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Highlights • A coupled mechanochemical model is proposed for buckling simulation. • The buckling behavior is strongly dependent on SOC & electrochemical process. • Lithiation-soften of active material remarkably reduces the buckling stability of cell system. • Design insights into enhancing the buckling resistance of electrode are provided. Abstract This work has proposed a coupled mechanochemical model to investigate the buckling performance of electrode and thereby enhance the mechanical integrity of lithium-ion batteries. This method based upon finite deformation theory is capable to simulate the state of charge (SOC) and path dependent buckling phenomenon of the layered structure. It is revealed that the buckling behavior of an electrochemical loaded electrode depends not only on the material properties and the electrode geometry but also on the charging/discharging process, SOC as well as the operation current rate. Moreover, with regarding to the lithiation stiffening active material, the results show that increasing the current density in lithiation while decreasing it upon delithiation can increase the relatively critical buckling load, and contribute the electrode to withstand buckling failure. As for the lithiation softening one, it is disclosed that the bucking resistance would be impaired in lithiation and recovered upon full delithiation. In addition, to eliminate the adverse effect of lithiation soften on the electrode buckling resistance, design insights into the current collector have been provided. [ABSTRACT FROM AUTHOR]

An extended Ritz formulation for the analysis of buckling and post-buckling behaviour of cracked composite multilayered plates is presented. The formulation is based on: (i) the First-order Shear Deformation Theory to model the mechanics of the multilayered plate; (ii) the von Kármán’s theory to account for geometric non-linearities; (iii) the use of an extended set of approximating functions able to model the presence of an embedded or edge crack and to capture the crack opening fields as well as the global behaviour within a single cracked domain. The numerical results of the buckling analyses and the equilibrium paths in the post-buckling regime are compared with the results from finite elements simulations, confirming the accuracy and potential of the formulation. [ABSTRACT FROM AUTHOR]

A general analytical model is developed to evaluate buckling behavior of a bilayer beam-column with a through-the-width asymmetric delamination under simply supported boundary conditions. Both transverse shear deformation and local deformation at delamination tip are taken into account in the model by considering two sublayers in both delaminated and intact regions as two individual shear deformable ones. Interface continuity conditions, which account for effect of interface normal and shear stresses, are also introduced in the intact regions. Furthermore, the present model is capable of dealing with the case of delamination located arbitrary through thickness and along length of beam-columns. In comparisons with the results of classical Euler-Bernoulli beam model, Timoshenko beam model (rigid joint model) and finite element analysis, better agreements are achieved for the present flexible joint model, which captures local deformation at delamination tip due to consideration of interface normal and shear stress components. Parametric studies are conducted to evaluate influences of sublayer thickness ratio, delamination length, delamination location, specimen length, and material parameters on the critical buckling strain with emphasis on transverse shear deformation and local deformation at delamination tip. The developed model can be used with confidence in buckling analysis of layered structures with an arbitrary delamination through the length and thickness. [ABSTRACT FROM AUTHOR]

This paper discusses the buckling and post-buckling of thick composite plates having large initial geometrical imperfections. Within the theory of large transformations, the proposed formulation uses generalised forces and deformations derived from the energy conjugacy of the second Piola-Kirchhoff stress and Green-Lagrange strain. In addition, it provides partial differential equations of equilibrium that are easy to solve using common techniques such as the Galerkin-Ritz method. Unlike existing contributions, which are (i) limited to imperfections that are proportional to current deformations, (ii) address small to moderate initial imperfections only, and/or (iii) require advanced and time consuming numerical methods, the present approach is based on analytical solution and takes into account large initial imperfections. Despite the complexity of the energy balance formulation, the resulting governing equations are simple and applicable to design practical composite structures. The proposed model was compared to numerical results obtained using the finite element method. Overall, good agreements have been obtained when the assumptions fall within the range of validity of the commercial software used for simulation. [ABSTRACT FROM AUTHOR]

The Koiter–Newton method has been proved to be a computationally efficient method for buckling and post-buckling analysis of structures, using a novel reduced-order modeling strategy. In this paper, the existing method is extended for laminated composite plates with delamination. We develop a 4-node quadrilateral element S4DE as a geometric linear element in the co-rotational formulation of the Koiter–Newton method. The assumed layerwise displacement model of the developed element is enriched with Heaviside unit step functions to model delamination. The displacement fields of each layer are described using the superposition of first-order shear deformation and layerwise functions. The zig–zag theory is applied to enhance the numerical accuracy and computational efficiency of the developed element. The construction of the reduced order model requires derivatives of the strain energy with respect to the degrees of freedom up to the fourth order, which is two orders more than traditionally needed for a Newton based nonlinear finite element technique. The geometrical nonlinearities are taken into account using derivatives of the local co-rotational frame with respect to global degrees of freedom. Various laminated plates with different thicknesses, delamination lengths and stacking sequences are considered to validate the good performance of the present method in terms of numerical reliability, accuracy and computational effort. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the thermal and mechanical buckling analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) plates by using isogeometric analysis (IGA) based on modified couple stress theory (MCST). A refined hyperbolic shear deformation theory is used for buckling analysis, which satisfies free transverse shear stress conditions on the top and bottom surfaces of plate without a need for shear correction factor. The material properties of carbon nanotube reinforced composite plates are assumed to be temperature-dependent. For numerical analysis the IGA method using B-Spline or Non-Uniform Rational B-Spline (NURBS) functions is employed. The obtained results are compared with those available in the literature. Also, the influence of different parameters on mechanical and thermal buckling analysis is investigated. These parameters include material length scale parameter, boundary conditions, aspect and length-to-thickness ratios of plate, different types of FG-CNTRC distribution, volume fraction of CNTs and temperature dependency. [ABSTRACT FROM AUTHOR]

Abstract In this study, bending, free vibration, and buckling response of functionally graded porous micro-plates are investigated using the classical and first-order shear deformation plate theories. The Navier solution technique is utilized to obtain analytical solutions to simply supported rectangular plates. A power-law distribution is used to model the variation of two material constituents through the plate thickness. Three different porosity distributions are considered and assumed to take forms of cosine functions. The microstructure-dependent size effects are captured using the modified couple stress theory. Numerical results of bending, free vibration, and buckling are presented to determined the effects of constituent material variation, microstructure-dependent size effects, and porosity distributions on the mechanical response of functionally graded porous micro-plates. [ABSTRACT FROM AUTHOR]

This work presents an analytical investigation for analyzing the mechanical buckling of truncated conical shells made of functionally graded materials, subjected to axial compressive load and external uniform pressure. Shells are reinforced by closely spaced stringers and rings. The change of spacing between stringers in the meridional direction also is taken into account. Using the adjacent equilibrium criterion, the first order shear deformation theory (FSDT) and Lekhnitskii smeared stiffener technique, the linearization stability equations have been established. The resulting equations which they are the system of five variable coefficient partial differential equations in terms of displacement components are investigated by Galerkin method. The closed-form expression for determining the critical buckling load is obtained. The effects of material properties, dimensional parameters, stiffeners and semi-vertex angle on buckling behaviors of shell are considered. Shown that for thick conical shells, the use of FSDT for determining their critical buckling load is necessary and more suitable. [ABSTRACT FROM AUTHOR]

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

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

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

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

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

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

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

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

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

Present research deals with the postbuckling problem of carbon nanotube reinforced composite plates subjected to uniform temperature rise loading. Distribution of carbon nanotubes as reinforcements may be uniform or functionally graded. To account for the large deformations of the plate, von-Kármán type of geometrical nonlinearity is included into the formulation. The virtual displacements principle associated with the conventional Ritz formulation whose shape functions are selected as the Chebyshev polynomials is used to obtain the matrix representation of the nonlinear equilibrium equations. The solution method is general and may be used for arbitrary combination of boundary conditions. The postbuckling equilibrium path which is governed by a nonlinear eigenvalue problem is traced using a displacement control strategy. Results of this study are compared with the available data in the open literature for the cases of isotropic homogeneous plates and cross-ply laminated plates. Afterwards numerical results are given for FG-CNTRC plates. It is shown that, FG-X pattern results in higher buckling temperature and also decreases the postbuckling deflection of the plate. Furthermore, this type of composites are eager to exhibit the secondary instability which is designated with a snap-through phenomenon in the post-buckling equilibrium path. [ABSTRACT FROM AUTHOR]

This article presents a method to study the buckling of freely-supported functionally graded (FG) truncated and complete conical shells under external pressures in the framework of the shear deformation theory (SDT). The basic relations, modified Donnell type stability and compatibility equations have been obtained on the basis of SDT. The material properties of truncated conical shells are functionally graded in the thickness direction according to a volume fraction power law distribution. To solve this problem is used an unknown parameter λ in the approximation functions. One of innovations is to achieve closed-form solutions for critical lateral and hydrostatic pressures of freely-supported FG truncated and complete conical shells in the framework of the SDT. The parameter λ which is included in the obtained expressions is get from the minimum conditions of critical external pressures. Finally, influences of shear stresses, volume fraction index and shell characteristics on the critical lateral and hydrostatic pressures are investigated. [ABSTRACT FROM AUTHOR]

Abstract One of the main methods for improving the strength of the notched laminates, which are commonly used in the engineering structures, is to employ a stringer in a proper configuration. To optimize the design of these perforated laminates under compression loading, accurate characterization of the effects of various parameters on the instability behavior plays a significant role. For this purpose, after a review on the main previous researches, a semi-energy finite strip method (SE-FSM) is developed in the framework of nonlinear deformation to analyze the buckling behavior of stiffened/unstiffened laminated composites having a circular notch. The developed SE-FSM is based on the semi-analytical solution of von Karman's equations via Airy stress function and has the advantage of great versatility like the finite element method (FEM) and good economy like the Rayleigh-Ritz method. To verify the developed method and to examine the influence of various parameters (the thickness of specimen, the diameter of the hole and the thickness of stiffener) on the buckling behavior, a detailed experimental parametric study is performed and the extracted results are compared with those of the developed SE-FSM, the full-energy FSM and FEM. High accuracy and fast convergence of the developed method show its computational efficiency for prediction of stability behavior of composite laminates. [ABSTRACT FROM AUTHOR]

Based on the Reddy’s high-order shear deformation theory, buckling behaviors of the FGM cylindrical shells subjected to an axial compression in thermal environment are investigated analytically. Considering the temperature-dependent FGMs properties, the constituent distribution across the shell thickness is assumed to follow the volume fraction rule of mixture. Through the variational principle, basic equations are derived for shear deformable FGM cylindrical shell with the initial geometric imperfection. Method of separation of variables and Galerkin’s solving process are employed in dealing with the stability governing equations of perfect and imperfect shells, respectively. By changing the boundary conditions, material types, composition distributions, thermal load and temperature fields, the effect of the transverse shear deformation is evaluated by comparing with the results of the classical Donnell’s theory. Meanwhile, imperfection sensitivity for buckling of the shear deformable FGM cylindrical shell is discussed in detail. [ABSTRACT FROM AUTHOR]

In the present work, a semi-analytic solution is presented to analyze buckling behaviors of elastoplastic functionally graded circular cylindrical shells under torsional loads. The material properties vary smoothly through the shell thickness according to the power law distribution and a multi-linear hardening elastoplasticity of materials is included in the analysis. The Ritz energy method and both the flow and deformation constitutive theories help to develop the buckling government equation and the buckling critical condition. An iterative algorithm is resorted to derive the critical load and the buckling mode parameters. Numerical results reveal various effects of the constituent distribution of FGMs, dimensional parameters, and elastoplastic material properties. Meanwhile, the influences of material flow effect on buckling of elastoplastic FGM cylindrical shells are discussed. [ABSTRACT FROM AUTHOR]

The present study is an attempt to develop a finite element formulation for handling buckling and post buckling analysis of laminated composite plates subjected to mechanical and hygrothermal loads using the Inverse Hyperbolic Shear Deformation Theory. This theory satisfies zero transverse shear stresses conditions at the top and bottom surfaces of the plate and provides a non-linear transverse shear stress distribution. Geometric nonlinearity has been included in the von Karman sense. Mathematical formulation and programming in MATLAB environment have been done. Numerical results are presented. By this investigation, the validation of recently developed IHSDT has been proved for buckling and post buckling analysis in hygrothermal environment. [ABSTRACT FROM AUTHOR]

Abstract: The present paper deals with the onset of local buckling of compressively loaded thin-walled beams made of orthotropically laminated composite materials using discrete plate analysis. The analysis model focusses on the buckling of webs and flanges of composite beams with arbitrary cross-sections under uniform longitudinal compressive load. In order to account for transverse shear deformations as they are typical for moderately thick to thick laminated composite materials made of e.g. carbon fibre reinforced plastics, the present analysis is based on first-order shear deformation theory, thus employing the classical Reissner–Mindlin plate theory for the analysis of laminated composite structures. The idealisation consists of modelling the webs as being simply supported at all four edges, while at the longitudinal unloaded edges an elastic clamping is assumed which is represented by a clamping stiffness that takes material, geometry and layups of the adjacent flanges of the beams into account. Accordingly, the flanges are treated as plates with three simply supported edges and one free edge, wherein the unloaded simply supported edge is elastically clamped in order to represent the rotational support by the adjacent web. The analysis of the web and flange buckling loads is performed using the Rayleigh–Ritz-method employing specifically chosen shape functions for the out-of-plane displacements and the rotations of the cross-sections. The accuracy of the employed approaches is established by comparison with accompanying finite element simulations of actual thin-walled composite beams. It is revealed that the presented methodology is highly efficient in terms of computational effort and yet performs with satisfying accuracy which makes it very attractive for actual practical applications whenever the local stability behaviour of composite beams is to be considered. [Copyright &y& Elsevier]

Abstract: A single-walled carbon nanotube (SWCNT) is treated as a tubular Bernoulli–Euler beam and the higher-order deformation gradients are involved to establish a higher-order multiscale beam model. The higher-order Cauchy–Born rule is used to calculate the deformation of bond vectors in the representative cell and the strain energy density is equivalent to the energy per unit surface area, calculated from the Brenner potential. On the basis of the classical Bernoulli–Euler beam theory, the second-order deformation gradients with respect to the axial direction are also considered. The total strain energy is expressed as an integral equation, in which all parameters are obtained by calculating the constitutive response around the circumference. The physical meaning of these parameters is discussed in detail. The global buckling of SWCNTs is studied, and the critical buckling force is obtained as the analytical formula for different boundary conditions. The critical buckling force is plotted against the tube chirality, tube radius and tube length, and it is discovered that the contribution of the higher-order terms rapidly becomes large when the tube radius or length is small enough. [Copyright &y& Elsevier]

Abstract: The first order shear deformation theory (FSDT) is used to present the buckling and initial post-buckling characteristics of symmetrically cross-ply laminated plates. In the buckling phase the Von-Karman’s equilibrium equation is solved exactly for the FSDT to obtain out-of-plane mode shapes and critical loads. The current post-buckling study is effectively a single-mode analysis, which is attempted by utilizing the so-called semi-energy method. The Von-Karman’s compatibility equation is solved exactly in the post-buckling phase with the assumption that the deflected form immediately after buckling is the same as that obtained for buckling. The Principle of Minimum Potential Energy is invoked to solve for the unknown coefficients in the assumed out-of-plane deflections and rotation functions. [Copyright &y& Elsevier]

Abstract: The manufacture of advanced composite panels with variable fibre angles can lead to laminates with a flat profile on one side and a smooth, curved profile on the other. When modelling these laminates in two-dimensional form the flat plate assumptions may no longer accurately capture the structural behaviour. In this paper the buckling behaviour of laminates with one-dimensional fibre variations and symmetric stacking sequences is investigated. The assumptions of modelling the three-dimensional profile as a flat plate or a cylindrical panel are assessed, taking into account the effects of transverse shear deformation. The governing differential equations are solved in the strong form using the Differential Quadrature method and validated by 2D finite element models. The validity of the two modelling approaches is assessed by comparing the solutions to a 3D finite element model capturing the actual shape of the laminate. It is suggested that the buckling event of these variable angle tow, variable thickness laminates is characterised more accurately by “shell-like” than by “plate-like” behaviour. The idea of investigating the effects of two-dimensional fibre orientations with their associated doubly curved topologies is proposed. [Copyright &y& Elsevier]

Functionally graded materials have become more popular in recent decades due to its ability of efficient utilization of the constituents materials. The structural functionally graded plate (FGP) has variation of the properties in the thickness direction according to power law or exponential law. A recently developed non-polynomial shear deformation theory named as inverse trigonometric shear deformation theory (ITSDT) has proved its accuracy and efficiency in modeling and analyses of laminated composite and sandwich structures. However, its efficiency for the FGP has not examined so far in the literature. In the present study, an attempt is made to extend ITSDT for the static and buckling analysis of FGP. An analytical solution for all edges simply supported FGP is proposed in this work. The bending analysis includes calculation of in-plane and transverse displacements, along with the calculation of in-plane and transverse normal and shear stresses. The buckling analysis includes calculation of critical buckling load for various conditions. Also, the effect of power index, aspect ratio, span to thickness ratio, uniaxial and biaxial loading are studied. From the results, it is observed that the theory accurately predicts the static and buckling responses of FGP. [ABSTRACT FROM AUTHOR]

A linear buckling analysis is presented for nanocomposite conical shells reinforced with single walled carbon nanotubes (SWCNTs) subjected to lateral pressure. Material properties of functionally graded carbon nanotube reinforced composite (FG-CNTRC) conical shell are assumed to be graded across the thickness and are obtained based on the modified rule of mixture. Governing equilibrium equations of the shell are obtained based on the Donnell shell theory assumptions consistent with the first order shear deformation shell theory. General form of the equilibrium equations and the complete set of boundary conditions are obtained based on the concept of virtual displacement principle. Shell is assumed to be under lateral pressure. Prebuckling load of the shell is estimated based on the linear membrane analysis. Stability equations of the shell are extracted via the adjacent equilibrium criterion. Resulting stability equations are discreted by suitable trigonometric functions in circumferential direction and generalized differential quadrature method in axial direction. An eigenvalue problem is established to obtain the buckling pressure and circumferential buckling mode of the conical shell. It is shown that, CNTs volume fraction and CNTs distribution law are important factors on the buckling mode and buckling load of the FG-CNTRC conical shells. [ABSTRACT FROM AUTHOR]

Based on the first-order nonlinear von Karman theory, the post-buckling analysis of FG circular plates under asymmetric transverse and in-plane loadings are presented. The nonlinear governing equations are reformulated using a stress function and a boundary layer function, and solved by employing a multi-parameter perturbation technique and Fourier series method. The material properties are assumed to vary through the plate thickness according to a power-law distribution of the volume fractions of the constituents. The results are verified with the known results in the literature. The effects of loading, material properties, and boundary conditions on different response quantities are studied. It is observed that the buckling load in clamped FG plates under asymmetric in-plane loading is lower than that of the same plate under axisymmetric in-plane loading. It is concluded that under downward transverse loading, the snap buckling occurs in simply-supported FG plates with an initial considerable upward deflection caused by an in-plane load. In addition, the behavior of boundary layer in FG plates under in-plane loading is studied and compared with that in transverse loading. [ABSTRACT FROM AUTHOR]

Semi-analytical models for the linear buckling analysis of unstiffened laminated composite cylinders and cones with flexible boundary conditions are presented. The Classical Laminated Plate Theory and the First-order Shear Deformation Theory are used in conjunction with the Donnell’s non-linear equations to derive the buckling equations. Axial, torsion and pressure loads can be applied individually or combined in the proposed models. The stiffness matrices are integrated analytically and for the conical shells an approximation is proposed to overcome non-integrable expressions. Comparisons with the literature show that the classical base functions available for axial compression cannot capture the buckling modes for non-orthotropic laminates. For torsion loads these classical shape functions do not catch the buckling modes even when applying the assumption of pure orthotropy, and it is shown how the proposed models correlate well with experimental data from the literature and finite element results. The use of elastic constraints at the boundaries allows the simulation of different boundary conditions in a versatile way and it is shown how those constants can be adjusted in order to change from one type of boundary condition to another. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents the buckling analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates under various in-plane mechanical loads, using the element-free kp-Ritz method. The first-order shear deformation plate theory is applied and a set of mesh-free kernel particle functions are used to approximate two-dimensional displacement fields. Effective properties of materials of the plates reinforced by single-walled carbon nanotubes (SWCNTs) are estimated through a micromechanical model based on either the Eshelby–Mori–Tanaka approach or the extended rule of mixture. Comparison study and numerical simulations with various parameters are conducted to assess efficacy and accuracy of the present method for analysis of buckling of SWCNT-reinforced composite plates. Results demonstrate that the change of carbon nanotube volume fraction, plate width-to-thickness ratio, plate aspect ratio, loading condition and temperature have pronounced effects on buckling strength of CNTRC plates as well as the boundary condition. [Copyright &y& Elsevier]

Abstract: An exact finite strip for the buckling analysis of moderately thick symmetrically cross-ply laminated composite plates and plate structures is presented in this paper by using First-order Shear Deformation Theory (FSDT). Based on the concept that the so-called strip is effectively a plate, the critical buckling load and out-of-plane deflection mode shape are obtained by solving the Von-Karman’s equilibrium equation exactly. A transcendental stiffness matrix is obtained for an individual strip. The overall stiffness matrix for the whole section is obtained by assembling the individual stiffness matrices. Since the overall stiffness matrix is transcendental, it is not possible to identify a separate geometric stiffness matrix. In this paper a secure method i.e. bisection method is used to find the buckling load and the corresponding buckling mode of the plate structure. [Copyright &y& Elsevier]

Abstract: A semi-analytical approach is proposed to obtain the linear buckling response of conical composite shells under axial compression load. A first order shear deformation shell theory along with linear strain–displacement relations is assumed. Using the principle of minimum total potential energy, the governing equilibrium equations are found and Ritz method is applied to solve them. Parametric study is performed by finding the effect of cone angle and fiber orientation on the critical buckling load of the conical composite shells. [Copyright &y& Elsevier]

Abstract: This work presents the buckling analysis of laminated composite thin walled structures by the 1D finite element based unified higher-order models obtained within the framework of the Carrera Unified Formulation (CUF). In the present study, the refined beam theories are obtained on the basis of Taylor-type expansions. The finite element analysis has been chosen to easily handle arbitrary geometries as well as boundary conditions. Buckling behavior of laminated composite beam and flat panels are analyzed to illustrate the efficacy of the present formulation and various types of buckling modes are observed depending on the geometrical and material parameters. It is observed that the lower order models are unable to deal with torsion. [Copyright &y& Elsevier]

Abstract: A general analytical model based on shear-deformable beam theory has been developed to study the flexural–torsional coupled buckling of thin-walled composite beams with arbitrary lay-ups under axial load. This model accounts for all the structural coupling coming from the material anisotropy. The seven governing differential equations for coupled flexural–torsional–shearing buckling are derived. The resulting coupling is referred to as sixfold coupled buckling. Numerical results are obtained for thin-walled composite beams to investigate effects of shear deformation, fiber orientation and modulus ratio on the critical buckling loads and corresponding mode shapes. [Copyright &y& Elsevier]

Abstract: Dynamic buckling analysis of FGM plates has not been accomplished so far. In the present paper, vibration and dynamic buckling of FGM rectangular plates with surface-bonded or embedded piezoelectric sensors and actuators subjected to thermo-electro-mechanical loading conditions are investigated. A finite element formulation based on a higher-order shear deformation theory is developed. Both initial geometric imperfections of the plate and temperature-dependency of the material properties are taken into account. Dynamic buckling of plates already pre-stressed by other forms of loading conditions is assumed to occur under suddenly applied thermal or mechanical loads. A nine-node second order Lagrangian element, an efficient numerical algorithm for solving the resulted highly non-linear governing equations, and an instability criterion already proposed by the author are employed. A simple negative velocity feedback control is used to actively control the dynamic response of the plate. Results show that generally, initial geometric imperfections lead to an increased fundamental bending natural frequency and decreased buckling loads. Furthermore, buckling mitigation due to utilizing integrated piezoelectric sensors and actuators is mainly achieved in extremely high gain values. Therefore, the piezoelectricity effect on the buckling load is small in applicable voltages. It is also noticed that the temperature-dependency and initial geometric imperfections remarkably affect the buckling loads. [Copyright &y& Elsevier]

Abstract: In this paper, thermal buckling of a simply supported functionally graded skew plate is investigated using first-order shear deformation theory in conjunction with the finite element approach. The material properties are assumed to vary as a power form of the thickness coordinate. Linear and nonlinear temperature rise across the thickness are considered. The effects of aspect and thickness ratios, gradient index and skew angle on the critical buckling temperature difference are brought out. [Copyright &y& Elsevier]

Abstract: A series of finite element analyses on the delaminated composite cylindrical shells subject to combined axial compression and pressure are carried out varying the delamination thickness and length, material properties and stacking sequence. Based on the FE results, the characteristics of the buckling and postbuckling behaviour of delaminated composite cylindrical shells are investigated. The combined double-layer and single-layer of shell elements are employed which in comparison with the three-dimensional finite elements requires less computing time and space for the same level of accuracy. The effect of contact in the buckling mode has been considered, by employing contact elements between the delaminated layers. The interactive buckling curves and postbuckling response of delaminated cylindrical shells have been obtained. In the analysis of post-buckled delaminations, a study using the virtual crack closure technique has been performed to find the distribution of the local strain energy release rate along the delamination front. The results are compared with the previous results obtained by the author on the buckling and postbuckling of delaminated composite cylindrical shells under the axial compression and external pressure, applied individually. [Copyright &y& Elsevier]

Abstract: The elastic buckling of regular hexagonal honeycombs with non-uniform thickness cell edges under biaxial compression is numerically analyzed and presented here. A multi-cell honeycomb structure with appropriate periodic boundary conditions was proposed and employed to calculate the biaxial buckling strengths of regular hexagonal honeycombs with plateau borders using finite element analysis. The effects of solid distribution in cell edges on the biaxial buckling strengths of regular hexagonal honeycombs are evaluated and discussed. Numerical FEA results indicate that the biaxial elastic buckling strengths of regular hexagonal honeycombs depend on their relative density, the solid distribution in cell edges and biaxial stress state. Also, the failure surfaces caused by elastic buckling and plastic yielding for regular hexagonal honeycombs under biaxial compression are developed. [Copyright &y& Elsevier]

Abstract: Thin-walled members made of fiber-reinforced polymer (FRP) composites are increasingly being used for structural applications, due to the advantageous material properties such as low weight, high tensile strength and insensitivity to corrosion. When manufactured by “traditional” pultrusion, these members display a transversely isotropic constitutive behavior, with plane of isotropy perpendicular to the fiber direction. Previous research showed that, considering a thin-walled member subjected to two arbitrary distributions of applied stresses on the extreme faces, the state of stress and the global buckling load (moment) of the member may be influenced by the actual distribution of the applied pressures, to an extent depending on the values of the elastic constants. The reduction in buckling load (moment) due to this effect was shown to be possibly not negligible for transversely isotropic material behavior, and particularly for low ratios of transverse to longitudinal elastic constants. In order to evaluate how significant this weakening effect can be for design purposes, this work aims at quantifying it as a function of various influential parameters. The influence of symmetry properties of the cross-section on results is also studied. In particular, the I-section and the semicircular sections are taken as examples of a doubly symmetric and a singly-symmetric open cross-section, respectively. [Copyright &y& Elsevier]

Abstract: A Reddy type, third order shear deformation theory of plates is applied to the development of two versions of finite strip method (FSM), namely semi-analytical and spline methods, to predict the behavior of the moderately thick plates containing cutouts. The internal cutouts are modeled based on two different modeling approaches, and the effects of cutouts on the buckling critical stresses as well as natural frequencies are investigated. [Copyright &y& Elsevier]

Abstract: If external axial forces are not acting on a cantilevered beam, the resultant axial force at any cross section along the beam is equal to zero. Thus according to classical beam theories the lateral vibrations of a cantilevered beam are not influenced by applying a constant electric voltage to collocated surface bonded piezoelectric layers or patches. The purpose of this note is to show that in-plane cross sectional deformations due to small lateral vibrations, that are assumed to have negligible influence in the case of classical beam theories, may change the situation drastically. When coupled with the internal stresses due to the constant electric voltage, these small cross sectional deformations result in a significant influence on the free lateral vibrations. A simple example exhibits the phenomenon. Good agreement between experimental and theoretical results is presented, concerning the frequencies of the first mode of free vibrations and the buckling voltage. [Copyright &y& Elsevier]

Abstract: Dynamic pulse buckling of woven E-Glass/Vinyl Ester and laminated E-Glass/Epoxy cylindrical shells subjected to uniform overpressure and asymmetric pressure pulse (side-on explosion) were examined. The solutions for the radial shell deformations were represented by Mathieu differential equations. The dynamic instability of the shells was determined from a Mathieu stability diagram. It was found that the stability of the shells depended on lay-up, aspect ratio as well as impulse distribution. The stable vibration response of the shells with side-on explosion compared well with finite element solutions using a Dynamic, Implicit analysis in ABAQUS Standard. First-ply failure of the woven E-Glass/Vinyl Ester shell with side-on explosion was predicted using a modified Hashin–Rotem failure criterion. It was shown that the thinner woven E-Glass/Vinyl Ester shells were more likely to fail by dynamic instability, whereas the thicker woven E-Glass/Vinyl Ester shells were more likely to fail by first-ply failure. [Copyright &y& Elsevier]

Abstract: A postbuckling analysis is presented for an anisotropic laminated cylindrical shell of finite length subjected to combined loading of axial compression and torsion. The governing equations are based on classical shell theory with von Kármán–Donnell-type of kinematic nonlinearity and including the extension–twist, extension–flexural and flexural–twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine interactive buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, anisotropic laminated cylindrical shells for different values of load-proportional parameters. The results show that the postbuckling characteristics depend significantly upon the load-proportional parameter. The results reveal that in combined loading cases the postbuckling equilibrium path is unstable and the shell structure is imperfection-sensitive. [Copyright &y& Elsevier]

Abstract: The buckling of an orthotropic piezoelectric rectangular laminate with weak interfaces is investigated. The state-space formulations established directly from the three-dimensional theory of elasticity are employed. The solution is completely exact and can be used as a benchmark to clarify various plate theories or numerical methods. [Copyright &y& Elsevier]

Abstract: Buckling of rectangular orthotropic plates subjected to non-uniform compressive loads is considered in this study. This involves a two step procedure – first the determination of the in-plane stress distribution using a rigorous superposition approach and then the analysis for stability using Galerkin’s method. It is shown that the net critical load varies significantly with changes in the edge load distribution and such variations can be much more serious here than for isotropic plates because of slower St Venant decay. Further, the effects of various relevant parameters are examined with respect to partially loaded plates, plates with different load distributions on opposite edges, moderately thick plates and plates with simply supported/clamped edge conditions. [Copyright &y& Elsevier]

Abstract: The results of the stability analysis of simply supported layered isosceles trapezoidal plate subjected to axial in-plane compression are presented. The layup configuration is confined to symmetric laminates. The solution has been obtained by means of the Galerkin orthogonalisation method combined with the proposed method of the coordinate system transformation. The results of the analytical solution are compared with the verifying FEM calculation. The computed results in the form of graphs of the buckling force as a function of material and geometrical parameters of the panel are included. [Copyright &y& Elsevier]

An accurate buckling analysis for piezoelectric fiber-reinforced composite (PFRC) cylindrical shells subjected to combined loads comprising compression, external voltage and thermal load is presented in this paper. Based on Reddy’s higher-order shear deformation theory, the governing equations for the coupled displacement field and induced piezoelectric field are established. Considering two different kinds of fiber-reinforced configurations, i.e. uniformly distributed (UD) and functionally graded (FG) reinforcements, the buckling solutions of perfect and imperfect PFRC cylindrical shells are obtained by applying separation of variables and Galerkin’s method. The influence of geometric parameters, piezoelectric effect, external electric voltage, temperature field and fibers distribution configurations on buckling characteristics and imperfection sensitivity are discussed in detail. The formulation system thus developed is suitable to other shell theories and to account for the coupled electro-magneto-thermo-elastic effects. [ABSTRACT FROM AUTHOR]

Abstract: The durability of structures made of composite materials is affected by diverse factors, among which creep deformation, ageing and damage. Ageing is related to elapsed time (with different effects in different environmental conditions); damage is related to microstructural modifications due stress and/or strain inputs. The formal definition of these effects and the corresponding constitutive formulations are presented. These formulations are used to obtain analytical solutions and also to implement a Finite Element programme for viscoelastic analysis of laminar structures in a large displacement with small strains context. Then, the effects of ageing and damage on both the short and the long term stability of beam columns are analyzed. Some examples for verification of the formulation and for the comparison of effect are presented. [Copyright &y& Elsevier]