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In this study, the deflection and stress field of perfect and imperfect (with and without porosities) functionally graded (FG) cylindrical panels are determined following the first-order shear deformation theory (FSDT). The panel rested on the twoparameter elastic foundation (Pasternak foundation) under pressure loads and worked in a hygro-thermal environment. Navier's solution has been used for simply supported cylindrical panels to analyze the effects of porosity, geometrical and foundation parameters, as well as temperature and humidity on deflection and stress field. The validated examples demonstrate the reliability of the solution and the self-written Matlab program. Numerical investigations show a significant hygro-thermal effect on the static response of the FG panel. [ABSTRACT FROM AUTHOR]

This paper presents a new semi-analytical approach for the nonlinear vibration and dynamic responses of functionally graded graphene platelet-reinforced composite (FG-GPLRC) panels with complex curvature reinforced by orthogonal and/or inclined stiffeners in the thermal environment resting on the nonlinear viscoelastic foundation with the nonlinearities of von Kármán in the framework of the higher-order shear deformation theory (HSDT). The three curvature types of complexly curved panels are considered to be cylindrical, sinusoid, and parabola panels. Orthogonal and/or inclined stiffeners are modeled utilizing an improved smeared stiffener technique. The stress function form is estimated by applying the like-Galerkin method for complexly curved panels. By applying the Lagrange function and Euler–Lagrange equation, the nonlinear equations of motion of the panels are obtained. The viscous damping effects of the viscoelastic foundation are considered by utilizing the Rayleigh dissipation function. Numerical results are examined utilizing the Runge–Kutta method to acquire the time-deflection curves, and by utilizing the Budiansky–Roth criterion, the critical dynamic buckling loads are determined. From the investigated results, it is possible to evaluate the nonlinear vibration and buckling dynamic responses of three forms of panels with stiffeners. [ABSTRACT FROM AUTHOR]

In this study, free vibration and damping behavior of cylindrical sandwich panel with electro-rheological core and graphene platelets reinforced composite (GPLRC) facing sheets based on first-order shear deformation theory of thick cylindrical shells referred by Qatu (FSDTQ) is investigated. Effective material properties of graphene platelets reinforced composite are determined according to the Halpin–Tsai micromechanical model. The governing equations of motion with required boundary conditions are derived using Hamilton's principle. Afterward, these equations are solved analytically using the Fourier series solution for simply-supported boundary conditions, and for the other edges boundary conditions, we used the generalized differential quadrature method. The exactness and correctness of the present formulation are validated by comparing the results with those of existing literature. Finally, the influences of various parameters such as the electric fields, geometrically parameters, boundary conditions, the volume fraction of GPL, and GPL distributions pattern on vibration behavior and modal loss factor is examined. According to the results, the influence of the GPL volume fraction and electric field on the frequencies and modal loss factor is significant. This achievement can help design intelligent controlling structures for various applications. [ABSTRACT FROM AUTHOR]

This work presents an analytical study on the dynamic instability of rotating functionally graded porous cylindrical panels subjected to periodic axial load under simply supported boundary conditions. Considering the Coriolis acceleration, centrifugal component, and hoop stress, the partial general equations of motion have been derived based on first-order shear deformation theory (FSDT) and by using Hamilton's principle. The excitation frequencies of rotating functionally graded porous cylindrical panels were calculated by substituting all motion equations for the transverse displacement and then applying the Galerkin method to the resulting equation. Numerical results are employed to validate the analytical results and show good agreement. The influences of the porosity distribution method, porosity coefficient, static and dynamic load factors, angular velocity, Coriolis acceleration, initial hoop stress, circumferential wave number, angle of the cylindrical panel, and cylindrical panel dimensions on the dynamic instability of rotating functionally graded porous cylindrical panels were investigated. Some of the important outputs that were reached in this study are that static and dynamic loads increase the width of the instability zone and that the structure is more stable when the porosity moves away from the surface and when the angular velocity increases. In addition, the cylindrical panel has a large frequency when the panel's angle is small (i.e., θ0 = 30°), but it is less sensitive to dynamic load when the angle is large (i.e., θ0 ≥ 100°).Please confirm if the author names are presented accurately and in the correct sequence (given name, middle name/initial, family name). Author 1 Given name: [specify authors given name] Last name [specify authors last name]. Also, kindly confirm the details in the metadata are correct.Thank you for this inquiry, author names have been given accurately and in the correct sequence. [ABSTRACT FROM AUTHOR]

• A novel third-order shear deformable model was developed. • Porous functionally graded graphene platelet reinforced cylindrical panels. • A blast pressure acted on the structures. • Temperature-dependent mechanical responses. In this paper, a novel shear deformable model is developed to investigate the temperature-dependent thermo-mechanical responses of porous functionally graded graphene reinforced composite (FG-GPLRC) cylindrical panels subjected to an initial blast pressure. An improved third order shear deformation theory, which has more rigorous kinematic of displacement, is implemented in the construction of the proposed model. Then, the current model is used to predict the thermo-mechanical responses of the nanocomposite panels made of metal foams reinforced by graphene platelets (GPLs). Lagrange equations are used to derive the governing equations corresponding to thermal buckling as well as the free and forced vibrations of the porous FG-GPLRC cylindrical panels. A Navier-type solution, which is free from computational errors, is implemented. Validation works demonstrate that the present model provides accurate predictions of mechanical responses for composite structures. A comprehensive parameter study is carried out to explore the influences of several key parameters regarding the thermo-mechanical behaviors of the porous FG-GPLRC cylindrical panels. [ABSTRACT FROM AUTHOR]

This work presents an analytical study of the parametric instability of cylindrical panels containing functionally graded porous exposed to static and dynamic periodic axial loads under simply supported boundary conditions. Based on Hamilton’s principle, the governing equation of motion by using first-order shear deformation theory (FSDT) has been obtained. By applying the Galerkin technique, an excitation frequency expression is derived, which helps identify areas of instability of functionally graded porous cylindrical panels. Numerical simulations are used to validate the analytical results. Eventually, the impacts of the porosity coefficient, porosity distribution method, static and dynamic periodic axial loads, panel angle, circumferential wave number, and cylindrical panel characteristics on the region of instability are displayed in the section of results and discussions. The findings show that when the porosity is further from the surface, the more stable the structure is. Furthermore, a small angle of the cylindrical panels gives a better dynamic response than a large angle. In addition, increased static and dynamic loads lead to an expansion of areas of instability.

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.

In this study, torsional buckling behavior of a laminated composite cylindrical shell panel reinforced with graphene nano-sheets is analyzed. Using the theory of linear three-dimensional elasticity and based on the principle of virtual work and finite element method, equilibrium equations are extracted. Buckling loads are obtained based on a generalized geometric stiffness concept. Halpin-Sai equations are also used to obtain the mechanical properties of the composite material. The effects of weight fractions and graphene distribution pattern along the thickness of the shell, and zigzag and armchair layup of graphene platelets on the torsional buckling loads are investigated. Five graphene distribution patterns FG-X, FG-O, FG-Ʌ, FG-V and UD are utilized in this study. The 15 models of GPL distribution and arrangement of composite layers are investigated. [ABSTRACT FROM AUTHOR]

In this work, the nonlinear free vibration analysis of the imperfect cylindrical panels in contact with discontinuous unilateral elastic base are conducted, evaluating the influence of the type of contact, unilateral or bilateral, and the contact area of the elastic base on the natural frequencies and nonlinear frequency-amplitude relations. For that, the structural cylindrical panel model considers the Donnell's nonlinear shallow shell theory to obtain the partial differential equilibrium equation and the compatibility and continuity equation. To represent the unilateral capability of the elastic base, a signum function is inserted in the reaction force of the elastic base to describe its dependence of the transversal displacement field of the cylindrical panel. To apply the elastic base in certain subdomain of the cylindrical panel, a Heaviside-type function is also inserted into elastic base's reaction forces. The nonlinear equilibrium equation is discretized by the Galerkin method, using a consistent transversal displacement field that it was obtained from a perturbation technique. The discretized set of equilibrium equations is employed to obtain the natural frequencies and the nonlinear frequency-amplitude relations, evaluating the influence of the unilateral contact and the contact region of the elastic base on these results. Depending on the signal of the imperfection's magnitude and the type of contact of the elastic base, the imperfect cylindrical panel can display an initial gap between the cylindrical panel and the elastic base, and this possibility is also investigated in this work. From the numerical results, it is observed that the unilateral elastic base applies less structural stiffness than the bilateral elastic base, decreasing the natural frequencies for the same imperfect cylindrical panel. The localization of the elastic base in the cylindrical panel also affects the natural frequencies, increasing or decreasing them depending on the modifications on the structural stiffness. The frequency-amplitude relations are strongly influenced by both unilateral contact of elastic base and the type of the contact consideration between the cylindrical panel and elastic base, exhibiting an intricated nonlinear behavior. • Inclusion of a discontinuous and unilateral elastic base on the nonlinear equilibrium equation of imperfect cylindrical panels. • Novel results on the influence of the unilateral elastic base on natural frequencies and nonlinear frequency-amplitude relations. • Simultaneous evaluation of the influence of the initial geometrical imperfections and the unilateral elastic base on the nonlinear free vibration analysis. • Results of a detailed parametric analysis confirm that natural frequencies and backbone curves are sensitive to the magnitude of initial geometric imperfections and the unilateral elastic base's parameters. [ABSTRACT FROM AUTHOR]

In this paper, an exact elasticity solution of cylindrical panel under cylindrical bending is presented. The formulation is based on the displacement approach in which 3D elasticity equations are reduced to 2-D equations using plane-strain conditions. In the present formulation, an exact elasticity solution is feasible due to the consideration of simply supported boundary conditions with applied loads expressed in harmonic forms. Single layered and multi-layered orthotropic composite panels subjected to realistic transverse normal loads are analysed. Solutions have been presented for uni-directional, bi-directional, and symmetric three-layered cross-ply laminated composite cylindrical panels. Variation of displacements and stresses through the thickness has been investigated for the panel subjected to single sinusoidal load, uniformly distributed load, hydrostatic load, and strip load. Validation of results is presented using reference results in the literature. The extensive results presented in this paper can be served as benchmark solutions for the assessment of improved panel theories.

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]

In this paper, a mathematical model of complex oscillations of a flexible micropolar cylindrical mesh structure is constructed. Equations are written in displacements. Geometric nonlinearity is taken into account according to the Theodore von Karman model. A non-classical continual model of a panel based on a Cosserat medium with constrained particle rotation (pseudocontinuum) is considered. It is assumed that the fields of displacements and rotations are not independent. An additional independent material parameter of length associated with a symmetric tensor by a rotation gradient is introduced into consideration. The equations of motion of a panel element, the boundary and initial conditions are obtained from the Ostrogradsky – Hamilton variational principle based on the Kirchhoff – Love’s kinematic hypotheses. It is assumed that the cylindrical panel consists of n families of edges of the same material, each of which is characterized by an inclination angle relative to the positive direction of the axis directed along the length of the panel and the distance between adjacent edges. The material is isotropic, elastic and obeys Hooke’s law. To homogenize the rib system over the panel surface, the G. I. Pshenichnov continuous model is used. The dissipative mechanical system is considered. The differential problem in partial derivatives is reduced to an ordinary differential problem with respect to spatial coordinates by the Bubnov – Galerkin method in higher approximations. The Cauchy problem is solved by the Runge – Kutta method of the 4th order of accuracy. Using the establishment method, a study of grid geometry influence and taking account of micropolar theory on the behavior of a grid plate consisting of two families of mutually perpendicular edges was conducted.

• A dynamic model of graphene reinforced cylindrical panel subjected to the pulse or steady-state excitation is proposed. • Distributing more GPLs to the outer surfaces shows the optimal performance for the composite structure. • Nonlinear transient responses, bifurcation and chaotic dynamics are investigated. • Double-parameter maximum Lyapunov exponents are plotted to intuitively judge the chaotic regions. The present paper is concerned with nonlinear vibration of a simply supported functionally graded graphene reinforced composite (GRC) cylindrical panel subjected to the transverse excitation. Functionally graded structure is proposed to distribute more graphene platelets (GPLs) to the most needed layer for the optimal performance. The modified Halpin-Tsai model and the rule of mixture are carried out to predict the effective material properties of the GRC cylindrical panel, such as Young's modulus, Poisson's ratio and mass density. Nonlinear partial differential equations of motion are established within the framework of Hamilton principle in conjunction with first-order shear deformation theory (FSDT) and von Karman geometric nonlinearity. Navier approach is adopted to calculate natural frequencies of the GRC cylindrical panel. Then, considering the external excitation, Galerkin method is applied to realize the model reduction, which is expressed by the ordinary differential equations. Backward Differentiation Formula (BDF) is used to perform nonlinear transient responses of the system subjected to the pulse excitation (step load or triangular load). Finally, Runge-Kutta method is employed to carry out bifurcations and chaotic dynamics of the system subjected to the steady-state excitation. Results are presented in the form of natural frequencies and nonlinear responses to perform the parametric studies, such as distribution types and weight fractions of GPLs, geometry parameters and excitation parameters of the GRC cylindrical panel. [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]

Natural frequency characteristics of functionally graded multilayer hybrid composite cylindrical shell panel reinforced by graphene platelets (GPLs) and carbon nanotubes (CNTs) are scrutinized in the present study for the first time. Effective material properties of the composite media are evaluated using a modified micromechanical model based on the Halpin-Tsai approach and rule of mixtures. First order shear deformation theory of shells, Hamilton's principle and finite element procedure are applied to obtain the effective stiffness and mass matrices of the structure. After validating accuracy of the presented solution procedure with the published literatures, influence of broad range of factors such as number of multilayers, weight fraction and distribution pattern of GPLs and CNTs reinforcements, CNTs and GPLs volume fraction index for the nonlinear distributions, thickness and length ratio of the shell panel, span angle, Winkler elastic foundation stiffness parameter and different boundary condition are presented and their trends are discussed in several tabular and graphical data in detail. Results denotes that cylindrical shells composed of three phases can make use of the advantages of both CNTs and GPLs reinforcing elements and can significantly improve the free vibration behavior of shell. • Investigating the natural frequencies of FG multilayer hybrid nanocomposite cylindrical shell panel reinforced by GPLs and CNTs for the first time. • Studying the effects of Winkler-type elastic foundation on the natural frequencies. • Deriving governing equations based on FSDT, Hamilton's principle and FEM. • A full comprehensive study considering the effects of the number of multilayers, weight fraction and distribution of GPLs and CNTs, CNTs and GPLs volume fraction index, thickness and length ratio, span angle, Winkler elastic foundation stiffness parameter and BCs. [ABSTRACT FROM AUTHOR]

In this study, the vibration and flutter characteristics of the graphene platelets reinforced functionally graded porous cylindrical panels subjected to the supersonic flow are investigated for the first time. The considered panels are constructed of the nanocomposites that made of matrix of open-cell metal foams with graded pore distributions and are reinforced uniformly by the graphene platelets. The typical mechanical properties of porous matrix are determined using open-cell metal foam model, which provides a typical mechanical feature to determine the relationship between coefficients of density and porosity. The effective elasticity modulus of the nanocomposite is determined based on a modified Halpin-Tsai micromechanics model, and the rule of mixture is used to calculate the Poisson's ratio and mass density. A high order shear deformable computational framework is developed with inclusion of the trapezoidal shape factor to eliminate the errors introduced by the curvature of the panels. The standard Lagrange processing in conjunction with the Navier-solution technique, with the help of the first-order piston theory, is applied to derive the equations of motion related to the vibration and flutter characteristics of the cylindrical panel with simple-supported boundary condition. Comparisons of the natural frequencies with the previous works are performed to validate the proposed model. Parameter studies are carried out, and the results in the form of graphs or tables reveal the effects of pore, graphene platelets on the supersonic flutter characteristics of the nanocomposite cylindrical panels subjected to the aerodynamic flow. • Supersonic flutter of GPL-reinforced FG porous panels is studied for the first time. • The total masses of various FG porous cylindrical panels are the same. • A computational framework based on Reddy's TSDT is developed. • The comparisons indicate the proposed method is accurate. • Revealing effects of some important parameters on flutter characteristics. [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]

Abstract As a first attempt, the combined application of the differential quadrature method (DQM) and the Newton Raphson method is used to solve the non-Fourier heat conduction equations to obtain temperature, displacements, and stresses in a cylindrical panel made of functionally graded, carbon nanotubes (CNTs) reinforced composite. The heat conduction of a domain made of nanocomposites subjected to heat generation is simulated with a finite heat wave speed. Furthermore, based on the three-dimensional elasticity theory, the thermoelastic analysis of the nanocomposite cylindrical panel subjected to the transient heat conduction is presented. The dynamic Young's modulus of Single-Walled Carbon Nanotubes (SWCNT) can be expressed as a function of loading rate and environmental temperature. All material properties such as heat capacity (C p), thermal relaxation time (τ), density (ρ) and thermal conductivity (K) are considered as a function of both temperature and CNT volume fraction. The hyperbolic heat conduction is solved to obtain temperature in the spatial and temporal domains. Then by implementing the obtained temperature in thermoelastic equations of the cylindrical panel, the displacements and stresses will be obtained at each time step. The proposed method marches in the time direction block by block. In each block, there are several time levels, and the numerical results at these time levels are obtained simultaneously. Through this way, the numerical solution at the (n + 1)th time level depends on the solutions at its previous levels from the 1 st to the n th levels. The final results in the temporal domain are obtained using the Newton–Raphson method. Accuracy of the present solution is confirmed by comparing with some available results in the literature. A detailed numerical study is conducted to examine the effects of heat wave speed and heat flux, CNT volume fraction and the geometrical parameters on the deflection of the cylindrical panel. [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]

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]

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]

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]

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]

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, 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]

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]

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]

This paper presents an investigation on the nonlinear behaviors of nanocomposite cylindrical panels subjected to the combined action of uniform lateral pressure and compressive edge loads. The panels may rest on elastic foundations and be in a varying temperature environment. The nanocomposite consists of reinforcing carbon nanotubes either uniformly distributed (UD) or functionally graded (FG) along the thickness direction of the panels. The two cases of nonlinear bending of initially compressed cylindrical panels and postbuckling of initially pressurized cylindrical panels are considered. A high-order shear deformation shell theory in association with von Kármán nonlinear strain–displacement relationships is applied to derive the governing equations for the carbon nanotube reinforced composite (CNTRC) panels. Furthermore, the effects of the panel-foundation interaction and the temperature variation are also included in the analysis and the material properties of CNTRC panels are assumed to be temperature-dependent. Numerical results are presented to illustrate the nonlinear bending responses and the postbuckling behaviors of CNTRC cylindrical panels resting on the Pasternak-type elastic foundations. The present solutions also highlight the effects of the CNT volume fraction, temperature rise, foundation stiffness as well as initial stress on the nonlinear behaviors of CNTRC cylindrical panels. [ABSTRACT FROM AUTHOR]

Polymeric foams are new materials which prefer special mechanical and thermal properties for mechanical designers. The best mathematical model for polymeric and metallic foams is functionally graded viscoelastic (FGV) materials. So, this paper has concentrated on presenting a reliable and accurate method for free vibration of FGV panels. For this purpose, Levy-type circular cylindrical panel consisting of FGV material is modeled based on Sanders first order shear deformation type theory, as geometrical model, and linear Zener model with variable properties through the thickness, as the best constitutive relation for FGV materials. Validity and accuracy of present method are approved by comparing it with finite element in different tables. Also, effects of various geometrical and material parameters on natural frequencies and decay rate are studied. [ABSTRACT FROM AUTHOR]

A postbuckling analysis is presented for functionally graded material (FGM) cylindrical panels resting on elastic foundations subjected to axial compression under heat conduction. Two kinds of micromechanics models, namely, Voigt model and Mori-Tanaka model, are considered. The material properties of FGMs are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents and are assumed to be temperature-dependent. The formulations 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 nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A singular perturbation technique along with a two-step perturbation approach is employed to determine the buckling loads and postbuckling equilibrium paths. The effects of volume fraction index, temperature variation, foundation stiffness, panel curvature ratio as well as the inplane boundary condition of straight edges on the postbuckling behavior of FGM cylindrical panels are discussed in detail. [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]

In this paper three dimensional free vibration and transient response of a cylindrical panel made of two directional functionally graded materials (2D-FGMs) based on three dimensional equations of elasticity and subjected to internal impact loading is considered. Material properties vary through both radial and axial directions continuously. The 3D graded finite element method (GFEM) based on Rayleigh-Ritz energy formulation and Newmark direct integration method has been applied to solve the equations in space and time domains. The fundamental normalized natural frequency, time history of displacements and stresses in three directions and velocity of radial stress wave propagation for various values of span angel of cylindrical panel and different power law exponents have been investigated. The present results show that using 2D-FGMs leads to a more flexible design than conventional 1D-FGMs. The GFEM solution have been compared with the results of an FG thick hollow cylinder and an FG curved panel, where a good agreement between them is observed. [ABSTRACT FROM AUTHOR]

• A novel higher-order porosity distribution for the foam core sandwich panels is introduced. • The governing equations are derived based on the third-order shear deformation theory utilizing the Hamilton principle. • The Navier technique is implemented to derive the closed-form solutions. • The presented porosity can increase the buckling load and natural frequency by 10% and 5% in comparison to the conventional porosity, respectively. • For the flexural vibration, the in-plane and rotary inertias can be ignored to reduce the computational complexity without large effect on the natural frequencies. In this research paper, a novel higher-order porosity distribution is proposed, and free vibration and buckling behavior of cylindrical sandwich panels with functionally graded metal foam core are investigated. It is assumed that the sandwich panel is made of two thin face metal sheets and a moderately thick functionally graded metal foam core. The dynamic governing equations are obtained based on the third-order shear deformation theory and utilizing the Hamilton principle. It is assumed that the voids are distributed non-uniformly along the thickness of the functionally graded metal foam core. The elastic modulus of the core depends on the square of the relative density, thus is changing nonlinearly through the thickness of the core. The Navier technique is implemented to derive closed form solutions for the natural frequencies and the buckling load of the simply supported cylindrical sandwich panels. The accuracy and effectiveness of the proposed model are verified by comparison with previous researches. Results revealed that the presented higher-order porosity distribution can increase the buckling load and fundamental natural frequency by 10% and 5% in comparison to the conventional porosity distributions, respectively. In addition, it is shown that if the flexural vibration is of interest, ignoring the in-plane and rotary inertias, which can significantly reduce the computational complexity, does not have any considerable effect on the natural frequencies. [ABSTRACT FROM AUTHOR]

Nonlinear bending analysis is presented for nanocomposite cylindrical panels subjected to a transverse uniform or sinusoidal load resting on elastic foundations in thermal environments. Carbon nanotubes are used to reinforce the cylindrical panels in two distinguished patterns, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements. The material properties of CNTRCs are assumed to be temperature-dependent and are estimated by a micromechanical model. The governing equations of the panel are derived based on a higher-order shear deformation theory with a von Kármán-type of kinematic nonlinearity and are solved by a two-step perturbation technique. The nonlinear bending behaviors of the CNTRC panels with different CNT volume fraction distributions, foundation stiffnesses, temperature rise, and the character of in-plane boundary conditions are studied in details. [ABSTRACT FROM AUTHOR]