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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]

The paper presents the thermodynamic response of a composite cylindrical panel on an elastic substrate under thermal shock loading for the first time, owing to the many aeronautical uses of these panels. A novel class of advanced composites known as multi-directional functionally graded materials (MD-FGMs) lacks internal borders and interfacial stress concentrations while having mechanical and structural characteristics that are constantly changing. Because of the exceptional qualities of these cutting-edge materials, this work is the first to investigate the impact of an immediate thermal shock on the thermo-dynamic response of a multi-directional functionally graded (MD-FG) panel lying on an elastic substrate. Peripheral discontinuities at the loaded and unloaded surface boundaries and the shear coupling between the several Winkler spring components are considered in this proposed regime of a Kerr-type elastic substrate. Following the 3D-elasticity technique's extraction of the mathematical governing equations, the equations are solved using the Laplace transform and the three-dimensional differential quadrature method (3D-DQM). Once the equations are solved, the present system's findings are compared to those of a previously published paper, demonstrating a high degree of agreement between the two sets of results. Data-driven solution with the help of the deep neural network (DNN) with input, hidden, and output layers, independent variables, and other related parameters is presented to give a low computational cost method to solve engineering problems like this research. This is done with the help of presented mathematical modeling and verification of the current outputs' results. Lastly, for further study of this structure for aerospace applications, a database including bending information (normal, shear, and displacement fields in different directions) of the MD-FG cylindrical shell under thermal shock loading is provided. [ABSTRACT FROM AUTHOR]

• The nanocomposite panel is fabricated using GPL-reinforced metal foam. • Temperature-dependent elastic properties are used. • A nonlinear FSDT-based cylindrical panel model is established. • Distributed moving loads act on the surface of cylindrical panel. • Nonlinear dynamic responses of the nanocomposite panel are investigated. This paper is the first attempt, to the best of the authors' knowledge, to explore the nonlinear temperature-dependent dynamic responses of a porous functionally graded graphene nanoplatelet-reinforced composite (FG-GPLRC) cylindrical panel subjected to a moving distributed load. The desired porous FG-GPLRC structure can be achieved by reasonably designing the inner pore size and GPL dispersion patterns. A temperature-dependent dynamic model is proposed by introducing the equivalent thermo-mechanical parameters of the porous FG-GPLRCs with the help of the Halpin–Tsai micromechanics model, extended rule of mixtures, and open-cell metal foam model. The nonlinear governing equations of motion of nanocomposite cylindrical panels are derived based on the first-order shear deformation theory and the standard Lagrange equation with the aid of von Kármán geometric nonlinearity. Additionally, a closed-form Navier-type solution is implemented to model the simply-supported edges of the structures. Finally, the nonlinear dynamic response is determined using the Newmark direct integration technique combined with the Newton–Raphson iterative scheme. A parametric analysis is conducted, and the results indicate that the present model can predicate the temperature-dependent buckling behaviors and transient dynamic responses of the porous FG-GPLRC cylindrical panel. It is also found that dispersing more GPLs and fabricating more internal pores near the mid-surface of the panel can greatly reduce the response amplitudes induced by the moving loads, and the moving distributed load with a shorter length can result in a higher response. [ABSTRACT FROM AUTHOR]

In this paper, buckling analysis of cylindrical panels made of functionally graded material under the action of three types of thermal loads is investigated. At first, Governing equations of panels are obtained based on the second Piola-Kirchhoff stress tensor using three dimensional theory of elasticity. Stability equations of the shells subjected to thermal loading based on the Donnell shell theory are considered. Two methods of solution are employed. In the first method governing equations obtained by benchmark solution are discretized and solved using differential quadrature method. Then the closed form solution is presented for the buckling equations based on the Donnell shell theory. It is assumed that material properties of the shell vary continually through the thickness according to a power law distribution of the volume fraction of constituent materials, while the Poissonâs ratio is constant. The effects of various parameters including the power law exponent, panel angle, different thermal load conditions and geometric ratios on the buckling behavior of functionally graded cylindrical panels are studied.

Experimental studies were made on isotropic cylindrical panels made of Aluminum 7075-T6 under uniaxial compression. The experimental values of the critical buckling load were determined using four different methods. The critical buckling load was also determined using MSC/NASTRAN and CQUAD8 finite element. The experimental values of the critical buckling load obtained by different methods were compared with the finite element solution. The effects of the panel angle, panel length and panel thickness on the critical buckling load of isotropic cylindrical panels made of Aluminum 7075-T6 were studied. It is found that the Method III (based on a plot of applied load versus average axial strain) yields the highest value for critical buckling load and Method II (based on a plot of applied load versus square of out-of-planede deflection) the lowest value for critical buckling load. The experimental values given by Method III are seen to be closest to the finite element solution. Critical buckling load increases monotonically as panel angle increases.

In this paper, free vibrations are investigated in a homogeneous transversely isotropic, rotating cylindrical panel, in context of the linear theory of thermoelasticity. Three displacement potential functions have been introduced in the equations of motion and heat conduction in order to decouple purely shear and longitudinal motions. The purely transverse wave is not affected by thermal field. By using the method of separation of variables, the system of governing partial differential equations is reduced to four second order coupled ordinary differential equations in radial coordinate. The Matrix Frobenius method of extended power series is employed to obtain the solution in radial direction. The secular equations are obtained by using traction free and thermally insulated boundary conditions. In order to illustrate the analytic results, the numerical solution of various relations and equations has been carried out to compute the lowest frequency, phase velocity, frequency shift and damping factor of vibrations in a rotating cylindrical panel of zinc material with MATLAB software programming. The computer simulated results have been presented graphically.

Abstract As a first endeavor, the full layer-wise method is presented for elasto-up to yielding analysis of a functionally graded cylindrical panel with different boundary conditions and under steady state thermal and nonuniform mechanical loads. Static load and thermal field are applied in large and nonuniform scales which are acted on the inner and outer layers of the panel. Tresca and von Mises yield criteria are compared together and with TTO (Tamura–Tomota–Ozawa) model to find the yielded regions in the panel. The results of the used method are compared with a simulation using the commercial ABAQUS. The stress and temperature fields were expressed on the basis of an analytical solution using trigonometric terms for the full simply supported boundary conditions and simply-free boundary conditions and the derived results are presented graphically. Yielded areas vary by changing the geometry of boundary conditions and are closer to the supports. Both von Mises and Tresca criteria predicted same yielded region with the distinction that von Mises criterion is more conservative compared to Tresca criterion. Yield modes vary in different layers of the panel through its thickness and according to von Mises and Tresca yield criteria and the TTO model in this analysis, yield begins from the inner layer of the panel. By increasing the temperature, yield stress in the panel increased and by increasing FGM index and thickness of the panel, yield stress decrease in the panel. [ABSTRACT FROM AUTHOR]

Abstract The aim of this study is to give a numerical solution for free vibration problem of functionally graded and carbon nanotube reinforced (CNTR) circular cylindrical panel. Based on the Love’s shell theory and first-order shear deformation theory (FSDT), related equations of motion have been obtained. Then, the methods of harmonic differential quadrature (HDQ) and discrete singular convolution (DSC) are used for numerical computations. Two different material properties are assumed to change continuously in the thickness direction according to the volume fraction power law and the general four-parameter power law distributions. Accuracy and convergence of the methods have been validated by comparing the obtained results with the existing results available in the open literature. Frequency values have been given for different material and geometric parameters, modes and boundary cases for circular cylindrical panels with FGM and CNTR cases. The effects of types of distributions of CNTR material are also discussed. [ABSTRACT FROM AUTHOR]

Present research deals with the geometrically nonlinear bending of a long cylindrical panel made of a through-the-thickness functionally graded material subjected to thermal load. A panel under the action of uniform temperature rise loading is considered. Formulation of the shell is based on the third-order shear deformation shell theory, where the first-order shear deformation and classical shell theory may be extracted as special cases. Thermomechanical properties of the shell are assumed to be temperature dependent and are estimated according to a power law function across the shell thickness. Also, it is assumed that shell is in contact with an elastic foundation which acts in tension as well as in compression. The nonlinear governing equations of the shell are obtained using the von Kármán type of geometrical nonlinearity. The obtained governing equations are solved for two cases, i.e., simply supported shells and clamped shells. The developed equations are solved using a two-step perturbation technique. Accurate closed-form expressions are provided to obtain the mid-span deflection of the shell as a function of temperature elevation. Numerical results are provided to analyze the effects of power law exponent, boundary conditions, temperature dependency, side to radius ratio, and side to thickness ratio. [ABSTRACT FROM AUTHOR]

The dynamic behavior of singly and doubly curved panels of the rectangular planar form subjected to different types of loadings is presented. The mathematical formulation is based on the higher order shear deformation theory, and the principle of virtual work is used to derive the equations of motion. The fast converging finite double Chebyshev series and Houbolt time-marching scheme are used for evaluating the dynamic response of the panel. The effect of the magnitude and duration of pulse loadings on the transverse central displacement and bending moment responses is evaluated for different parameters. The accuracy of the present solution methodology is established by the convergence study of non-dimensional central deflection and central moments and comparison of the present results with those available in the literature. Some new results are presented for the hyperboloid panels. [ABSTRACT FROM AUTHOR]

In this study, dynamic behavior of moderately thick symmetrically laminated composite cylindrical panel under moving load is investigated using Ritz solution approximations. Hamilton’s principle (also referred to as dynamic version of Virtual work principle) is used to derive the equation of motion. First order shear deformation theory is used to consider transverse shear effect. Time integration of equation of motion is carried out using implicit Newmark average acceleration method. Parametric study is conducted in order to investigate the dynamic behavior of composite cylindrical panel for different velocities of moving load, curvature ratios, stacking schemes and boundary conditions. [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]

Mechanical behavior of a viscoelastic cylindrical panel with various edge boundary conditions, made up of functionally graded material (FGM) and subjected to thermal or mechanical load is investigated. For cases of simply supported boundary conditions, analytical solution is presented through Fourier series expansion along the axial and circumferential coordinates as well as state space method along the radial coordinate. For nonsimply supported conditions, semi-analytical solution is performed using differential quadrature method instead of Fourier series solution. Governing differential equations are transformed to Laplace transform domain and using inverse Laplace transform, obtained solutions are converted to time domain. In the present work, relaxation modulus of FGM is supposed to be according to the Prony series with power law variations along the radial direction. Numerical comparison was made with the available published results to assess the validity of present technique. Effect of relaxation time constant, thickness to mid-radius ratio, edges boundary condition and outer surface temperature on stress and displacement fields are discussed. Besides, time history of stresses for different relaxation time constant and for various boundary conditions is presented. [ABSTRACT FROM AUTHOR]

A finite strip method is formulated in order to extract the stability characteristics of laminated composite cylindrical panels containing embedded square delamination region. The material properties are assumed to vary along the panel axial length of any lamina according to a linear fiber orientation variation. The effects of existence of a square delamination region are studied on the stability characteristics of the curved panel. The friction effects, contact conditions, and delamination growth phenomenon at delaminated interfaces and edges are overlooked. The natural frequencies of the panel have been investigated based on two composite micromechanical schemes. The dynamic behavior of the delaminated panel has been extracted through using an enhanced B-spline finite strip method formulated based on the principle of virtual work. A third-order Reddy-type shear deformation theory is utilized in order to bring the effects of moderately thick laminate in to account besides a Koiter–Sanders strain–displacement theory of shallow shells. The effects of material volume fractions, layup, micromechanical model, delamination size, and location on dynamic stability characteristics of the structure are studied. In order to demonstrate the capabilities of the developed method in predicting the structural dynamic behavior, some representing results are obtained and compared with those available in the literature. [ABSTRACT FROM AUTHOR]

Exact and numerical solution of eccentrically stiffened panels in the industry is a major step forward in the design of these structures. This paper presents an analytical approach to investigate the nonlinear stability analysis of eccentrically stiffened thin FG cylindrical panels on elastic foundations subjected to hygro-thermo-mechanical loads. The stiffeners are assumed to be spiral-type. The panel has the initial geometrical imperfection. The material properties are assumed to be temperature-dependent and graded in the thickness direction according to a simple power law distribution. The elastic foundation is considered based on Winkler and Pasternak proposed model. Governing equations are derived basing on the Lekhnitsky smeared stiffeners technique and classical shell theory incorporating Von Karman- Donnell geometrical type nonlinearity. Explicit relations of load-deflection curves for FG cylindrical panels are determined by applying stress function and Galerkin method. The effects of angel of stiffener, different dimensional parameters, volume fraction index, initial geometrical imperfection, the stiffness of elastic foundation and moisture concentration on the postbuckling of FG panel are investigated. Also effects of temperature gradient through the thickness and effects of different boundary conditions are investigated for thermo-mechanical loading. The obtained results are validated by comparing with those in the literature. [ABSTRACT FROM AUTHOR]

Based on three-dimensional theory of elasticity, static analysis of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical panel subjected to mechanical uniformed load with simply supported boundary conditions is carried out. In the process, stress and displacement fields are expanded according to the Fourier series along the axial and circumferential coordinates. From constitutive law, stress-displacement relations and equilibrium equations, state space equation is obtained. The obtained first order governing differential equations can be solved analytically. The effects of CNT distribution cases, the volume fraction of CNT, length to mid radius ratio, span of the cylindrical panel, variation of mechanical load and radius to thickness ratio on the bending behaviour of the cylindrical panel are examined. It should be noted that by using Fourier series solution it is possible only to solve the static behaviour of cylindrical panel with simply supported for all of edges and for the non-simply supported boundary conditions it is possible to solve numerically. The obtained analytical solution can be used to validate the results of approximate two dimensional conventional theories.

The current work is devoted to the damage detecting inside the composite cylindrical panels. The applied method is based on the analysis of the natural vibration and corresponding mode shapes. The analysis is performed with use of finite element method. The internal defect is modeled by the reduction of the composite material stiffness and density in arbitrary chosen elements. In the first step the natural frequencies of the intact structure are computed with use of the modal analysis. Next, the corresponding mode shapes are determined (harmonic analysis) for the damage and intact structure. For the each mode shape the curvature in the longitudinal and circumferential direction are determined. In the location of the damage the change of mode shape curvature are quite different in comparison with intact structure. The proposed method of the damage detecting in the investigated here multilayered cylindrical panel are very sensitive. Even single small flaws with relatively low reduction of the material stiffness as well as its position can be effectively detected and localized.

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]

In this paper, nonlinear stability of axially compressed cylindrical panels simply supported according to two types of boundary conditions (with possible or limited circumferential displacements of unloaded sides) is presented. Panels made of functionally graded materials (FGMs) of two constituents (metallic and ceramic phases) are treated as multi-layered composite structures with transverse inhomogeneity. Volume fractions of ceramics and metal distribution throughout the layer thickness are described by a simple power law. The influence of the transverse inhomogeneity of FGM panels on unsymmetrical stable post-buckling paths is shown. Special attention is paid to effect of the imperfection sign on post-buckling paths of investigated FGM panels. Some validations of the finite element analysis are discussed for isotropic panels compressed according to two (force and kinematic) loading schemes. [ABSTRACT FROM AUTHOR]

A cylindrically curved panel in a state of generalized plane strain subject to a radial temperature gradient is discussed by analytical means. The ends of this thick-walled shell are presupposed to be guided in such a way that a displacement in circumferential direction may occur and that the radius of the middle surface remains unchanged. Then, couples act on those ends, giving rise to pure bending condition. The material is power-law functionally graded, and - based on the rule of mixtures - a coherent dependence of all the material properties (except for Poisson's ratio) on the radial coordinate is taken into account. The stresses occurring for both a positive and a negative temperature gradient are analyzed, and one finds that, depending on the grading exponent, the yield limit according to von Mises may be reached either at the inner surface, the outer surface or at both surfaces simultaneously. Numerical results are provided for a steel/aluminum FGM, and it is shown that by appropriate grading not only a reduction of the couples acting at the supports but in some cases also a considerable reduction of the weight of the panel may be achieved. [ABSTRACT FROM AUTHOR]

In this paper, the buckling load optimisation is performed on sandwich cylindrical panels. A finite element program is developed in MATLAB to solve the governing differential equations of the global buckling of the structure. In order to find the optimal solution, the genetic algorithm Toolbox in MATLAB is implemented. Verifications are made for both the buckling finite element code and also the results from the genetic algorithm by comparisons to the results available in literature. Sandwich cylindrical panels are optimised for the buckling strength with isotropic or orthotropic cores with different boundary conditions. Results are presented in terms of stacking sequence of fibers in the face sheets and core to face sheet thickness ratio.

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]

Based on 3D elasticity theory, static analysis of viscoelastic cylindrical panel made up of functionally graded material (FGM) and subjected to transverse uniform pressure is performed. Analytical solution presented, using state space method and Fourier expansion for simply supported edges, and semi-analytical approach by state space differential quadrature method (DQM) used for other boundary conditions. Field equations are solved in Laplace domain and results are transferred back to time domain numerically by Laplace inverse technique. In this investigation relaxation modulus of panel is assumed to obey Prony series form and varies in accordance to power law along the radial direction due to inhomogeneous property of FGM across the thickness. Numerical results for elastic cylindrical panel are compared with published results to validate exactness and accuracy of the present approach. In numerical illustration displacement and stress fields are studied. Moreover, effect of relaxation time constant, boundary conditions, mid-radius to thickness ratio and power law index on bending behavior of viscoelastic cylindrical panel are investigated. [ABSTRACT FROM AUTHOR]

In this study, thickness and curvature effects on high velocity impact behavior of flat and cylindrical panels are investigated numerically. Four different samples are analyzed by using LS-DYNA software and the results are compared with regard to the absorbed energy, contact force, reaction force on the boundaries, displacement at the center of the backplane surface and residual velocity of the impacting object. Penetration values of projectile and contact forces of the cylindrical panels are higher than those for flat panels. Ply vibration leads to high contact force, especially for the 8-ply cylindrical panel. [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]

The present paper presents the complete bifurcation structure of nonlinear boundary problem of thin-walled systems for cylindrical panel subjected to uniform external pressure. We examine various boundary conditions on straight edges (free, simply supported, rigidly clamped edges, edges with prescribed fixed joint conditions); curvilinear edges are simply supported. To construct solutions of the boundary problem in question and to trace equilibrium paths, we employ the non-linear extended Kantorovich method in conjunction with a conventional path-tracing technique. The structure has bifurcation paths associated with symmetric, skew-symmetric, asymmetric, and snap-through deformed shapes that provides a basis for analysis of the worst shape imperfections. [ABSTRACT FROM AUTHOR]

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]

Based on the three-dimensional elasticity theory, the investigation of the free vibration response of a carbon nanotube-reinforced cylindrical panel resting in elastic foundation in thermal environments is presented. The response of the elastic medium is formulated by the Winkler/Pasternak model. The cylindrical panel has been reinforced by carbon nanotube in the radial direction and the material properties are temperature dependent and estimated by the extended rule of mixture. Dynamic Young’s modulus of single-walled carbon nanotubes can be expressed a function of loading rate and environmental temperature. Differential quadrature method is being utilized and natural frequencies of cylindrical panel are obtained. An accuracy of the present solution is confirmed by comparing with some available results in the article. A detailed numerical study is conducted to examine the effects of temperature rise, carbon nanotube volume fraction, elastic foundations and the geometrical parameters on the deflection of the cylindrical panels. [ABSTRACT FROM AUTHOR]

Based on 3D elasticity theory, thermoviscoelastic analysis of cylindrical panel made by functionally graded materials (FGMs) under thermal and/or mechanical load is carried out. In this investigation Fourier series expansion used along the axial and circumferential coordinate which satisfy simply supported edges boundary conditions and state space method is applied along the radial coordinate. State space governing equations are transformed to Laplace domain and solved analytically. By employing the inverse Laplace, solution is transformed to time domain numerically. In this investigation relaxation modulus of FGM is assumed to obey Prony series with varying according to power law along the radial direction. To assess the validity of the present approach, numerical results are computed and compared to the published results in literature. Moreover, parametric study is performed and effect of relaxation time constant, mid-radius to thickness ratio and length to mid-radius ratio on behavior of viscoelastic cylindrical panel is discussed. [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 study, free vibration characteristics of composite plates reinforced with single walled carbon nanotubes is investigated. Distribution of the carbon nanotubes through the thickness of the panel may be uniform or functionally graded. Properties of the composite media are obtained according to a refined rule of mixtures approach which contains the efficiency parameters. First order shear deformation shell theory and Donnell-type kinematic assumptions are used. To establish the eigenvalue problem of the system, the energy based Ritz method with Chebyshev polynomials as the basis functions is implemented. The resulting eigenvalue problem is solved to obtain the natural frequencies of the system as well as the associated mode shapes. After performing comparison studies for the simpler cases, numerical results are given for vibration characteristics of carbon nanotube reinforced cylindrical panels. Numerical results reveal that, frequencies of the panel are dependent to both, volume fraction of carbon nanotubes and their distribution pattern across the thickness. Increasing the volume fraction of carbon nanotubes increases the frequencies of the panel. [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]