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This paper examines the postbuckling behaviors of pressure-loaded laminated cylindrical shells made of carbon nanotube reinforced composite (CNTRC) under thermal environmental conditions. The shell has negative in-plane or out-of-plane effective Poisson's ratio (EPR). The thermo-mechanical properties of CNTRCs are temperature dependent. The CNT volume fraction of the shell is in a piece-wise functionally graded (FG) distribution across the shell thickness. The extended rule of mixture (EROM) model is applied to determine the thermo-mechanical properties of CNTRCs. Based on the framework of the Reddy's third order shear deformation shell theory and the von Kármán-type of kinematic assumptions, the governing partial differential equations for pressure-loaded CNTRC laminated cylindrical shells are formulated. The thermal environmental condition effect is also included. The postbuckling solution for pressure-loaded FG-CNTRC laminated cylindrical shell is obtained in the asymptotic sense by means of a singular perturbation technique in associate with a two-step perturbation approach. Numerical investigations are carried out for the (10/60/10)S shell including in-plane NPR effect, and (20/-20/20)S and (70/-70/70)S shells including out-of-plane NPR effect. Assessment is presented through numerical comparisons. [ABSTRACT FROM AUTHOR]

This article presents an investigation on the postbuckling behavior of doubly curved graphene-reinforced composite (GRC) laminated panels supported by an elastic foundation and subjected to lateral pressure and in thermal environments. The piece-wise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the panels. The overall mechanical properties of the FG-GRCs are assumed to be temperature dependent and are estimated through the extended Halpin-Tsai micromechanical model. The governing differential equations for the doubly curved panels are based on a higher order shear deformation shell theory with von Kármán strain-displacement relationships and the panel-foundation interaction. 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. The postbuckling equilibrium path for the perfect and geometrically imperfect GRC laminated doubly curved panels are obtained by applying a singular perturbation technique along with a two-step perturbation approach. The impacts of material property gradient, temperature variation, panel curvature ratio, as well as foundation stiffness on the postbuckling behavior of FG-GRC laminated doubly curved panels are investigated. [ABSTRACT FROM AUTHOR]

Bio-inspired helicoidal carbon fiber reinforced polymer composite (CFRPC) laminates are one of the novel composite structures that have potential applications in many engineering fields. The optimization design of helicoidal layups with linear, nonlinear Recursive, Fibonacci, Exponential and their combination-form arrangements are carried out using ABAQUS and ASA algorithm on Isight platform. Two cases of the compressive postbuckling under uniaxial compression and the thermal postbuckling under uniform temperature rise of helicoidal CFRPC laminated plates stacked with optimal layups are performed and the secondary buckling and mode jumping in the postbuckling region are examined for the first time. Numerical investigations are carried out for 16-ply symmetrical helicoidal laminated plates with various width-to-thickness ratios under different boundary conditions and are compared with quasi-isotropic counterparts. The results show that the bio-inspired helicoidal CFRPC laminated plates can enhance the buckling load and the buckling temperature as well as the compressive and the thermal postbuckling strength. In some cases, the secondary buckling and mode jumping may occur for rectangular helicoidal laminated plate in the postbuckling region. [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]

Abstract This paper presents the buckling and postbuckling behaviors of graphene-reinforced composite (GRC) laminated cylindrical shells subjected to torsion in thermal environments. The GRC layers of the shell are arranged in a piece-wise functionally graded (FG) distribution pattern in the thickness direction and each layer of the shell contains different volume fraction of graphene reinforcement. The extended Halpin-Tsai micromechanical model is employed to determine the temperature dependent material properties of GRC layers. The governing equations of the GRC laminated cylindrical shells under torsion are derived based on a higher-order shear deformation shell theory with the geometric nonlinearity being defined by the von Kármán strain-displacement relationship. A singular perturbation technique along with a two-step perturbation approach is employed to determine the buckling torques and the torsional postbuckling equilibrium paths of the FG-GRC laminated cylindrical shells in thermal environments. The numerical results obtained reveal that the piece-wise FG distribution of graphene volume fraction can enhance the buckling torque and the torsional postbuckling strength while the rise of temperature may lead to the reduction of the torsional buckling torques and torsional postbuckling strength of the GRC laminated cylindrical shell. Highlights • The concept of functionally graded materials is extended to the GRC laminated cylindrical shells. • A multi-scale approach for the postbuckling analysis of GRC laminated cylindrical shells is proposed. • Temperature-dependent material properties are taken into account. • A piece-wise FG reinforcement has a significant effect on the torsional postbuckling behaviors of the GRC laminated shells. [ABSTRACT FROM AUTHOR]

The current investigation deals with the buckling and postbuckling behaviors of graphene-reinforced composite (GRC) laminated cylindrical shells subjected to lateral or hydrostatic pressure under thermal environmental conditions. The piece-wise GRC layers are arranged in a functionally graded (FG) pattern along the thickness direction of the shells. 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 from a molecular dynamics simulation study. We employ the Reddy’s higher order shear deformable shell theory in association with the von Kármán geometric nonlinearity to model the shell buckling problem under different thermal environmental conditions. The buckling pressure and the postbuckling equilibrium path for the perfect and geometrically imperfect GRC laminated cylindrical shells are obtained by applying a singular perturbation technique along with a two-step perturbation approach. We observe that the piece-wise functionally graded distribution of graphene reinforcement can increase the buckling pressure and the postbuckling strength of the GRC laminated cylindrical shells subjected to external pressure. [ABSTRACT FROM AUTHOR]

Present investigation deals with the buckling and postbuckling behavior of a sandwich plate with a homogeneous core and graphene-reinforced composite (GRC) face sheets resting on an elastic foundation in thermal environments. The material properties of GRC face sheets are assumed to be piece-wise functionally graded by changing the volume fraction of graphene in the thickness direction. The material properties of both the homogeneous core layer and the GRC face sheets are assumed to be temperature-dependent, and are estimated by the extended Halpin-Tsai micromechanical model. The higher order shear deformation plate theory and the von Kármán-type kinematic nonlinearity are used to derive the governing equations which account for the plate-foundation interaction and the thermal effects. The buckling loads and the postbuckling equilibrium paths are obtained by using a two-step perturbation technique. The impacts of the distribution type of reinforcements, core-to-face sheet thickness ratio, plate aspect ratio, temperature variation, foundation stiffness and in-plane boundary conditions on the postbuckling behavior of sandwich plates with functionally graded GRC face sheets are studied in detail. [ABSTRACT FROM AUTHOR]

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

The current study re-examines compressive postbuckling and thermal postbuckling responses of porous sandwich plates resting on an elastic foundation. The core of the sandwich plates is made of porous graphene platelets reinforced composite (GPLRC). Compressive postbuckling of the porous sandwich plates under uniaxial compression at elevated temperature and thermal postbuckling of the same plates under uniform thermal loading are studied. The GPLRC core is made of multilayers, and each layer may have different values of porosity coefficient to obtain a piecewise functionally graded (FG) pattern. The Young's moduli along with the shear modulus of the porous GPLRC core are estimated through a generic Halpin–Tsai model in which the porous nature of the material is taken into consideration. The material properties of the metal face sheets and the porous GPLRC core are assumed to be temperature dependent. The governing equations for the postbuckling of the porous sandwich plates reinforced by GPLs are established based on the Reddy's third order shear deformation theory (TSDT). In the modeling, we also consider the von Kármán nonlinear strain–displacement relationships, the plate-foundation interaction and the thermal effect. A two-step perturbation approach is utilized in solving the postbuckling problem. Numerical studies are performed to compare the results obtained from the present model and the equivalent isotropic model (EIM). The results confirm that the EIM is not suitable for analyzing buckling and postbuckling of porous plates. • A novel porous FG-GPLRC model is proposed. • Young's modulus, shear modulus and Poisson's ratio of porous matrix are all functions of porosity coefficient. • EIM is not suitable for analyzing buckling and postbuckling of porous sandwich plates reinforced by GPLs. [ABSTRACT FROM AUTHOR]

This paper presents the modeling and analysis for the thermal postbuckling of graphene-reinforced composite laminated plates resting on an elastic foundation and subjected to in-plane temperature variation. A micromechanical model is used to estimate the temperature-dependent material properties of the graphene-reinforced composites (GRCs). Piece-wise functionally graded (FG) GRC layers along the thickness direction of a plate is considered in this study. Employing the higher order shear deformation plate theory, the governing equations for FG-GRC plates are derived and the effects of plate-foundation interaction and temperature variation are included in the modeling. A two-step perturbation technique is applied to obtain the buckling temperature and the thermal postbuckling load-deflection curves for perfect and imperfect FG-GRC laminated plates. The results show that the buckling temperature as well as thermal postbuckling strength of the plates can be increased as a result of the functionally graded graphene reinforcement for the plates. [ABSTRACT FROM AUTHOR]

Modeling and analysis of the postbuckling behavior of graphene-reinforced composite (GRC) laminated plates are presented in this paper. The GRC plates are in a thermal environment, subjected to uniaxial compression and resting on an elastic foundation. The temperature-dependent material properties of functionally graded graphene-reinforced composites (FG-GRCs) are assumed to be graded in the plate thickness direction with a piece-wise type, and are estimated through a micromechanical model. The postbuckling problem of FG-GRC laminated plates is modeled using a higher order shear deformation plate theory and the plate-foundation interaction and thermal effects are taken into consideration. A two-step perturbation technique is employed to determine the buckling loads and the postbuckling equilibrium paths. The compressive buckling and postbuckling behavior of perfect and imperfect, geometrically mid-plane symmetric FG-GRC laminated plates under different sets of thermal environmental conditions is obtained and is also compared with the behavior of uniformly distributed GRC laminated plates. The results show that the buckling loads as well as the postbuckling strength of the GRC laminated plates may be enhanced through piece-wise functionally graded distribution of graphene. [ABSTRACT FROM AUTHOR]

This paper presents an investigation on the nonlinear bending and thermal postbuckling behaviors of nanocomposite beams in thermal environments and supported by an elastic foundation. Graphene-reinforced composite (GRC) material is used for the beams with piece-wise functionally graded (FG) graphene reinforcement along the thickness direction of the beams. A refined micromechanical model is applied to estimate the material properties of GRCs and the effect of temperature is included in the model. The governing equations of a GRC beam are based on a higher third order beam theory with the effect of temperature variation and foundation interaction and the von Kármán geometric nonlinear strain terms are also considered. Applying a two-step perturbation technique, the governing equations of the GRC beams are solved to determine the nonlinear bending load-deflection curves and the thermal postbuckling equilibrium paths of the beams. The effects of the graphene reinforcement distribution, laminate layer stacking sequence, temperature variation and foundation stiffness on the nonlinear bending and thermal postbuckling behaviors of the beams are discussed in details. [ABSTRACT FROM AUTHOR]

This paper investigates the small- and large-amplitude vibrations of thermally postbuckled sandwich plates with carbon nanotube-reinforced composite (CNTRC) face sheets resting on elastic foundations. Two types of CNTRC face sheets, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. The motion equations are derived based on a higher order shear deformation plate theory. The nonlinearity effect is taken into account in the sense of von Kármán nonlinear kinematic assumption. The plate-foundation interaction and the initial deflection caused by thermal postbuckling are also included. The numerical illustrations concern small- and large-amplitude vibration characteristics of thermally postbuckled sandwich plates with CNTRC face sheets under uniform temperature field. The effects of CNT volume fraction and distribution pattern of face sheets, the core-to-face sheet thickness ratio as well as foundation stiffness on the vibration characteristics of sandwich plates are examined in detail. [ABSTRACT FROM AUTHOR]

This paper studies the compressive buckling of near-square rippled monolayer graphene sheets in thermal environments by using molecular dynamics simulations. Armchair and zigzag graphene sheets are both considered and the four edges of a graphene sheet are either simply supported or clamped. Compressive force instead of the commonly used compressive strain is gradually applied to the edges of the graphene sheet until the graphene sheet is crushed. It is found that ripples in the graphene are formed owing to thermal fluctuations even before the compressive force is applied. The amplitude of ripples is reduced when the compressive force is applied to the graphene. The buckling mode of the graphene may show local or global mode shape features, depending on the chirality, the support conditions and the size of the graphene. Most buckling modes of the graphene sheets are very different from the global (1,1) mode of a uniaxially loaded and simply supported or clamped square plate as predicted by continuum mechanics models. A clamped graphene can take significantly more compressive force after the occurrence of initial buckling and before the graphene is completely crushed. A zigzag graphene has a larger initial buckling force than its armchair counterpart. Raising the environmental temperature may either increase or decrease the initial buckling force of the graphene depending on the support conditions and the chirality of the graphene. [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]

This paper investigates the nonlinear bending in thermal environments and thermal postbuckling of hybrid laminated beams with piezoelectric fiber reinforced composite (PFRC) actuators resting on an elastic foundation. The beam is made of fiber-reinforced composites (FRCs) with the reinforcement being distributed either uniformly (UD) or functionally graded (FG) of piece-wise type along the thickness of the beam. The formulations are based on a higher order shear deformation theory and von Kármán strain displacement relationships. The beam–foundation interaction and thermo-piezoelectric effects are also included, and the material properties of both FRCs and PFRCs are estimated through a micromechanical model and are assumed to be temperature dependent. The nonlinear bending load-deflection curves and the thermal postbuckling equilibrium paths of hybrid laminated beams are determined by means of a two-step perturbation approach. The effects of the material property gradient, temperature variation, applied voltage, stacking sequence as well as the foundation stiffness on the nonlinear bending and thermal postbuckling behaviors of the hybrid laminated beams are investigated through a comprehensive parametric study. [ABSTRACT FROM AUTHOR]

Modeling and analysis for the postbuckling of FGM doubly curved panels resting on elastic foundations and subjected to lateral pressure under heat conduction are presented. The initial deflections caused by lateral pressure and thermal bending stresses are both taken into account. The temperature-dependent material properties of functionally graded materials (FGMs) are assumed to be graded in the thickness direction based on Mori–Tanaka micromechanics model. The formulations are based on a higher order shear deformation theory with von Kármán strain–displacement relationships. The panel-foundation interaction and thermal effects are also included. The governing equations are first deduced to a boundary layer type that includes nonlinear prebuckling 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 effects of volume fraction index, temperature variation, the panel geometric parameters as well as foundation stiffness on the postbuckling behavior of FGM doubly curved panels are discussed in detail. [ABSTRACT FROM AUTHOR]

In this part, the extensive parametric studies performed are reported and numerical results are presented for the nonlinear vibration, nonlinear bending and thermal postbuckling of uniformly distributed and functionally graded fiber reinforced cross-ply and angle-ply laminated beams resting on Pasternak elastic foundations under different sets of hygrothermal environmental conditions. The numerical results reveal that a functionally graded reinforcement has a significant effect on the nonlinear vibration characteristics, nonlinear bending behaviors, and thermal postbuckling behaviors of fiber reinforced composite (FRC) laminated beams. The results show that the temperature/moisture variation has a moderately effect on the natural frequencies of the FRC laminated beam, but only has a small effect on the nonlinear to linear frequency ratios of the same beam. In contrast, it has a significant effect on the nonlinear bending load–deflection curves of the FRC laminated beam. The results confirm that the thermal postbuckling equilibrium path of mid-plane unsymmetric FG-FRC laminated beams with immovable simply supported end conditions is no longer the bifurcation type. [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]

This paper presents a postbuckling analysis of carbon nanotube-reinforced composite (CNTRC) cylindrical panels resting on elastic foundations and subjected to axial compression in thermal environments. The cylindrical panels are reinforced by aligned single-walled carbon nanotubes (SWCNTs) which are assumed to be functionally graded (FG) through the thickness direction with different types of distributions. The material properties of FG-CNTRC panels are estimated through an extended rule of mixture micromechanical model. The governing 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. A singular perturbation technique along with a two-step perturbation approach is employed to determine the buckling loads and postbuckling equilibrium paths. Numerical results reveal that the CNT volume fraction, temperature rise, foundation stiffness, and the panel geometric parameters have a significant effect on the buckling load and postbuckling behavior of CNTRC cylindrical panels. The results for uniformly distributed (UD) CNTRC cylindrical panels are compared with those of FG-CNTRC cylindrical panels. The results also confirm that for an CNTRC cylindrical panel with immovable unloaded straight edges, the postbuckling path of the panel is no longer the bifurcation type. [ABSTRACT FROM AUTHOR]

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

A postbuckling analysis is presented for a functionally graded composite cylindrical shell reinforced by single-walled carbon nanotubes (SWCNTs) subjected to torsion in thermal environments. The multi-scale model for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells under torsion is proposed. A singular perturbation technique along with a two-step perturbation approach is employed to determine the buckling load and postbuckling equilibrium path. The numerical illustrations concern the torsional buckling and postbuckling behavior of perfect and imperfect, FG-CNTRC cylindrical shells under different sets of thermal environmental conditions. The results for uniformly distributed CNTRC shell, which is a special case in the present study, are compared with those of the FG-CNTRC shell. The results show that the linear functionally graded reinforcements can increase the buckling torque as well as postbuckling strength of the shell under torsion when the reinforcement has a symmetrical distribution. The results reveal that the carbon nanotube volume fraction has a significant effect on the buckling load and postbuckling behavior of CNTRC shells under torsion. [ABSTRACT FROM AUTHOR]

Highlights: [•] We propose a nonlocal shear deformable shell model for torsional buckling of MTs in thermal environments. [•] We show that the buckling torque is decreased with increase in the small scale parameter e 0 a. [•] We show that the MT under torsion has a weakly unstable postbuckling path. [Copyright &y& Elsevier]

Thermal buckling and postbuckling behavior is presented for fiber-reinforced laminated plates subjected to in-plane temperature variation and resting on an elastic foundation. Two kinds of fiber-reinforced laminated plates, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of fiber-reinforced laminated plates are based on a micromechanical model and are assumed to be temperature dependent. The governing equations are based on a higher order shear deformation plate theory that includes plate–foundation interaction and the thermal effect. Numerical illustrations are carried out for fiber-reinforced polymer matrix and metal matrix composite laminated plates without or resting on elastic foundations. The numerical results show that the buckling temperature as well as thermal postbuckling strength of the plate can be increased as a result of functionally graded fiber reinforcements. The results reveal that the effect of functionally graded fiber reinforcements on the thermal buckling and postbuckling strength of the plate with polymer matrix is more pronounced compared to the plate with metal matrix. [ABSTRACT FROM AUTHOR]

Modelling and analysis of compressive and thermal postbuckling of sandwich cylindrical panels supported by an elastic foundation are presented in this paper. The sandwich cylindrical panel is composed of auxetic graphene-reinforced metal matrix composite (GRMMC) core with negative Poisson's ratio (NPR) and two metal face sheets. Two cases of the compressive postbuckling of auxetic sandwich cylindrical panels under axial compression in thermal environments and the thermal postbuckling of auxetic sandwich cylindrical panels caused by uniform temperature rise are considered. In the GRMMC core, the volume fraction of graphene through the thickness domain is arranged as a piece-wise functionally graded (FG) pattern. The material properties of both metal face sheets and the GRMMC core are assumed to be temperature dependent. The governing equations of the auxetic sandwich cylindrical panels are formulated based on the framework of the Reddy's third order shear deformation theory. The von Kármán-type kinematic nonlinearity, the thermal effect, the panel-foundation interaction and the initial geometric imperfection of the panel are also taken into account. The postbuckling solutions are obtained by employing a singular perturbation technique along with a two-step perturbation approach. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and foundation stiffness on the postbuckling behavior of sandwich cylindrical panels with FG auxetic GRMMC core are studied in detail. [ABSTRACT FROM AUTHOR]

In this paper, modeling and analysis of postbuckling of sandwich cylindrical shells surrounded by an elastic medium are presented. The sandwich cylindrical shells consist of two metal face sheets and auxetic graphene-reinforced metal matrix composite (GRMMC) core with in-plane negative Poisson's ratio (NPR). Two cases of the compressive postbuckling of sandwich cylindrical shells under axial compression in thermal environments and the thermal postbuckling of sandwich cylindrical shells caused by a uniform temperature rise are considered. Each ply of auxetic GRMMC core possesses in-plane NPR and can have different graphene volume fraction to achieve a piece-wise functionally graded (FG) distribution through the thickness domain of the core. The thermo-mechanical properties of both metal face sheets and the GRMMC core are temperature dependent. The governing equations are formulated based on the Reddy's third order shear deformation shell theory coupled with von Kármán kinematic nonlinearity. The shell-foundation interaction and the thermal effects are considered in the modeling. Applying a singular perturbation technique in conjunction with a two-step perturbation approach, we obtain the postbuckling solutions for perfect and imperfect sandwich cylindrical shells. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and the foundation stiffness on the postbuckling behaviors of sandwich cylindrical shells with auxetic GRMMC core are studied in detail. • Postbuckling of sandwich cylindrical shells with auxetic GRMMC core is presented for the first time. • Both in-plane negative Poisson's ratios and functionally graded patterns are considered. • The material properties of GRMMC core and face sheets are temperature dependent. [ABSTRACT FROM AUTHOR]

This paper investigates the postbuckling behavior of carbon fiber reinforced thermoplastic composite (CFRTPC) laminated plates under uni-axial compression-after-impact (CAI). A physical model is proposed where both internal damage and local geometric imperfection of the plate caused by impact are taken into account. The distributed damage and impacted region of the plate are determined by using X-ray computed tomography analysis. An experiment-based approach is utilized to obtain the nonlinear constitutive law along with the stiffness degradation for the CFRTPC laminated plates. The experiments for two CFRTPC laminated plates under uni-axial compression-after-impact are carried out firstly. Then the experimental data are compared with finite element numerical results to validate the present method. The numerical results reveal that the postbuckling load-deflection curves of CFRTPC laminated plates under CAI are significantly influenced by the initial local geometric imperfection, impact point position, plate width-to-thickness ratio and boundary conditions. In contrast, the initial local geometric imperfection and impact point position only have a small effect on the postbuckling load-shortening curves of CFRTPC laminated plates under CAI. [ABSTRACT FROM AUTHOR]

Abstract: Thermal buckling and postbuckling behavior are presented for fiber reinforced composite (FRC) laminated cylindrical shells embedded in a large outer elastic medium and subjected to a uniform temperature rise. The surrounding elastic medium is modeled as a Pasternak foundation. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The governing 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 FRC laminated cylindrical shells are estimated through a micromechanical model and are assumed to be temperature dependent. Numerical illustrations are carried out for perfect and imperfect, UD and FG fiber reinforced metal matrix composite laminated cylindrical shells with different values of shell parameters and stacking sequence. The numerical results show that the buckling temperature as well as thermal postbuckling strength of the FRC shells can be increased as a result of functionally graded fiber reinforcements. The results reveal that the thermal postbuckling equilibrium path of the FRC shells with metal matrix may be stable or weakly unstable due to the different values of shell parameter and stacking sequence. [Copyright &y& Elsevier]

This paper presents a study on the thermal postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium. The surrounding elastic medium is modeled as a Pasternak foundation. Two kinds of micromechanics models, namely the Voigt model and Mori-Tanaka model, are considered. The governing 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 functionally graded materials (FGMs) are assumed to be temperature dependent. The governing equations are solved by a singular perturbation technique. The numerical results show that in some cases the FGM cylindrical shell with intermediate volume fraction index does not have intermediate buckling temperature and thermal postbuckling strength. The results reveal that Voigt model and Mori-Tanaka model have the same accuracy for predicting the thermal buckling and postbuckling behavior of FGM shells. The results confirm that for the case of heat conduction, the postbuckling equilibrium path for geometrically perfect FGM cylindrical shells with simply supported boundary conditions is no longer of the bifurcation type. [ABSTRACT FROM AUTHOR]

This article investigates the buckling and postbuckling behavior of an anisotropic laminated cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The governing equations are based on a higher order shear deformation shell theory with von Kármán-type of kinematic nonlinearity and including the extension-twist, extension- flexural, and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical illustrations concern the buckling and postbuckling response of laminated cylindrical shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for laminated shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large. [ABSTRACT FROM PUBLISHER]

Abstract: This paper deals with the large amplitude vibration, non-linear bending and postbuckling of fiber reinforced composite laminated plates resting on an elastic foundation in hygrothermal environments. Two kinds of fiber reinforced laminated plates, namely, uniformly distributed and functionally graded reinforcements, are considered. The material properties of fiber reinforced laminated plates are estimated through a micromechanical model and are assumed to be temperature-dependent and moisture-dependent. The motion equations are based on a higher order shear deformation plate theory that includes plate-foundation interaction and the hygrothermal effect. A two-step perturbation technique is employed to determine the non-linear to linear frequency ratios of plate vibration, the load-deflection and load-bending moment curves of plate bending, and postbuckling equilibrium paths of laminated plates. [Copyright &y& Elsevier]

Abstract: This paper investigates compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise are presented of a sandwich plate with carbon nanotube-reinforced composite (CNTRC) face sheets resting on an elastic foundation. The material properties of CNTRC face sheets are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations of the plate are based on a higher-order shear deformation plate theory that includes plate-foundation interaction. The thermal effects are also included and the material properties of both CNTRC face sheets and homogeneous core layer are assumed to be temperature-dependent. A two-step perturbation technique is employed to determine buckling loads (temperature) and postbuckling equilibrium paths. The numerical illustrations concern the compressive and thermal postbuckling behavior of perfect and imperfect, sandwich plates with functionally graded CNTRC face sheets resting on Pasternak elastic foundations under different thermal environmental conditions, from which results for the sandwich plate with uniformly distributed CNTRC face sheets are also obtained for comparison purposes. The results reveal that the foundation stiffness, the temperature changes, the nanotube volume fraction of face sheet, and the core-to-face sheet thickness ratio have significant effects on the compressive buckling load and postbuckling behavior of the sandwich plate, whereas this effect on the thermal postbuckling behavior is less pronounced for the same sandwich plate. [Copyright &y& Elsevier]

Abstract: Thermal postbuckling analysis is presented for nanocomposite cylindrical shells reinforced by single-walled carbon nanotubes (SWCNTs) subjected to a uniform temperature rise. The SWCNTs are assumed to be aligned and straight with a uniform layout. Two kinds of carbon nanotube-reinforced composite (CNTRC) shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are based on a higher order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. Based on the multi-scale approach, numerical illustrations are carried out for perfect and imperfect, FG- and UD-CNTRC shells under different values of the nanotube volume fractions. The results show that the buckling temperature as well as thermal postbuckling strength of the shell can be increased as a result of a functionally graded reinforcement. It is found that in most cases the CNTRC shell with intermediate nanotube volume fraction does not have intermediate buckling temperature and initial thermal postbuckling strength. [Copyright &y& Elsevier]

Abstract: In this Part, the extensive parametric studies performed are reported and numerical results are presented for the buckling and postbuckling of fiber reinforced polymer matrix and metal matrix composite laminated shells subjected to axial compression or external pressure under different sets of environmental conditions. Two kinds of fiber reinforced composite laminated shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The numerical results show that the buckling loads as well as postbuckling strength of the shell can be increased as a result of functionally graded fiber reinforcements. The results reveal that the effect of functionally graded fiber reinforcements on the buckling loads and postbuckling strength of shell with polymer matrix is more pronounced compared to the shell with metal matrix in the case of axial compression. In contrast, in the case of external pressure, the functionally graded fiber reinforcements may have a significant effect on the buckling pressure and postbuckling strength of the shell with metal matrix. [Copyright &y& Elsevier]

Postbuckling, nonlinear bending, and nonlinear vibration analyses are presented for a simply supported Euler-Bernoulli beam resting on a two-parameter elastic foundation. The nonlinear model is introduced by using the exact expression of the curvature. Two kinds of end conditions, namely movable and immovable, are considered. The nonlinear equation of motion, including beam-foundation interaction, is derived separately for these two kinds of end conditions. The analysis uses a two-step perturbation technique to determine the postbuckling equilibrium paths of an axially loaded beam, the static large deflections of a bending beam subjected to a uniform transverse pressure, and the nonlinear frequencies of a beam with or without initial stresses. The numerical results confirm that the foundation stiffness has a significant effect on the nonlinear behavior of Euler-Bernoulli beams. The results also reveal that the end condition has a great effect on the nonlinear bending and nonlinear vibration behaviors of Euler-Bernoulli beams with or without elastic foundations. [ABSTRACT FROM AUTHOR]

Abstract: A postbuckling analysis is presented for nanocomposite cylindrical shells reinforced by single-walled carbon nanotubes (SWCNTs) subjected to axial compression in thermal environments. Two kinds of carbon nanotube-reinforced composite (CNTRC) shells, namely, uniformly distributed (UD) and functionally graded (FG) reinforcements, are considered. The material properties of FG-CNTRCs are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. The governing equations are based on a higher order shear deformation theory with a von Kármán-type of kinematic nonlinearity. The thermal effects are also included and the material properties of CNTRCs are assumed to be temperature-dependent. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of axially-loaded, perfect and imperfect, FG-CNTRC cylindrical shells under different sets of thermal environmental conditions. The results for UD-CNTRC shell, which is a special case in the present study, are compared with those of the FG-CNTRC shell. The results show that the linear functionally graded reinforcements can increase the buckling load as well as postbuckling strength of the shell under axial compression. The results reveal that the CNT volume fraction has a significant effect on the buckling load and postbuckling behavior of CNTRC shells. [Copyright &y& Elsevier]

Abstract: This paper studied compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise for a shear deformable laminated plate with piezoelectric fiber reinforced composite (PFRC) actuators based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The material properties are assumed to be temperature-dependent and the initial geometric imperfection of the plate is considered. The compressive and thermal postbuckling behaviors of perfect, imperfect, symmetric cross-ply and antisymmetric angle-ply laminated plates with fully covered or embedded PFRC actuators are conducted under different sets of thermal and electric loading conditions. The results reveal that, the applied voltage usually has a small effect on the postbuckling load–deflection relationship of the plate with PFRC actuators in the compressive buckling case, whereas the effect of applied voltage is more pronounced for the plate with PFRC actuators, compared to the results of the same plate with monolithic piezoelectric actuators. [Copyright &y& Elsevier]

Abstract: Postbuckling, nonlinear bending and nonlinear vibration analyses are presented for single-wall carbon nanotubes (SWCNTs) resting on a two-parameter elastic foundation in thermal environments. The SWCNT is modeled as a nonlocal nanobeam which contains small scale effects. The elastomeric substrate with finite depth is modeled as a two-parameter elastic foundation. The thermal effects are included and the material properties of both SWCNTs and the substrate are assumed to be temperature-dependent. The governing equation that includes beam–foundation interaction is solved by a two-step perturbation technique. The numerical results reveal that the small scale parameter e 0 a reduces the postbuckling equilibrium paths, the static large deflections and natural frequencies of SWCNTs resting on an elastic foundation. The results also reveal that the effect of the small scale parameter is significant for compressive buckling, but less pronounced for static bending and marginal for free vibration of SWCNTs resting on an elastic foundation. [ABSTRACT FROM AUTHOR]

Abstract: A nonlocal shear deformable shell model is developed for buckling of microtubules embedded in an elastic matrix of cytoplasm under bending in thermal environments. The results reveal that the lateral constraint has a significant effect on the buckling moments of a microtubule when the foundation stiffness is sufficiently large. [ABSTRACT FROM AUTHOR]

Abstract: Thermal buckling and postbuckling behavior is presented for functionally graded nanocomposite plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to in-plane temperature variation. The material properties of SWCNTs are assumed to be temperature-dependent and are obtained from molecular dynamics simulations. The material properties of functionally graded carbon nanotube-reinforced composites (FG-CNTRCs) are assumed to be graded in the thickness direction, and are estimated through a micromechanical model. Based on the multi-scale approach, numerical illustrations are carried out for perfect and imperfect, geometrically mid-plane symmetric FG-CNTRC plates and uniformly distributed CNTRC plates under different values of the nanotube volume fractions. The results show that the buckling temperature as well as thermal postbuckling strength of the plate can be increased as a result of a functionally graded reinforcement. It is found that in some cases the CNTRC plate with intermediate nanotube volume fraction does not have intermediate buckling temperature and initial thermal postbuckling strength. [Copyright &y& Elsevier]

Abstract: This paper presents an investigation on the buckling and postbuckling of microtubules (MTs) subjected to a uniform external radial pressure in thermal environments. The microtubule is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent. A singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium paths. The small scale parameter e 0 a is estimated by matching the buckling pressure of MTs measured from the experiments with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling pressure and postbuckling behavior of MTs are very sensitive to the small scale parameter e 0 a. The results reveal that the 13_3 microtubule has a stable postbuckling path, whereas the 13_2 microtubule has an unstable postbuckling behavior due to the presence of skew angles. [Copyright &y& Elsevier]

Compressive postbuckling under thermal environments and thermal postbuckling due to uniform temperature field are presented for an anisotropic laminated cylindrical thin shell with piezoelectric fiber reinforced composite (PFRC) actuators. The governing equations are based on the classical shell theory with a von Karman-Donnell-type of kinematic nonlinearity and including the extension-twist, extension-flexural and flexural-twist couplings. The thermo-piezoelectric effects are also included and the material properties are assumed to be temperature-dependent and the electric field considered only has non-zero-valued component EZ. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine buckling loads (temperature) and postbuckling equilibrium paths. The numerical illustrations concern the compressive and thermal postbuckling behavior of perfect and imperfect, anisotropic laminated cylindrical shells with fully covered or embedded PFRC actuators under different sets of thermal and electric loading conditions, from which results for monolithic piezoelectric actuators are obtained as comparators. The results reveal that, in the compressive buckling case, the control voltage only has a small effect on the postbuckling load-deflection curves of the shell with PFRC actuators, whereas in the thermal buckling case, the effect of control voltage is more pronounced for the shell with PFRC actuators, compared to the results of the same shell with monolithic piezoelectric actuators. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a study on the postbuckling response of a functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to internal pressure in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless elastic foundation of the Pasternak-type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that the unilateral constraint has a significant effect on the postbuckling response of shells subjected to internal pressure in thermal environments when the foundation stiffness is sufficiently large. [Copyright &y& Elsevier]

Abstract: This paper presents an investigation on the buckling and postbuckling of double-walled carbon nanotubes (CNTs) subjected to torsion in thermal environments. The double-walled carbon nanotube is modeled as a nonlocal shear deformable cylindrical shell which contains small scale effects and van der Waals interaction forces. The governing equations are based on higher order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and include the extension-twist and flexural-twist couplings. The thermal effects are also included and the material properties are assumed to be temperature-dependent and are obtained from molecular dynamics (MD) simulations. The small scale parameter is estimated by matching the buckling torque of CNTs observed from the MD simulation results with the numerical results obtained from the nonlocal shear deformable shell model. The results show that buckling torque and postbuckling behavior of CNTs are very sensitive to the small scale parameter . The results reveal that the size-dependent and temperature-dependent material properties have a significant effect on the torsional buckling and postbuckling behavior of both single-walled and double-walled CNTs. [Copyright &y& Elsevier]

Abstract: Compressive postbuckling under thermal environments and thermal postbuckling due to a uniform temperature rise are presented for a simply supported, shear deformable functionally graded plate with piezoelectric fiber reinforced composite (PFRC) actuators. The material properties of functionally graded materials (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 the material properties of both FGM and PFRC layers are assumed to be temperature-dependent. The governing equations are based on a higher order shear deformation plate theory that includes thermo-piezoelectric effects. The initial geometric imperfection of the plate is taken into account. A two step perturbation technique is employed to determine buckling loads (temperature) and postbuckling equilibrium paths. The numerical illustrations concern the compressive and thermal postbuckling behaviors of perfect and imperfect, geometrically mid-plane symmetric FGM plates with fully covered or embedded PFRC actuators under different sets of thermal and electric loading conditions. The results for monolithic piezoelectric actuator, which is a special case in the present study, are compared with those of PFRC actuators. The results reveal that, in the compressive buckling case, the applied voltage usually has a small effect on the postbuckling load–deflection curves of the plate with PFRC actuators, whereas in the thermal buckling case, the effect of applied voltage is more pronounced for the plate with PFRC actuators, compared to the results of the same plate with monolithic piezoelectric actuators. [Copyright &y& Elsevier]

Abstract: A postbuckling analysis is presented for a functionally graded cylindrical shell subjected to torsion in thermal environments. Heat conduction and temperature-dependent material properties are both taken into account. The temperature field considered is assumed to be a uniform distribution over the shell surface and varied in the thickness direction. The material properties of functionally graded materials (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 governing equations are based on a higher order shear deformation theory with a von Kármán–Donnell-type of kinematic non-linearity. The non-linear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling load and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of twist, perfect and imperfect, FGM cylindrical shells under different sets of thermal fields. The results reveal that the volume fraction distribution of FGMs has a significant effect on the buckling load and postbuckling behavior of FGM cylindrical shells subjected to torsion. They also confirm that the torsional postbuckling equilibrium path is weakly unstable and the shell structure is virtually imperfection–insensitive. [Copyright &y& Elsevier]

Abstract: This paper presents a study on the postbuckling response of a shear deformable functionally graded cylindrical shell of finite length embedded in a large outer elastic medium and subjected to axial compressive loads in thermal environments. The surrounding elastic medium is modeled as a tensionless Pasternak foundation that reacts in compression only. The postbuckling analysis is based on a higher order shear deformation shell theory with von Kármán–Donnell-type of kinematic nonlinearity. The thermal effects due to heat conduction are also included and the material properties of functionally graded materials (FGMs) are assumed to be temperature-dependent. The nonlinear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the postbuckling response of the shells and an iterative scheme is developed to obtain numerical results without using any assumption on the shape of the contact region between the shell and the elastic medium. Numerical solutions are presented in tabular and graphical forms to study the postbuckling behavior of FGM shells surrounded by an elastic medium of tensionless Pasternak foundation, from which the postbuckling results for FGM shells with conventional elastic foundations are also obtained for comparison purposes. The results reveal that the unilateral constraint has a significant effect on the postbuckling responses of shells subjected to axial compression in thermal environments when the foundation stiffness is sufficiently large. [Copyright &y& Elsevier]

Abstract: A postbuckling analysis is presented for a 3D braided composite cylindrical shell of finite length subjected to torsion in thermal environments. Based on a micro–macro-mechanical model, a 3D braided composite may be as a cell system and the geometry of each cell is deeply dependent on its position in the cross section of the cylindrical shell. The material properties of epoxy are expressed as a linear function of temperature. The governing equations are based on a higher-order shear deformation shell theory with a von Kármán–Donnell-type of kinematic nonlinearity and including thermal effects. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, braided composite cylindrical shells with different values of geometric parameter and of fiber volume fraction in different cases of thermal environmental conditions. The results show that the shell has lower buckling loads and postbuckling paths when the temperature-dependent properties are taken into account. The results reveal that the temperature changes, the fiber volume fraction, and the shell geometric parameter have a significant effect on the buckling load and postbuckling behavior of braided composite cylindrical shells. They also confirm that the torsional postbuckling equilibrium path of a moderately thick shell is stable and the shell structure is virtually imperfection–insensitive. [Copyright &y& Elsevier]

A postbuckling analysis is presented for a shear deformable anisotropic laminated cylindrical shell of finite length subjected to torsion. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear deformation shell theory with von Karman-Donnell-type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a shear stress along with an associate compressive stress when the shell is subjected to torsion. The postbuckling equilibrium path is stable for a moderately thick laminated cylindrical shell under torsion and the shell structure is virtually imperfection-insensitive. [ABSTRACT FROM AUTHOR]

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to axial compression. The material of each layer of the shell is assumed to be linearly elastic, anisotropic and fiber-reinforced. The governing equations are based on a higher order shear-deformable shell theory with the von Kármán–Donnell type of kinematic nonlinearity and including the extension/twist, extension/flexural and flexural/twist couplings. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling response of perfect and imperfect, moderately thick, anisotropic laminated cylindrical shells with different values of shell parameters and stacking sequence. The results confirm that there exists a compressive stress along with an associate shear stress and twisting when the anisotropic shell is subjected to axial compression. The postbuckling equilibrium path is unstable for the moderately thick cylindrical shell under axial compression and the shell structure is imperfection-sensitive. [ABSTRACT FROM AUTHOR]