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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]

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]

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]

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]

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]

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]

Nonlinear thermal bending analysis is presented for a simply supported functionally graded cylindrical panel resting on an elastic foundation. Material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent, and graded in the thickness direction based on Mori–Tanaka micromechanics model. The formulations are based on a higher order shear deformation shell theory with a von Kármán-type of kinematic nonlinearity and include shell panel-foundation interaction and the thermal effects. A two-step perturbation technique is employed to determine the thermal load–deflection and thermal load-bending moment curves induced by heat conduction. The numerical illustrations concern nonlinear thermal bending response of FGM cylindrical panels with two constituent materials resting on Pasternak elastic foundations from which results for Winkler elastic foundations are obtained as a limiting case. The effects of the volume fraction index, foundation stiffness, the panel geometric parameters as well as the character of in-plane boundary conditions are also examined. [ABSTRACT FROM AUTHOR]

Abstract: This paper investigates the large amplitude vibration behavior of nanocomposite cylindrical panels resting on elastic foundations in thermal environments. Two kinds of carbon nanotube-reinforced composite (CNTRC) panels, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of FG-CNTRC panels are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The motion equations 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 and the material properties of CNTRCs are assumed to be temperature-dependent. The equations of motion are solved by a two-step perturbation technique to determine the nonlinear frequencies of the CNTRC panels. Numerical results demonstrate that the natural frequencies of the CNTRC panels are reduced but the nonlinear to linear frequency ratios of the CNTRC panels are increased as the temperature rises. In contrast, natural frequencies are increased but the nonlinear to linear frequency ratios are decreased by increasing the foundation stiffness. The results reveal that the natural frequencies are increased by increasing the CNT volume fraction, whereas the CNTRC panels with intermediate CNT volume fraction do not necessarily have intermediate nonlinear to linear frequency ratios. [Copyright &y& Elsevier]

Abstract: Based on the classical shell theory with the geometrical nonlinearity in von Karman–Donnell sense and the smeared stiffeners technique, the governing equations of motion of eccentrically stiffened functionally graded cylindrical panels with geometrically imperfections are derived in this paper. The characteristics of free vibration and nonlinear responses are investigated. The nonlinear dynamic buckling of cylindrical panel acted on by axial loading is considered. The nonlinear dynamic critical buckling loads are found according to the criterion suggested by Budiansky–Roth. Some numerical results are given and compared with the ones of other authors. [Copyright &y& Elsevier]

Abstract: In this article, the free vibration and dynamic response of simply supported functionally graded piezoelectric cylindrical panel impacted by time-dependent blast pulses are analytically investigated. Using Hamilton’s principle, the equations of motion based on the first-order shear deformation theory are derived. Also, Maxwell’s electricity equation is taken as one of the governing equations. Three sets of electric surface conditions including closed circuit and two mixtures of closed and open circuit surface conditions are considered. By introducing an analytical approach and using the Fourier series expansions, the Laplace transform and Laplace inverse method, the solution of unknown variables are obtained in the real time domain based on a combination of system frequencies. Finally, the effects of various electric surface conditions, geometric parameters and the material power law index on the free vibration and transient response of functionally graded piezoelectric cylindrical panels subjected to various impulsive loads are examined in detail. [Copyright &y& Elsevier]

Abstract: In this paper three-dimensional steady-state response of a functionally graded fiber reinforced cylindrical panel are studied. The functionally graded orthotropic panel is simply supported at the edges and assumed to have a linear variation of reinforcement volume fraction in the radial direction. Suitable temperature and displacement functions that identically satisfy the simply supported boundary conditions are used to reduce the thermoelastic equilibrium equations to a set of coupled ordinary differential equations with variable coefficients, which can be solved by differential quadrature method. Results are presented for the fiber reinforced functionally graded cylindrical panel with graded fiber volume fractions and compared with traditional discretely laminated composite panel. Results indicate the advantages of using functionally graded fiber reinforced composite shell with graded fiber volume fractions over traditional discretely laminated composite shells. [Copyright &y& Elsevier]

Abstract: This paper presents an analytical approach to investigate nonlinear response of functionally graded cylindrical panels under uniform lateral pressure with temperature effects are incorporated. Material properties are assumed to be temperature-independent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of constituents. Equilibrium and compatibility equations for cylindrical panels are derived by using the classical shell theory with both geometrical nonlinearity in von Karman–Donnell sense and initial geometrical imperfection are taken into consideration. The resulting equations are solved by Galerkin method to determine explicit expressions of nonlinear load-deflection curves. Stability analysis for a simply supported panel shows the effects of material and geometric parameters, in-plane restraint and temperature conditions, and imperfection on the nonlinear response of the panel. [Copyright &y& Elsevier]

Abstract: Stress analysis of moderately thick laminated cylindrical panels with different loading and boundary conditions is presented. Boundary conditions include clamped, simply supported and free while uniform and sinusoidal distributed loadings are considered. Assuming effects of shear deformation and initial curvature, governing equations of the problem are derived. The governing partial differential equations (PDEs) in terms of three displacement components, two rotations and ten stress resultants include a system of 15 first order PDEs. Application of the extended Kantorovich method (EKM) to the governing equations yields to a double set of algebric-differential equations in terms of x and θ. The resulted systems are then solved iteratively with very fast convergence. It is demonstrated that the method converges rapidly independent of initial guess functions. Comparisons of the EKM predictions with other analytical and FEM analyses are in close agreement. More results for panels with particular boundary conditions are presented for future studies. [Copyright &y& Elsevier]

Abstract: A multi-objective optimization strategy for optimal stacking sequence of laminated cylindrical panels is presented, with respect to the first natural frequency and critical buckling load, using the weighted summation method. To improve the speed of the optimization process, artificial neural networks are used to reproduce the behavior of the structure both in free vibration and buckling conditions. Based on first order shear deformation theory of laminated shells, a finite element code, capable of evaluating the first natural frequency and buckling load, is prepared of which the outputs are used for training and testing the developed neural networks. In order to find the optimal solution, a genetic algorithm is implemented. Verifications are made for both finite element code results and utilization of neural networks in the optimization process. With the purpose of illustrating the optimization process, numerical results are presented for a symmetric angle-ply six layer cylindrical panel. [Copyright &y& Elsevier]

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