfection-sensitive cylindrical shells exhibits a promising prospect in recent years. In this study, buckling design of imperfection-sensitive cylindrical shells under axial compression based on the energy barrier approach is systematically investigated. The methodology about buckling design based on the energy barrier approach is described in detail first taking advantage of the cylindrical shells whose buckling loads have been extensively tested. Then, validation and discussion about this buckling design method have been carried out by the numerical and experimental analyses on the cylindrical shells with different geometrical and boundary imperfections. Results in this study together with the available experimental data have verified the reliability and advantage of the buckling design method based on energy barrier approach. A design criterion based on the energy barrier approach is therefore established and compared with the other criteria. Results indicate that buckling design based on energy barrier approach can be used as an efficient way in the lightweight design of thin-shell structures. [ABSTRACT FROM AUTHOR]

A superconvergent isogeometric method is developed for the buckling analysis of thin beams and plates, in which the quadratic basis functions are particularly considered. This method is formulated through refining the quadrature rules used for the numerical integration of geometric and material stiffness matrices. The criterion for the quadrature refinement is the optimization of the buckling load accuracy under the assumption of harmonic buckling modes for thin beams and plates. The method development starts with the thin beam buckling analysis, where the material stiffness matrix with quadratic basis functions does not involve numerical integration and thus the refined quadrature rule for geometric stiffness matrix can be obtained in a relatively easy way. Subsequently, this refined quadrature rule for thin beam geometric stiffness matrix is conveniently generalized to the thin plate geometric stiffness matrix via the tensor product operation. Meanwhile, the refined quadrature rule for the thin plate material stiffness matrix is derived by minimizing the buckling load error. It turns out that the refined quadrature rule for the thin plate material stiffness matrix generally depends on the wave numbers of buckling modes. A theoretical error analysis for the buckling loads evinces that the isogeometric method with refined quadrature rules offers a fourth-order accurate superconvergent algorithm for buckling load computation, which is two orders higher than the standard isogeometric analysis approach. Numerical results well demonstrate the superconvergence of the proposed method for the buckling loads corresponding to harmonic buckling modes, and for those related with non-harmonic modes, the buckling loads given by the proposed method are also much more accurate than their counterparts produced by the conventional isogeometric analysis. [ABSTRACT FROM AUTHOR]

Perforated composite laminates are frequently encountered in multiple engineering applications as sub-components of complicated structures. In many of these applications, the primary objective of using the panel is to resist buckling under diverse environmental and loading conditions. This paper is mainly focused on the vibration and buckling responses of composite laminates with elliptical cutouts subjected to localized edge loads under different hygrothermal environments. Toward this, a nine-noded heterosis plate element has been utilized to discretize the plate by adopting a refined meshing pattern around the elliptical cutout. The geometric nonlinearity has been incorporated to predict free vibrations under the hygrothermal environment. Considering the plethora of applications of composite laminates in hygrothermal conditions, a new temperature/moisture-dependent model is presented by taking into consideration various mechanical loadings. For a given environmental and loading condition, the stress distribution within the perforated panel is highly non-uniform in nature and hence, a novel dynamic approach has been proposed to solve buckling problems by adopting two sets of boundary conditions. A MATLAB program has been developed to investigate the effect of various parameters such as elliptical cutout size, elliptical orientation, elliptical cutout eccentricity, thickness and boundary conditions of the laminated composite plate under diverse hygrothermomechanical loading conditions. A notable difference in the critical buckling load is observed when the locally prestressed perforated panels are subjected to complex hygrothermal environments, especially at larger elliptical cutouts and hence the importance of localized edge loads under hygrothermal environment is emphasized. [ABSTRACT FROM AUTHOR]

The transfer matrix method is applied to the buckling of end-bearing piles partially or fully embedded in a layered elastic medium with a constant coefficient of subgrade reaction for each layer. The solution of the governing differential equation for each pile segment can be expressed as the product of a fourth-order matrix and a coefficient determinant. Using the transfer matrix method and combining the boundary conditions at both ends of the pile, the buckling load is obtained by solving the eigenvalue equation. A parametric study is performed to investigate the effects of the properties of the soil–pile system on the stability capacity of the pile. It is shown that the effects of the embedment ratio, soil layer thickness, and soil stiffness on the buckling of piles are quite significant. Several calculation examples are presented to verify the present method. [ABSTRACT FROM AUTHOR]

In this paper, a high-order cylindrical beam model, where the shear deformation is taken into account, will be used to analyze the buckling behaviors of the functionally graded cylindrical beams with radially and axially varying material inhomogeneities. The coupled governing equations for buckling of a cylindrical beam under axial compression are derived, which can be translated into a single differential equation by introducing an auxiliary function. The shifted Chebyshev polynomials are used to compute the critical buckling loads for kinds of boundary conditions. By comparing with the three-dimensional solutions for buckling of homogeneous circular beams, the validity of the introduced model is confirmed. Two typical material property distributions defined by the exponential- and power-law are considered. A parametric study is carried out to investigate the effects of material gradient indexes on the critical buckling loads. [ABSTRACT FROM AUTHOR]

This paper studies the critical issue of thin-walled beams with laterally fixed ends. The method for defining the formulae of twist moment for the beams subjected to combined loads was elucidated. Based on this, the governing differential equations of the beam were developed. The procedure for determining the critical state of the beam by the energy method was presented. With this procedure, the critical state of the beam concerned under three types of loadings such as axial force F , bending moment M and distributed load q (or concentrated load P) was examined deliberately. The outcomes were presented in explicit closed-form, which can be illustrated in 2D and 3D graphs. Also, the analytical solution obtained was in agreement with the numerical one obtained by the commercial software NX Nastran. Furthermore, the analytical solutions were applied straightforwardly to explore the stability and design optimization of the tooth-blade for the new frame-type saw machine under an eccentric load. The result can also be promisingly used to study problems of thin-walled beams with laterally fixed ends subjected to other types of loads. [ABSTRACT FROM AUTHOR]

This paper considers the load–deflection behavior of a pyramid-like, shallow lattice structure. It consists of four beams that join at a central apex and when subject to a lateral load, it exhibits a propensity to snap-through: a classical buckling phenomenon. Whether this structural inversion occurs, and the routes by which it happens, depends sensitively on geometry. Given the often sudden nature of the instability, the behavior is also examined within a dynamics context. The outcome of numerical simulations are favorably compared with experimental data extracted from the testing of three-dimensional (3D)-printed specimens. The key contributions of this paper are that despite the continuous nature of the physical system, its behavior (transient and equilibria) can be adequately described using a discrete model, and the paper also illustrates the utility of 3D-printing in an accessible research context. [ABSTRACT FROM AUTHOR]

Composite cellular beams are an advantageous solution that can be used to reduce floor height by solving service ducts problems. In the previous literature, there is little information on numerical modeling that considers sensitivity analysis in composite cellular beams, varying the constitutive models of steel and concrete materials. The concrete, when submitted by external loading, undergoes volume variations caused by inelastic deformations. The parameter that measures dilatancy is known as the dilation angle. This work aims to analyze the sensitivity of the computed response of composite cellular beams to the constitutive models of steel and concrete materials, and the parameters that constitute concrete damage plasticity (CDP). Geometrical nonlinear analyses are performed based on tests, considering solid elements for the composite slab and shear connectors, and shell elements for the cellular beam. It was concluded that the flexural behavior was not sensitive to dilation angles, unlike structures in which the resistance is governed by shear forces. For a dilation angle equal to 4 0 ∘ , a better post-peak behavior was observed in the load-displacement relationship. It was found that by varying the viscosity parameter (or relaxation time), the load-displacement behavior relationship is not affected. [ABSTRACT FROM AUTHOR]

Local support settlement is a typical differential settlement which may take place under steel storage tanks and can adversely affect the stability performance of such thin-walled structures. Considering the practical applications of the thin-walled steel storage tanks in industry, proper treatment of this problem is essential to ensure the high structural performance of such members which albeit requires detailed investigations. On this basis, this study investigates the effects of the local support settlement on the buckling stability of two tanks without and with a top stiffening ring through the experimental and numerical approaches. The considered tanks are small-scale models with the height-to-radius and radius-to-thickness (slenderness) ratios of 1.0 and 834, respectively. Both experimental and numerical results show that the behavior of the tank under the local support settlement is nonlinear. Moreover, the effectiveness of the top stiffening ring in limiting the buckling deformation and improving the buckling performance of the tank is demonstrated in this study. [ABSTRACT FROM AUTHOR]

Instabilities in nanosized, externally pressurized spherical shells are important for their applications in nano and biotechnology. Mechanics at such length scale is described by nonlocal and Strain Gradient (SG) field theories. However, analysis of shell buckling is involved and becomes even more complicated in presence of nonlocal and SG interactions. This paper demonstrates that such analysis can be largely simplified by a shallow segment representation of the shell by assuming short wave lengths for the incipient buckling modes. The governing equations are derived and linearized equations are solved to obtain a closed form solution for the critical external pressure causing buckling for a pressurized nonlocal shell. Nonlocal interactions are shown to reduce, whereas the SG interaction increases the critical pressure. The relative reduction/increase becomes more prominent for higher modes of buckling and for increasingly thinner shell. A constricting relationship between the two set of wave numbers expressing the buckling modes is also shown to be modified by the nonlocal and SG scale parameters. Consequent wave numbers increase/decrease, accompanied by decreasing/increasing number of wavelengths, thereby further justifying the shallow segment representation employed herein. [ABSTRACT FROM AUTHOR]

In this research, a new analytical solution is used for finding the buckling loads of rectangular plates with vertically and rotationally restrained edges. The solution method in this study is based on the development of a static solution for a plate. The solution is obtained in series form, and the coefficients are solved to match the edge conditions. The solution fits all the combinations of possible boundary conditions, of the deflection, slope, shear force and bending moment along the edges of the plate. In the case of springs, the edge force and moment boundary conditions are modified to include these effects. Any number of edges, from one to four, with both types of stiffening springs can be solved. Using this new method, the exact buckling loads and modes are found. The results are verified with published data, and many new cases are presented for uni-axially and bi-axially loaded isotropic, orthotropic, and composite plates. [ABSTRACT FROM AUTHOR]

In this paper, the buckling characteristic of FGM plate considering the surface effect is studied based on general third-order plate theory and non-local theory. The surface effect of FGM plate is captured by the surface elasticity theory. The Kirchhoff hypothesis is released by employing parabolic variation of transverse shear strains. By using Navier solution technique, analytical solutions of buckling loads of FGM plate with surface effect are given, and detailed parametric studies are presented to show the relationship between surface effects and the plate thickness, power-law index, surface residual stress, surface moduli and non-local parameter. Furthermore, the surface effect on the buckling characteristic of FGM plate is also discussed. [ABSTRACT FROM AUTHOR]

Investigated herein is the buckling of Euler–Bernoulli nano-beams made of bi-directional functionally graded material with the method of initial values in the frame of gradient elasticity. Since the transport matrix cannot be calculated analytically, the problem was examined with the help of an approximate transport matrix (matricant). This method can be easily applied with buckling analysis of arbitrary two-directional functionally graded Euler–Bernoulli nano-beams based on gradient elasticity theory. Basic equations and boundary conditions are derived by using the principle of minimum potential energy. The diagrams and tables of the solutions for different end conditions and various values of the parameters are given and the results are discussed. [ABSTRACT FROM AUTHOR]

An accurate buckling response analysis for functionally graded graphene platelet (GPL) reinforced piezoelectric cylindrical nanoshells subject to thermo-electro-mechanical loadings is presented by a rigorous symplectic expansion approach. Three types of GPL reinforced patterns are considered, and the modified Halpin–Tsai model is employed to determine their effective material properties. By using Eringen's nonlocal stress theory and Reissner's shell theory, new governing equations are established in the Hamiltonian form. Exact solutions are expanded into symplectic series and three possible forms are derived. A comparison with the existing study is presented to validate the solution and very good agreement is observed. The effects of material and geometrical properties of GPLs, electric voltage and temperature rise on critical buckling stresses are investigated and discussed in detail. [ABSTRACT FROM AUTHOR]

This paper concentrates on the work by Petrus van Musschenbroek published in 1729, constituting apparently the first study in the literature on column buckling. To understand the significance of Musschenbroek's contribution, we provide the combined personal, historic and scientific contexts in which he carried out his studies; he was the first researcher to deal with the failure of compressed elements as a new phenomenon. Most unfortunately, his name is not currently known except for a small circle of historians of science, whereas engineering students at present are told that buckling should be associated with the name of Leonhard Euler. We fully share the idea of Benvenuto stating that "Musschenbroek's experimental law is of considerable historical interest." The contributions in his 1729 book are shown not only to include his experimental work but Musschenbroek also devised a design procedure for column buckling. [ABSTRACT FROM AUTHOR]

The present study focusses on buckling and post-buckling of graphene-reinforced laminated composite plates subjected to uniaxial and biaxial loadings. Poly-methyl-methacrylate (PMMA) is used for matrix. Depending on the type of graphene distribution in each layer, three patterns are considered for the plate cross-section. Graphene sheets are considered in both perfect and defective forms. Kinematics of the plate is modeled using the first shear deformation theory and for large deformation, von Karman nonlinearity is considered. Mechanical properties of each layer are evaluated using the molecular dynamics simulation. Besides, Halpin–Tsai and rule of mixtures are calibrated for graphene PMMA composite. Stability equations are solved based on the incremental-iterative type of Ritz method. In order to validate the solution procedure, comparison studies are conducted on isotropic plates. Numerical results are presented for four different types of boundary conditions. It is shown that, for all types of boundary condition, X-pattern provides higher buckling load. Furthermore, it is found that plates reinforced by defective graphene sheets with 5% vacancy provide lower buckling and post-buckling resistance with respect to those reinforced by pristine graphene. [ABSTRACT FROM AUTHOR]

In this paper, first a complete buckling experiment of the sandwich beams with the foam core is carried out, which includes the manufacturing of specimens and their experimental verification. Second, a refined sinusoidal zig-zag theory (RSZT) is established, which can describe the zig-zag effect during the in-plane compression of sandwich beam and accommodate the transverse shear free surface boundary conditions. Based on the established model combined with Hu–Washizu variational principle, a two-node beam element has been developed to address the buckling problem of the sandwich beams. Thus, the established beam element is able to accommodate interlaminar continuous conditions of transverse shear stress. Several examples have been investigated to validate the accuracy of the established method. The comparative analysis of the results including experimental data, the results acquired from three-dimensional finite element (3D-FEM) and diverse models has been made. Comparative analysis shows that the accurate buckling loads can be acquired from the established model. Nevertheless, other models discarding the continuous conditions of transverse stresses among the adjacent layers largely overestimate the critical loads. [ABSTRACT FROM AUTHOR]

The buckling mode is important to determine the critical load of specially orthotropic rectangular plates under axial compression with simply supported boundary. However, in classical laminated plate theory (CLPT), the critical buckling mode can only be obtained by iterative or numerical methods. This paper derives the critical buckling mode mathematically and presents the critical buckling load in closed form. By taking advantage of the derived closed-form solution, it is convenient to investigate the effects of aspect ratio, load ratio, and fiber orientation on the buckling load, and the parameters affecting the buckling mode can be easily obtained. The first-order shear deformation theory (FSDT)-based finite element method is developed to verify the closed-form solution. The bending-torsional coupling effects are analyzed and discussed to assess the approximation of the buckling behavior of specially orthotropic plates to general laminates. The obtained finite element solutions of general laminates are compared with the closed-form solutions of specially orthotropic plates. The accuracy of approximation of the buckling behavior of specially orthotropic plates to the general laminates increases as the bending-torsional coupling coefficients decrease. The closed-form solution can be applied to laminates with small bending-torsional coupling coefficients. [ABSTRACT FROM AUTHOR]

A new bistable shell with two symmetric configurations is proposed by using the nanotechnology, surface mechanical attrition treatment (SMAT), to locally treat a rectangular region. The impacts from randomly fast moving balls during the process induce nanotwins and mesh material grains into nanoscale on originally flat plates, which largely increase the material's yield strength and elastic deformation capacity. Also, the plastic deformations accumulated from thousands of impacts may stretch the plate under the constraint from the untreated region, while inducing internal compressive forces in the processed region. The experiments show that, when the accumulated plastic deformations are large enough, the locally nanostructured plate may buckle transversely by the internal forces to hold two different stable configurations, resulting in the bistable feature. An analytical model is developed to predict the stable configurations, which is numerically verified and experimentally validated. The parameters, including the SMAT region, plate dimensions, and SMAT process, to design the stable configurations of the bistable shells are systematically studied experimentally, analytically, and numerically. [ABSTRACT FROM AUTHOR]

Presented herein is a matrix method for buckling analysis of general frames based on the Hencky bar-chain model comprising of rigid segments connected by hinges with elastic rotational springs. Unlike the conventional matrix method of structural analysis based on the Euler–Bernoulli beam theory, the Hencky bar-chain model (HBM) matrix method allows one to readily handle the localized changes in end restraint conditions or localized structural changes (such as local damage or local stiffening) by simply tweaking the spring stiffnesses. The developed HBM matrix method was applied to solve some illustrative example problems to demonstrate its versatility in solving the buckling problem of beams and frames with various boundary conditions and local changes. It is hoped that this easy-to-code HBM matrix method will be useful to engineers in solving frame buckling problems. [ABSTRACT FROM AUTHOR]

The present study aims to analyze the buckling and post-buckling behavior of the geometrically imperfect functionally graded pin-ended tube. Imperfect FGM tube is surrounded by nonlinear elastic medium and is subjected to the axial compression or various thermal loads. Pinned-pinned boundary conditions are movable or immovable for the FGM tube under axial compression or thermal loads, respectively. In thermal analysis, different types of thermal loads such as uniform temperature rise, linear temperature distribution, and heat conduction are analyzed and contrasted. Displacement field of the FGM tube satisfies the tangential traction-free boundary conditions on the inner and outer surfaces. Properties of the FGM tube are assumed to be temperature-dependent and are distributed through the radial direction of tube using a power law function. The governing equilibrium equations of the FGM tube are obtained by means of the virtual displacement principle. These are nonlinear coupled differential equations based on a higher order shear deformation tube theory and the von Kármán nonlinear assumption. The coupled nonlinear dimensionless differential equations are solved using the two-step perturbation method. These asymptotic solutions are as explicit functions of the axial compression or different types of thermal load. Numerical results are provided to explore the effects of the linear and nonlinear spring stiffness of elastic medium and imperfection parameter of the tube. The effects of the volume fraction index and two geometrical parameters of the FGM tube are also included. [ABSTRACT FROM AUTHOR]

This paper investigates the nonlinear instability of eccentrically stiffened functionally graded (ES-FG) sandwich truncated conical shells subjected to the axial compressive load. The core of the FG sandwich truncated conical shells, assumed to be thin, is made of pure metal or ceramic materials and the two skin layers are made of a FG material. The shell reinforced by orthogonal stiffeners (stringers) is also made of FG materials. The change of spacing between the stringers in the meridional direction is considered. The governing equations are derived using the Donnell shell theory with von Karman geometrical nonlinearity along with the smeared technique for stiffeners. The resulting coupled set of three nonlinear partial differential equations with variable coefficients in terms of displacement components are solved by the Galerkin's method. The closed-form expressions for determining the critical buckling load and for analyzing the postbucking load–deflection curves are obtained. The accuracy of present formulation is verified by comparing the results obtained with available ones in the literature. The effects of various parameters such stiffeners, foundations, material properties, geometric dimensions on the stability of the shells are studied in detail. [ABSTRACT FROM AUTHOR]

This paper studies the structural stability of circular steel tubular stub columns at elevated temperatures under axial compression. Fifty-one specimens are subjected to high-temperature treatment and axial compression. The variables of the specimen are temperature, wall thickness of steel tube and duration of high temperature. The displacement–load curve, strain–load curve, ultimate load, axial compressive stiffness and failure characteristics of the specimens were analyzed. Test results show that after exposure to high temperatures, the specimens' failure phenomenon in the axial compression loading test is consistent with that at room temperature, the bearing capacity decreases considerably, the ductility decreases slightly and the axial compressive stiffness changes irregularly. Temperature is the determining factor of the ultimate load of the specimen, and the reducing extent of ultimate load increases with the temperature. When the temperature reaches 1000∘C, its maximum reducing extent exceeds 50%. Among the three parameters considered in this study, the duration of high temperature has the least influence on the specimen. [ABSTRACT FROM AUTHOR]

In this paper, a novel optimization-based method is proposed to analyze steel space truss structures undergoing large deformations. The geometric nonlinearity is considered using the total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to the displacement-type constraints. The proposed approach can fully follow the equilibrium path of the geometrically nonlinear space truss structures not only before the limit point, but also after it, namely, including both the pre- and post-buckling paths. Moreover, a direct estimation of the buckling loads and their corresponding displacements is possible by using the method. Particularly, it has been shown that the equilibrium path of a structure with highly nonlinear behavior, multiple limit points, snap-through, and snap-back phenomena can be traced via the proposed algorithm. To demonstrate the accuracy, validity, and robustness of the proposed procedure, four benchmark truss examples are analyzed and the results compared with those by the modified arc-length method and those reported in the literature. [ABSTRACT FROM AUTHOR]

The dynamics of a thin rod under the action of compressive force is considered. The compressive force increases abruptly and then remains constant. The compression of the rod is assumed to take place instantly throughout its length. The motion of the rod is studied, depending on the magnitude and time of action of the compressive force defined by the phase of the initial free oscillation of the rod. Only the initial stage of the process is investigated, for which the linear bending theory is valid. The friction forces are not taken into account. An essential relationship is shown to exist between the dynamics of the rod and the initial conditions determined by the phase of the bending oscillations at the instant of impact. Relatively weak impact leads to excitation of the bending oscillations. Rearrangement of harmonics develops with time under specified initial maximum deflection from a straight line and zero velocity. The fastest buckling takes place at some initial deflection with the velocity directed toward the increasing bend. [ABSTRACT FROM AUTHOR]

In the present study, free vibration and buckling characteristics of a sandwich functionally graded material (FGM) plate resting on the Pasternak elastic foundation have been investigated. The formulation is based on non-polynomial higher-order shear deformation theory with inverse hyperbolic shape function. A new modified sigmoid law is presented to compute the effective material properties of sandwich FGM plate. The governing equilibrium equations have been derived using Hamilton's principle. Non-dimensional frequencies and critical buckling loads are evaluated by considering different boundary conditions based on admissible functions satisfying the desired primary and secondary variables. Comprehensive parametric studies have been performed to analyze the influence of geometric configuration, volume fraction exponent, elastic medium parameter, and non-dimensional load parameter on the non-dimensional frequency and critical buckling load. These parametric studies have been done for various boundary conditions and different configurations of the sandwich plate. The computed results can be used as a benchmark for future comparison of sandwich S-FGM plates. [ABSTRACT FROM AUTHOR]

This paper focuses on development of a new mathematical model and its analytical solution for buckling analysis of elastic columns weakened simultaneously with transverse open cracks and partial longitudinal delamination. Consequently, the analytical solution for buckling loads is derived for the first time. The critical buckling loads are calculated using the proposed analytical model. A parametric study is performed to investigate the effects of transverse crack location and magnitude, length and degree of partial longitudinal delamination, and different boundary conditions on critical buckling loads of weakened columns. It is shown that the critical buckling loads of weakened columns can be greatly affected by all the analyzed parameters. Finally, the presented results can be used as a benchmark solution. [ABSTRACT FROM AUTHOR]

In this paper, the Ritz-based solutions are developed for the bending, buckling and vibration behaviors of laminated composite beams with arbitrary lay-ups. A quasi-3D theory, which accounts for a higher-order variation of both the axial and transverse displacements, is used to capture the effects of both shear and normal deformations on the behaviors of composite beams. Numerical results for various boundary conditions are presented and compared with existing ones available in the literature. Besides, the effects of fiber angle, span-to-height ratio, material anisotropy and Poisson's ratio on the displacements, stresses, natural frequencies and buckling loads of the composite beams are investigated. [ABSTRACT FROM AUTHOR]

This paper is concerned with the buckling and post-buckling behaviors of a simply supported symmetric functionally graded (FG) microplate lying on a nonlinear elastic foundation. The modified couple stress theory is used to capture the size effects of the FG microplate, and the Mindlin plate theory with von Karman’s geometric nonlinearity taken into account is adopted to describe its deflection behavior. Based on these assumptions and the principle of minimum potential energy, the equilibrium equations of the FG microplate and associated boundary conditions are derived. By applying the Galerkin method to the equilibrium equations, closed-form solutions for the critical buckling load and the load–displacement relation in the post-buckling stage are obtained. Furthermore, the effects of the power law index, the material length scale parameter to thickness ratio, the stiffness of the elastic foundation, and in-plane boundary conditions on the buckling and post-buckling behaviors of the FG microplate are discussed in detail. [ABSTRACT FROM AUTHOR]

Cyclic bending of tubes leads to progressive ovalization of the tube cross-section, and persistent cycling causes catastrophic buckling of the tube. This paper presents the response and stability of SUS304 stainless steel tubes with local sharp-notched depths of 0.2, 0.4, 0.6, 0.8, and 1.0mm and notch directions of 0∘, 30∘, 60∘, and 90∘ under cyclic bending. The experimental results reveal that the moment–curvature relationship first exhibits cyclic hardening and then a steady loop after a few cycles. Because the notches are small and localized, notch depth and direction show minimal influence on the moment–curvature relationship. In contrast, the ovalization–curvature relationship demonstrates an increasing and ratcheting pattern along with the bending cycle, whereas notch depth and direction show a strong influence on this relationship. Finite-element analysis via ANSYS is used to simulate the moment–curvature and ovalization–curvature relationships, and an empirical model is proposed to simulate the relationship between the controlled curvature and number of cycles required to ignite buckling. The experimental and analytical data agree well with each other. [ABSTRACT FROM AUTHOR]

We present a computational study that develops isogeometric analysis based on higher-order smooth NURBS basis functions for the analysis of in-plane laminated composites. Focusing on the stress, vibration and stability analysis of angle-ply and cross-ply 2D structures, we compare the convergence of the strain energy error and selected stress components, eigen-frequencies and buckling loads according to overkill solutions. Our results clearly demonstrate that for in-plane laminated composite structures, isogeometric analysis is able to provide the same accuracy at a significantly reduced number of degrees of freedom with respect to standard finite elements. In particular, we observe that the smoothness of spline basis functions enables high-quality stress solutions, which are superior to the ones obtained with conventional finite elements. [ABSTRACT FROM AUTHOR]

Tensegrity structures are classified as kinematically determinate ones with two subcases and kinematically indeterminate ones with three subcases in view of their respective stability properties. How the stiffness of a tensegrity structure changes as the level of prestress changes is explored for different scenarios using six carefully chosen samples. For a tensegrity structure merely satisfying the prestress-stability condition, a new optimization model is presented to determine its critical buckling state corresponding to zero stiffness. A real-coded genetic algorithm (RCGA) is then developed to solve this problem, featured by the fact that a special sign-control technique is embedded in the fundamental genetic operations, making the individuals generated in each step fall into the admissible region automatically. The stability of the neutral equilibrium state for tensegrity structures violating the prestress-stability condition is also discussed. Several numerical examples are tested to validate the efficiency of the present approach. [ABSTRACT FROM AUTHOR]

Buckling loads of laminated panels calculated by analytical approaches are usually based on the assumptions that the panels are subjected to uniform in-plane edge loads without cutouts, despite of the fact that real structural components are subjected to various kinds of non-uniform in-plane edge loads along with different sized cutouts. The main objective of this paper is to study the effects of reinforced/unreinforced circular cutouts and non-uniform in-plane edge loads on the buckling behavior of composite panels with different ply-orientations by the finite element technique. Furthermore, it addresses the effects of different boundary conditions and thickness of panels. To carry out the analyses, a nine-noded heterosis plate element and a compatible three-noded beam element are developed, including the effect of shear deformation and rotary inertia for both the plate and the stiffeners. In structural modeling, the plate and the stiffener elements are treated separately, with their displacement compatibility maintained using transformation matrices. It has been illustrated in this study that presence of larger-sized reinforced cutouts predominantly increases the buckling strength of the panel as compared to those with smaller sized cutouts. [ABSTRACT FROM AUTHOR]

The buckling response and free vibration characteristics of a single pile in the elastic foundation are investigated. Considering the effect of soil-structure interaction and geometric nonlinearity, the nonlinear equation of motion for a single pile is derived by Hamilton's principle. Then, closed-form solutions of the critical load and buckled configuration of the pile are obtained analytically, and the natural frequencies of the pre- and post-buckling pile are examined. Finally, the effect of elastic foundation parameter on the critical load of the pile is discussed, and the effect of axial load on the natural frequencies of the pile is also explored. Numerical results show that the effect of elastic foundation parameter plays a dominant role on the critical load and buckled configuration of the pile, and the shear parameter affects the critical load directly. The axial load effect on the dynamic characteristics of the pre-buckling pile is significant, meanwhile, it may contribute very small to the post-buckling pile when the axial load exceeds some specific values. [ABSTRACT FROM AUTHOR]

This paper investigates the buckling behavior of graphene platelets (GPL) reinforced composite cylindrical shells with cutouts via finite element method (FEM) simulation. Young's modulus of the composites is determined by the modified Halpin-Tsai micromechanics model while the mass density and Poisson's ratio of the composites are approximated by the rule of mixture. Comprehensive parametric study is conducted to investigate the effects of the weight fraction and the shape of GPL fillers, the geometry of the shell and the position and orientation of the cutout on the buckling behaviors of the cylindrical structures. The results demonstrate that the addition of GPLs can significantly increase the load bearing capacity of the cylindrical shells. Larger sized GPLs with fewer single graphene layers are favorable reinforcing fillers in enhancing the buckling performances of the structures. The buckling load is sensitive to the location of the cutout with larger aspect ratio. Moreover, the orientation of the cutout is found to have significant effects on the buckling load when the orientation angle is falling within the ranges - /2 - /4 and /4 /2. [ABSTRACT FROM AUTHOR]

A semi-analytical procedure is presented to solve the elastoplastic buckling problem of cylindrical shells made of functionally groded materials (FGMs) under combined axial and torsional loads. The elastoplastic properties are assumed to vary smoothly according to the power law distribution rule, introduced in the J2 deformation theory for formulation of the constitutive relation of FGMs in the framework of the Tamura-Tomota-Ozawa (TTO) model, which is a volume fraction-based material model. The critical condition is deduced by the Ritz method. Assuming the uniform prebuckling strain, a biaxial stress state analysis is conducted to determine the analytical position of the elastoplastic interface, which is used in the integration of the elastoplastic internal force and all the material-related structural parameters. Finally, an iterative procedure is adopted to find the exact elastoplastic critical load. Numerical results indicate the effects of the inhomogeneous parameter and the elastoplastic material properties of their constituents on the stability region and plastic flow region of the materials. [ABSTRACT FROM AUTHOR]