This paper studies the small and large amplitude vibration behaviors of graphene-reinforced composite (GRC) laminated cylindrical panels supported by an elastic foundation under thermal environmental ...conditions. The temperature dependent material properties of GRC are assumed to be functionally graded in a piece-wise pattern by changing the volume fraction of graphene in the panel thickness direction and are estimated by the extended Halpin-Tsai micromechanical model. The motion equations for the nonlinear vibration problem of the panels are obtained from the higher order shear deformation shell theory and take into consideration of the effects of the von Kármán geometric nonlinearity, the elastic foundation and the temperature change. The nonlinear vibration solutions for the FG-GRC laminated cylindrical panels can be obtained by applying a two-step perturbation technique. We observe that the natural frequencies of FG-GRC panel with symmetrical distribution of graphene reinforcements are higher, whereas the nonlinear to linear frequency ratios of the same panel are lower than those of panels with uniform or unsymmetrical distribution of graphene reinforcements.
This paper investigates the large amplitude vibration behavior of a shear deformable FGM cylindrical shell of finite length embedded in a large outer elastic medium and in thermal environments. The ...surrounding elastic medium is modeled as a Pasternak foundation. Two kinds of micromechanics models, namely, Voigt model and Mori–Tanaka model, are considered. The motion equations are based on a higher order shear deformation shell theory that includes shell-foundation interaction. The thermal effects are also included and the material properties of FGMs 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 FGM shells. Numerical results demonstrate that in most cases the natural frequencies of the FGM shells are increased but the nonlinear to linear frequency ratios of the FGM shells are decreased with increase in foundation stiffness. The results confirm that in most cases Voigt model and Mori–Tanaka model have the same accuracy for predicting the vibration characteristics of FGM shells.
The nonlinear dynamic responses of laminated plates consisting of graphene reinforced composite (GRC) layers in thermal environments are studied in this paper. The effect of visco-elastic foundation ...is also considered in the analysis. All layers in an FG-GRC laminated plate are assumed to have the same thickness, whereas the graphene volume fractions for the layers are assumed to be linearly varying in a piece-wise pattern along the plate thickness direction. The material properties of GRC are estimated by a extended Halpin-Tsai model. To include the effect of small scale, the efficiency parameters for graphene are introduced in the model and determined from the results of molecular dynamics (MD) simulations. The plate is modeled based on the Reddy’s higher order shear deformation plate theory and the effects of the von Karman geometric nonlinearity and the initial loading are included in the derivation of the motion equations. Once the applied load is determined, the deflection as the function of time can be solved by the fourth-order Runge-Kutta numerical method. The impacts of functionally graded (FG) pattern, visco-elastic foundations, temperature change and applied load type on the dynamic behaviors of the FG-GRC plate are presented and discussed.
The cylindrical sandwich shells with auxetic 3D double-V meta-lattice core and functionally graded (FG) GRC (graphene-reinforced composite) facesheets are designed, modeled and analyzed to reveal ...their nonlinear dynamic response when subjected to low-velocity impact. The 3D double-V meta-lattices, developed from the 2D double arrowed honeycombs, are further self-adapted to meet the requirements of the curved space between facesheets of sandwich shells. By means of micromechanical modeling according to the extended Halpin-Tsai model, the temperature-dependent properties are determined for GRC facesheets, which are further designed to possess FG configurations along the radical direction of the shell structures. Full-scale FE modeling and nonlinear dynamic analysis are then carried out. Numerical results reveal the novelty of FG configurations of GRC facesheets, and include the effects of drop-heights, shell lengths, strut radii, shell radii and thermal environments. Present models, including 3D meta-lattice cores and polymer matrix composite facesheets, are believed to provide new thoughts for the design of lightweight sandwich shells and their applications in the fields of ocean engineering.
•The 3D double-V meta-lattices are adapted to meet the curvature variation of the cylindrical sandwich shells.•The GRC facesheets are designed to possess FG configurations.•Thermal effects are taken into account, and material properties are assumed to be temperature-dependent.•The effects of curvature radii are revealed to be significant, both on contact forces and displacements.
•2D and 3D lattice metamaterials with negative effective Poisson’s ratios (EPRs) were modeled, analyzed, and compared.•The mechanical properties of GRCs were determined through a micromechanical ...model of extended Halpin-Tsai type.•Compared with a re-entrant honeycomb core having the same relative density, the auxetic 3D lattice core can lead to even better resistance.•FG configurations are found to have different effects on the impactor displacement and local transient thickness decrease of sandwich beams.
Auxetic metamaterials possess enhanced impact resistance and hence are the ideal core of sandwich structures. Here we present the enhancement of the drop-weight impact resistance of composite sandwich beams with nanocomposite facesheets by taking advantage of auxetic 3D lattice cores with FG (functionally graded) configurations. 2D and 3D lattice metamaterials with negative Poisson’s ratios (NPRs) were modeled, analyzed, and compared. Furthermore, the 3D lattice cores were designed to possess four FG patterns along the thickness direction. The mechanical properties of graphene reinforced composites (GRCs) were determined by means of micromechanical modeling according to the extended Halpin-Tsai model. In view of shape changes of lattices due to the localized deformation, full-scale finite element modeling is necessary, followed by nonlinear analysis. Compared with a re-entrant honeycomb core having the same relative density, the auxetic 3D lattice core can lead to even better resistance. Moreover, FG configurations are proven to have different effects on the impactor displacement and local transient thickness decrease of sandwich beams subjected to low-velocity impacts. Our results demonstrated the advantages of FG auxetic 3D lattices, and are expected to be beneficial to further studies and instructive for practical applications.
•Functionally graded auxetic 3D lattice metamaterials are designed for the first time.•Numerical and experimental investigates on the fundamental frequencies.•Full-scale modeling and nonlinear ...vibration analysis for sandwich plates.•FG configurations have distinct effect on the linear & nonlinear vibration behaviors.
Full-scale modeling and nonlinear FEA are presented for large amplitude vibration of sandwich plates with functionally graded (FG) auxetic 3D lattice core. For the first time, auxetic 3D lattice metamaterials with FG configurations along the out-of-plane direction are designed, of which the fundamental vibration frequencies are analyzed and verified by experiments using 3D printed specimens. Both results suggested that the effects of FG configurations and strut incline angles are significant, and the FG-X specimen possesses the highest fundamental frequency. Subsequently, by means of full-scale nonlinear FE simulations, the large amplitude vibration characteristics are investigated for the sandwich plates, in which the novel construction of auxetic 3D lattice core with three FG configurations along the thickness direction is proposed. And the constituent material properties are taken to be temperature-dependent. Results revealed that FG configurations have distinct effect on the natural frequencies, nonlinear-to-linear frequency ratios of sandwich plates, along with EPR-amplitude curves, which will become stable when the vibration amplitude is sufficiently large.
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•The initial deflection caused by lateral pressure is taken into account.•The initial deflection caused by thermal bending stresses is taken into account.•Temperature-dependent material properties ...are taken into account.•Nonlinear prebuckling deformations of the panel are taken into account.•The initial geometric imperfections of the panel are taken into account.
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.
The large amplitude vibration and nonlinear bending analyses for a perovskite solar cell (PSC) in thermal environments are presented through the plate-substrate model. The PSC film is modeled as a ...thin laminated plate which consists of five plies including ITO, PEDOT:PSS, perovskite, PCBM, and Au. Two kinds of graphene platelets reinforced composite (GPLRC) substrates are considered. The GPLRC substrate is modeled as a porous foundation with finite depth. The foundation stiffnesses are predicted by modified Vlasov model and the equivalent Young’s modulus of the foundation is estimated through a modified Halpin–Tsai model where the porosity coefficient is introduced. The material properties of GPLRC substrates are assumed to be temperature dependent. The thermal effect and plate-foundation interaction are involved in the governing equations which are solved by means of a two-step perturbation approach. The numerical investigations are carried out for the PSC plate rested on GPL/PMMA and GPL/Al substrates. It is shown that the substrate depth and porosity coefficient have substantial influences on the vibration response and nonlinear bending behavior of PSC plates.
•The concept of functionally graded materials is extended to the GRC laminated cylindrical panels.•A multi-scale approach for postbuckling analysis of FG GRC laminated cylindrical panels is ...proposed.•The panel-foundation interaction and temperature-dependent material properties are both taken into account.•A piece-wise FG reinforcement has a significant effect on the postbuckling behaviors of GRC laminated cylindrical panels.
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.
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•Both functionally graded configurations and negative Poisson's ratio are considered.•3D full scale FE simulations for FG-X, FG-O and UD sandwich beams.•The EPR-deflection curves are obtained for the ...first time.
This paper investigates the thermal post-buckling behavior of sandwich beams with functionally graded (FG) negative Poisson's ratio (NPR) honeycomb cores. Two symmetric FG configurations of re-entrant honeycomb cores along the beam thickness direction are proposed for the first time. The material properties of both face sheets and core of the sandwich beams are assumed to be temperature-dependent. The thermal post-buckling behavior and the variation of effective Poisson's ratio (EPR) of the sandwich beam in the large deflection region are studied by using 3D full scale finite element simulations. Numerical results are presented for the sandwich beams with FG-NPR honeycomb core under a uniform temperature field, from which results for the same sandwich beam with uniform distributed NPR honeycomb core are obtained as a comparator. The EPR-deflection curves are obtained for the first time, and the results reveal that greater bending stiffness could bring about higher EPR-deflection curve. The effects of functionally graded configurations, boundary conditions, facesheet-to-core thickness ratios, cell wall-to-facesheet thickness ratios and length-to-thickness ratios on the thermal post-buckling load-deflection curves and EPR-deflection curves of sandwich beams are discussed in detail.
