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This paper presents and analyzes the nonlinear buckling responses of three types of shallow imperfect panels (cylindrical panel, parabolic panel, and half‐sinusoid panel) made from functionally graded graphene reinforced composite (FG‐GRC) on nonlinear elastic foundations subjected to axial compressive load in thermal environments. The nonlinear governing equations are formulated on Reddy's higher‐order shear deformation shell theory (HSDST) and take into account von Karman‐type nonlinearity. A new approximation technique to determine the stress function in average sense is developed and Galerkin's method is used to obtain the algebraically nonlinear equation system. Then, the simple calculation process can be used to solve the obtained equation systems, and the formulations to calculate the critical buckling loads and postbuckling load‐deflection curves are expressed in explicit form. The results can be flexibly applied to FG‐GRC panels with different curvatures in engineering designs. The effects of panel types, geometrical parameters, temperature increase, initial imperfection, and nonlinear elastic foundations on the critical buckling loads and postbuckling curves of cylindrical, parabolic, and half‐sinusoid FG‐GRC panels are discussed in numerical results. Numerical results also show a small disadvantage in the load‐carrying capacity of cylindrical panels compared to parabolic panels and half‐sinusoid shallow panels. Highlights: Postbuckling of cylindrical, parabolic, and half‐sinusoid panels are studied.The panels are made of functionally graded graphene reinforced composite.Reddy's higher‐order shear deformation shell theory is applied.A new approximation technique to determine the stress function is developed.Critical buckling loads and postbuckling expressions are explicitly obtained. [ABSTRACT FROM AUTHOR]

Influence of geometric imperfections on postbuckling of layered (laminated) composite cylindrical panels has been performed under axial compression load using finite element code, ANSYS and validated experimentally. Finite element code was initially validated with available literature for performing the further analyses on the panel. Eigen imperfection irregularities were considered for predicting postbuckling loads of layered composite cylindrical panels with SSSS and SFSF boundary conditions with different r/t ratio and ply sequence and compared the results. Glass-polyester laminated cylindrical panels were fabricated and tested using fixture which accommodates different boundary conditions for investigating the postbuckling phenomenon. Experimental postbuckling analysis was carried out to validate the finite element analysis results and found satisfactory. The influence of imperfections with different r/t, stacking sequences with SSSS and SFSF boundary conditions were carried out and compared. As the r/t ratio of the cylindrical panel increases the postbuckling load decreases for a given boundary conditions and with magnitude of imperfection sensitivities. It has been observed that SFSF boundary conditions with angle play layup sequences taking more axial loads than SSSS boundary conditions with same layup sequence and imperfection sensitivity. [ABSTRACT FROM AUTHOR]

This research deals with the optimization of buckling and fundamental frequency of a cylindrical panel under various heating conditions, which varies across the surface of the panel. A multi-objective design indicator (MODI) is derived with fiber orientations as a design variable. Finite element analysis is used to calculate temperature variation according to the nature of heating, buckling temperature, and fundamental frequency. In this study, scientific computing software is used to incorporate the finite element method with artificial neural network and particle swarm optimization technique. Five different heating cases, including uniform temperature cases, are considered. It is observed from the analysis that the in-plane temperature field of non-uniform type has a significant influence on the buckling and vibration characteristics of the panel. Further, it is observed that panel with lamination scheme of (θ ° / − θ ° / θ ° / − θ °) S gives the higher value of MODI max compared to other lamination schemes considered. [ABSTRACT FROM AUTHOR]

In the analytic modeling of shell buckling, much attention has been paid to closed cylindrical shells or cylindrical panels with at least two opposite edges simply supported whose solutions are known to be Lévy-type solutions. However, there have been very few reports on analytic solutions of commonly used non-Lévy-type cylindrical panels, which is mainly attributed to the widely acknowledged difficulty in solving the governing higher-order partial differential equations under prescribed boundary conditions. To address this gap, the present study provides some new analytic buckling solutions of non-Lévy-type cylindrical panels within the Hamiltonian-system-based symplectic framework. The buckling of a cylindrical panel is first formulated in the Hamiltonian system to realize a new matrix-form governing equation. An original problem with non-Lévy-type boundary conditions is then treated as the superposition of two elaborated subproblems that are solved by the rigorous symplectic approach. The final solution is obtained according to the equivalence between the superposition of the subproblems and the original problem. For benchmark use, comprehensive buckling loads and buckling modes are presented for typical non-Lévy-type panels with different ratios of in-plane dimensions, different ratios of in-plane dimension to radius of curvature, and different ratios of thickness to in-plane dimension. The present study is the first successful extension of the symplectic superposition method to the buckling analysis of cylindrical panels, which may enable access to more new analytic solutions for similar issues. [ABSTRACT FROM AUTHOR]

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

Highlights • An efficient reduced order model, based on perturbation procedure, is derived. • An extensive range of geometrical values to cylindrical panel is evaluated. • Different types of bifurcation and loss of stability are determined. • Sensibility to shape of geometrical imperfections are strongly observed. Abstract The aim of this work is to analyse the influence of the nonlinear modal coupling and initial geometrical imperfection on the post-buckling path (perfect case) or nonlinear equilibrium path (imperfect case) of a simply supported, axially loaded cylindrical panel. The cylindrical panel is described by the Donnell nonlinear shallow shell theory and the lateral displacement field is based on a perturbation procedure, generating a precise low-dimensional model that satisfies out-of-plane boundary conditions and considers the forthcoming nonlinear modal coupling due to quadratic and cubic terms in a nonlinear equilibrium equation. The discretized equations of motion are determined by applying the standard Galerkin method. Various numerical techniques are employed to obtain the cylindrical panel's nonlinear static equilibrium path with its structural stability analysis. The results show the influence of geometry on the nonlinear response of the cylindrical panel, unveiling an intricate competition between different types of bifurcation diagrams (stable symmetric, unsymmetrical, and unstable symmetric). Completing the presented results, the initial geometrical imperfection could change the stability of the initial nonlinear equilibrium path (from unstable to stable) depending on the applied amplitude of the imperfection and its shape. It is possible to observe that the influence of the geometrical imperfection on the nonlinear equilibrium path of the imperfect cylindrical panel is determinant. [ABSTRACT FROM AUTHOR]

Abstract The current study deals with thermal postbuckling behavior of graphene-reinforced composite (GRC) laminated cylindrical panels resting on elastic foundations. The GRC layers of the panel are arranged in a piece-wise functionally graded (FG) distribution along the thickness direction, and each layer of the panel contains different volume fractions of graphene reinforcement. The temperature dependent material properties of GRCs are estimated by the extended Halpin–Tsai micromechanical model with graphene efficiency parameters being calibrated against the GRC material properties obtained from the molecular dynamics simulations. The nonlinear governing equations for the thermally-loaded GRC laminated cylindrical panels are derived based on the higher order shear deformation theory and include the geometric nonlinearity effects in the sense of the von Kármán nonlinear kinematic assumptions. The panel-foundation interaction and thermal effects are also considered. The thermal postbuckling equilibrium paths for the perfect and geometrically imperfect GRC laminated cylindrical panels are obtained by applying a singular perturbation method in conjunction with a two-step perturbation approach. An iterative scheme is developed to obtain the numerical thermal postbuckling solutions of the panels. We observe that the piece-wise functionally graded distribution of graphene reinforcement can enhance the thermal postbuckling strength of the GRC laminated cylindrical panel under a uniform temperature field. [ABSTRACT FROM AUTHOR]

Buckling, postbuckling, and nonlinear responses of composite cylindrical panels reinforced by single-walled carbon nanotubes (CNTs), supported by an elastic foundation, exposed to elevated temperature and axially compressed by uniform load are investigated in this article. Distribution of CNTs is uniform or graded in the thickness direction and the effective properties of CNT-reinforced composite are assumed to be temperature dependent, and are estimated by extended rule of mixture through a micromechanical model. Governing equations are established based on thin shell theory taking von Kármán-Donnell nonlinearity, initial geometrical imperfection, Pasternak-type elastic foundation and tangential elastic constraints of boundary edges into consideration. Approximate solutions of deflection and stress functions are assumed to satisfy simply supported boundary conditions, and Galerkin method is applied to derive explicit expressions of load-deflection relation from which critical buckling loads can be obtained. Unlike works in the literature, the present study accounts for elasticity of tangential restraint of two unloaded straight edges in model of cylindrical panel. The study also gives conditions for which bifurcation type buckling response can occur and novel findings in numerical examples. [ABSTRACT FROM AUTHOR]

Experimental investigation performed to evaluate buckling strength of a cylindrical panel exposed to non-uniform temperature field is presented. A novel experimental set-up developed in-house is used to evaluate buckling strength of a cylindrical panel made of Aluminum. Influence of nature of non-uniform temperature variation, structural boundary conditions and panel aspect ratio on buckling strength is investigated experimentally. Experimental results reveals that effect of nature of temperature field, resulting from the location of heat source, on buckling strength is significant. It is also observed that buckling strength is less when the least stiffness area of the panel is exposed to peak temperature of a particular temperature field. Similarly, CCCC boundary constraints results in high thermal stress which lowers the buckling strength of the panel as compared to CCFC boundary constraints. Temperature-deflection plot and corresponding buckling strength evaluated experimentally are compared with those obtained using non-linear finite element analysis, taking into account the initial geometric imperfection. [ABSTRACT FROM AUTHOR]

This paper investigates the buckling and postbuckling behaviors of graphene-reinforced composite (GRC) laminated cylindrical panels. The GRC layer is made of polymer matrix reinforced with graphene fillers. The GRC layers may contain different volume fractions of graphene fillers to achieve a piece-wise functionally graded distribution of graphene reinforcement along the thickness direction of the panels. The material properties of GRC layers are temperature dependent and are estimated by a micromechanical model based on the results from MD simulations. The governing equations for the postbuckling of the panels are based on the Reddy's higher order shear deformation shell theory and the von Kármán strain-displacement relationships. The panel-foundation interaction and the effects of thermal conditions are both considered. A singular perturbation technique along with a two-step perturbation approach is employed to determine the buckling loads and the postbuckling equilibrium paths. It is observed that the piece-wise functionally graded distribution of graphene reinforcement can increase the buckling loads and the postbuckling strengths of the panels. The postbuckling path of a GRC laminated cylindrical panel with immovable unloaded straight edges is no longer the bifurcation type. [ABSTRACT FROM AUTHOR]

Carbon nanotubes have drawn enormous attention in recent years due to their outstanding mechanical and multifunctional properties. In addition, the growing tendency of aeronautical engineering to incorporate advanced composite materials in aircraft structures suggests carbon nanotube reinforced composites as ideal materials for high-performance fuselage panels. Nevertheless, due to the theoretical difficulties in the underlying differential problem induced by curvature, along with the technology of carbon nanotube based composites that is still under development, the number of research works on the post-buckling behavior of carbon nanotube reinforced composite curved panels is still scant. Furthermore, numerous experimental results in the literature report about the wavy state of nanotubes in polymer matrices, as well as their tendency to gather in bundles due to their high van der Waals force attraction. Therefore, advanced homogenization approaches are needed to account for these phenomena and assist the structural design. In this context, this paper presents detailed parametric analyses of the post-buckling behavior of functionally graded carbon nanotube reinforced curved panels under uniaxial compression. In particular, the effects of filler content, fiber orientation, distribution along the thickness, and misalignment of fibers are investigated. To this aim, the overall elastic moduli of carbon nanotube reinforced composites are computed by the Eshelby-Mori-Tanaka method with consideration of waviness and agglomeration effects. The presented results prove the essential role of the micromechanical variables in the design of high-strength composite curved panels. Notably, the theoretical simulations highlight the detrimental effect of waviness and agglomeration on the mechanical response of these composites. In light of this study, it is concluded that the incorporation of the considered micromechanical variables is essential for the study of the post-buckling response of functionally graded carbon nanotube reinforced curved panels under axial compression. [ABSTRACT FROM AUTHOR]

The need for high-performance lightweight materials for the design of aerospace structures predicts a remarkable future role of carbon nanotubes (CNTs). In particular, thin curved fuselage panels are widely employed. However, the theoretical difficulties in the underlying differential problem induced by the curvature, as well as a still under development technology of CNT-based composites, the number of studies dealing with buckling behavior of this structural typology is limited. The present study aims to provide some insight into the linear buckling analysis of functionally graded carbon-nanotube reinforced (FG-CNTRC) cylindrical curved panels under compressive and shear loading. Effective properties of materials of the panels 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 mixtures. A series of numerical simulations have been carried out to inspect the influence of curvature, panel aspect ratio, the distribution profile of reinforcements (uniform and three non-uniform distributions) and CNTs orientation angle on the buckling critical load under compressive and shear loading in uniform thermal environments. Results demonstrate that the change of fiber orientation, CNTs distribution, panel aspect ratio, loading condition and temperature have noticeable effects on the buckling strength and buckling modes of FG-CNTRC curved panels. [ABSTRACT FROM AUTHOR]

In this study, the magnetic-mechanical buckling of a cylindrical panel made of two-dimensional functionally graded materials (2D-FGMs) has been investigated. The panel contains longitudinal and circumferential stiffeners and has been subjected to a uniform magnetic field as well as axial load. Material properties of the cylindrical panel are assumed to vary continuously in radial and thickness directions as a function of the volume fraction of the components. The magnetic field has been exerted radially. Equilibrium and stability equations have been derived using both Hamilton's principle and principle of minimum potential energy based on the third-order shear deformation theory (TSDT). The generalized differential quadrature method (GDQ) has been employed to solve the coupled differential equations. Moreover, the effect of geometry, load, magnitude of the magnetic field, number of stiffeners, and volume fraction coefficient on the critical buckling load has been determined. The results are in good agreement with the previous related works. [ABSTRACT FROM PUBLISHER]

Modeling and analysis for the postbuckling of carbon nanotube-reinforced composite (CNTRC) cylindrical panels resting on elastic foundations subjected to lateral pressure in thermal environments are presented. Various profiles of single walled carbon nanotubes (SWCNTs) which are assumed to be uniformly distributed (UD) or functionally graded (FG) distribution along the thickness are taken into consideration. The temperature dependent material properties of FG-CNTRC panels are estimated through a micromechanical model. The formulations are developed based on a higher order shear deformation theory. To capture the large deflections, geometrical nonlinearity in von Kármán sense is taken into account. The panel-foundation interaction and thermal effects are also included. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The governing equations are first deduced to a boundary layer type that includes nonlinear prebuckling deformations and initial geometric imperfections of the panel. These equations are then solved by means of a singular perturbation technique along with a two-step perturbation approach. The influences of CNT volume fraction, temperature variation, panel geometric parameters as well as foundation stiffness on the postbuckling behavior of FG-CNTRC cylindrical panels are investigated. [ABSTRACT FROM AUTHOR]

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

In this paper buckling and free vibration characteristics of an isotropic cylindrical panel subjected to uniform temperature rise has been investigated using finite element method. The procedure involves the determination of critical buckling temperature, which is followed by modal analysis considering pre-stress due to the thermal field in the cylindrical panel. Detailed studies are carried out to analyze the influence of curvature ratio, thickness ratio and aspect ratio on the critical buckling temperature and free vibration behavior of an isotropic cylindrical panel. It has been found that as the curvature ratio and the thickness ratio increases the thermal buckling strength of the cylindrical panel decreases. It has also been found that free vibration frequencies reduce with an increase in temperature and the reduction is more significant for the lowest frequency mode. It is observed that free vibration mode shapes at ambient temperature changes with an increase in temperature. [ABSTRACT FROM AUTHOR]

This paper presents an investigation on the thermal postbuckling behavior of nanocomposite cylindrical panels resting on elastic foundations and subjected to a uniform temperature rise. The cylindrical panels are made of carbon nanotube reinforced composite (CNTRC) material with the carbon nanotube reinforcement being distributed along the thickness of the panels either uniformly (UD) or functionally graded (FG). A micromechanical model together with molecular dynamics simulation results is employed to obtain the material properties of the FG-CNTRC panels. The governing equations for the cylindrical panels are based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The panel–foundation interaction and thermal effects are also included. The material properties of CNTRCs are assumed to be temperature-dependent and an iterative scheme is developed to obtain numerical results. The results reveal that the nanotube volume fraction, foundation stiffness, and the panel curvature ratio have a significant effect on the thermal postbuckling behavior of CNTRC cylindrical panels. It is found that in most cases the CNTRC panel with intermediate nanotube volume fraction does not necessarily have intermediate thermal postbuckling strength. [ABSTRACT FROM AUTHOR]

Thermal postbuckling analysis is presented for FGM cylindrical panels resting on elastic foundations. Heat conduction and temperature-dependent material properties are both taken into account. Material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction based on Mori–Tanaka micromechanics model. The formulations are based on a higher order shear deformation theory and von Kármán strain displacement relationships. The panel–foundation interaction and thermal effects are also included. The governing equations are first deduced to a boundary layer type that includes nonlinear prebuckling deformation and initial geometric imperfection of the panel. Thermal postbuckling equilibrium paths are determined by using a singular perturbation technique along with a two-step perturbation approach. The effects of volume fraction index, foundation stiffness, panel curvature ratio on the thermal postbuckling behavior of FGM cylindrical panels are discussed in detail. The results reveal that the thermal postbuckling equilibrium path of FGM cylindrical panels with immovable simply supported edge conditions is no longer the bifurcation type for both uniform and non-uniform temperature variations. [ABSTRACT FROM AUTHOR]

Abstract: Uni-lateral buckling behavior of cylindrical panels on tensionless elastic foundation under axial compression is investigated through Rayleigh–Ritz method. Derivation of the equations is based on Kirchhoff–Love’s hypotheses. All the contributed researches on the uni-lateral buckling problem are limited to plates. Buckling curves are produced that indicate relationships between buckling load and geometrical parameters. It is concluded that increasing the surface of panel does not necessarily lead to an increase in the contact region between panel and foundation. Influences of geometrical parameters and foundation on the uni-lateral buckling behavior are examined. The results for flat panel are validated with available data. [Copyright &y& Elsevier]

Abstract: The use of curved panels for the construction of steel bridges becomes more and more popular. Their design is however made difficult by a lack of specifications, especially in European Standards. The present study aims thus at developing a method for predicting the ultimate strength of cylindrical unstiffened curved panels subjected to uniform axial compression. The methodology used in this study is based on the formal procedure recommended by Eurocode 3 for all types of stability verifications. A series of numerical simulations is first carried out to identify the fundamental characteristics of curved panels'' elasto-plastic behaviour. Then on the basis of these numerical results, semi-empirical formulae for predicting the elastic buckling and ultimate strength are derived and illustrated on a practical example. [Copyright &y& Elsevier]

The influence of curvature of a cylindrical panel containing a crack on the value of the J-integral in the process of axial loading is investigated. We study the entire range of curvatures of the panel, namely, from a plate to a closed cylindrical shell. The critical values of the J-integral are determined numerically according to the experimentally obtained values of critical loads corresponding to the onset of crack propagation. The contributions of membrane and bending strains to the total value of the J-integral are evaluated. In the case of an almost plane panel, we analyze the influence of nonlinear bending (buckling) in the vicinity of the crack on the increase in the J-integral. The influence of crack length on the critical value of the J-integral is studied. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents thermo-mechanical post-buckling analysis of cylindrical panels that are made of functionally graded materials (FGMs) with temperature-dependent thermo-elastic properties that are graded in the direction of thickness according to a simple power law distribution in terms of the volume fractions of the constituents. The panel is initially stressed by an axial load, and is then subjected to a uniform temperature change. The theoretical formulations are based on the classical shell theory with von-Karman–Donnell-type nonlinearity. The effect of initial geometric imperfection is also included. A differential quadrature (DQ) based semi-analytical method combined with an iteration process is employed to predict the critical buckling load (where it is applicable) and to trace the post-buckling equilibrium path of FGM cylindrical panels under thermo-mechanical loading. Numerical results are presented for panels with silicon nitride and nickel as the ceramic and metal constituents. The effects of temperature-dependent properties, volume fraction index, axial load, initial imperfection, panel geometry and boundary conditions on the thermo-mechanical post-buckling behavior are evaluated in detail through parametric studies. [Copyright &y& Elsevier]

A postbuckling analysis is presented for a shear deformable laminated cylindrical panel of finite length subjected to lateral pressure. The governing equations are based on Reddy's higher order shear deformation shell theory with von Kármán-Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfectiosn of the shell, is extended to the case of shear deformable laminated cylindrical panels under lateral pressure. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, cross-ply laminated cylindrical panels. The effects played by transverse shear deformation, panel geometric parameters, total number of plies, fiber orientation, and initial geometric imperfections are studied. [ABSTRACT FROM AUTHOR]

Abstract: A postbuckling analysis is presented for a shear-deformable laminated cylindrical panel of finite length subjected to compressive axial loads. The governing equations are based on Reddy's higher-order shear deformation shell theory with a von Kármán-Donnell type of kinematic non-linearity. The non-linear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of non-linear prebuckling deformations, large deflections in the postbuckling range and initial geometric imperfections of the shell, is extended to the case of shear-deformable laminated cylindrical panels under axial compression. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick and thin cross-ply laminated cylindrical panels. The effects played by transverse shear deformation, panel geometric parameters, total number of plies, fibre orientation, the character of in-plane boundary conditions and initial geometric imperfections are studied. [ABSTRACT FROM AUTHOR]

A full understanding of the mechanical behaviors of a three-dimensional (3D) functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panel is important for structural design of engineering composite components. In this paper, the buckling and free vibration studies of FG-CNTRC cylindrical panel with different patterns of CNT distribution are investigated using the three-dimensional theory of elasticity. The cylindrical panels are subjected to axial and circumferential initial stresses, which frequently occur in real engineer structures. The state space technique along the radial direction and the Fourier series expansion along the in-plane coordinate (are) employed to formulate the problem and solve it analytically. A parametric study is carried out to examine the effects of the CNT distribution pattern, CNT volume fraction, length to mid radius ratio, and mid radius to thickness ratio on the buckling and vibration behaviors of FG-CNTRC cylindrical panels. Some interesting findings are observed, which may help design the CNTRC cylindrical panel structures. Besides, the presented studies may serve as benchmarks for researchers to check the validity of their future research works. [ABSTRACT FROM AUTHOR]

Abstract: This report presents an analytical approach to investigate the stability of functionally graded cylindrical panels under axial compression. Equilibrium and compatibility equations for functionally graded panels are derived by using the classical shell theory taking into account both geometrical nonlinearity in von Karman–Donnell sense and initial geometrical imperfection. The resulting equations are solved by Galerkin procedure to obtain explicit expressions of buckling loads and postbuckling load–deflection curves. Stability analysis for a simply supported functionally graded cylindrical panel shows the effects of material and geometric parameters as well as imperfection on buckling and postbuckling behaviors of the panel. [ABSTRACT FROM AUTHOR]