Pressure In Thermal Environments Research Articles

Buckling behavior of multilayer cylindrical shells composed of functionally graded nanocomposite layers under lateral pressure in thermal environments

In this study, the stability behavior of multilayer cylindrical shells made of functionally graded nanocomposite layers (FG-NCLs) subjected to the lateral pressure in thermal environments is investigated. It is postulated that nanocomposite layers forming layered cylindrical shells are made of single-walled carbon nanotube (SWCNT)-reinforced polymers that have four types of profiles based on the uniform and linear distributions of mechanical properties. The material properties of SWCNTs are assumed to be dependent on location as well as temperature and are obtained from molecular dynamics simulations. The governing equations are derived as partial differential equations within shear deformation theory (SDT) and solved in a closed form, using the Galerkin procedure, to determine the lateral critical pressure (LCP) in thermal environments. The numerical representations relate to the buckling behavior of multilayer cylindrical shells made of functionally graded nanocomposite layers under the uniform lateral pressure for different CNT patterns and temperatures within SDT and Kirchhoff-Love theory (KLT).

Buckling and postbuckling of functionally graded porous material nearly cylindrical shells under external lateral pressure in thermal environments

ABSTRACT This paper investigates the buckling and postbuckling of nearly cylindrical shell (NCS) made of functionally graded porous material (FGPM) and subjected to external lateral pressure (ELP) in thermal environments. The variation of two material constituents through the shell thickness is modelled by a power-law distribution. Porosities are assumed to distribute into FGPM according to forms of cosine functions. Basic equations in terms of deflection and stress function are established within the framework of classical shell theory taking into account von Kármán – Donnell nonlinearity. Boundary edges of the NCS are assumed to be simply supported and tangentially restrained. Multi-term analytical solutions are assumed and Galerkin method is used to derive expressions of buckling loads and nonlinear load–deflection relation. Parametric studies are carried out to assess the effects of coefficient and distribution type of porosity, thermal environments, geometry properties and in-plane boundary condition on the critical loads and postbuckling strength of pressure-loaded FGPM NCSs.

Nonlinear response of doubly curved sandwich panels with CNT-reinforced composite core and elastically restrained edges subjected to external pressure in thermal environments

An analytical investigation on the nonlinear response of doubly curved panels constructed from homogeneous face sheets and carbon nanotube reinforced composite (CNTRC) core and subjected to external pressure in thermal environments is presented in this paper. Carbon nanotubes (CNTs) are reinforced into the core layer through uniform or functionally graded distributions. The properties of constituents are assumed to be temperature dependent and effective properties of CNTRC are determined using an extended rule of mixture. Governing equations are established within the framework of first order shear deformation theory taking into account geometrical imperfection, von Kármán–Donnell nonlinearity, panel-foundation interaction and elasticity of tangential edge restraints. These equations are solved using approximate analytical solutions and Galerkin method for simply supported panels. The results reveal that load carrying capacity of sandwich panels is stronger when boundary edges are more rigorously restrained and face sheets are thicker. Furthermore, elevated temperature has deteriorative and beneficial influences on the load bearing capability of sandwich panels with movable and restrained edges, respectively.

Nonlinear buckling behavior of functionally graded material sandwich cylindrical shells with tangentially restrained edges subjected to external pressure and thermal loadings

An analytical investigation on buckling and postbuckling behavior of sandwich cylindrical shells comprising functionally graded material layers and subjected to uniform temperature rise and external pressure in thermal environments is presented in this paper. Two sandwich models corresponding to functionally graded material face sheets and core layer are considered. The properties of constitutive materials are assumed to be temperature dependent and effective properties of functionally graded material are determined according to linear rule of mixture. Formulations are based on the classical shell theory taking Von Karman–Donnell nonlinearity and elastic constraint at edges into consideration. Multi-term solutions of deflection and stress function are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to derive nonlinear load–deflection relations from which buckling loads and postbuckling paths are determined. The effects of sandwich configurations, material gradation, tangential constraints of edges, and temperature dependence of material properties on buckling loads and postbuckling curves are analyzed through numerical examples.

Nonlinear flexural behavior of temperature-dependent FG-CNTRC laminated beams with negative Poisson’s ratio resting on the Pasternak foundation

Nanocomposite materials, such as carbon nanotube-reinforced composites (CNTRCs), have emerged as a novel engineering material. They have received growing attentions in various engineering sectors. The fabrication process has also offered the possibility to design and make this type of material to have desired features, such as being functionally graded (FG) or/and having negative Poison’s ratio. This paper reports an investigation on the nonlinear flexural behavior of auxetic laminated beams with each layer is made of CNTRC. Each layer may have different CNT volume fractions and the functional grading occurs in the thickness direction of the beam in the piece-wise pattern. The extended rule of mixture model is used to evaluate the temperature-dependent material properties of CNTRCs. The governing equations for the nonlinear bending of FG-CNTRC laminated beams are derived based on the high order shear deformation beam theory. These equations include the geometrical nonlinearity in the von Kármán sense and take into account the thermal effect and the beam-foundation interaction. The nonlinear bending solutions can be obtained by employing a two-step perturbation approach. The nonlinear flexural responses of FG-CNTRC laminated beams under a uniform pressure in thermal environments are revealed and examined in details through a parametric study. Results showed that the negative Poisson’s ratio has a significant impact on the nonlinear flexural behavior of CNTRC laminated beams.

Thermomechanical nonlinear stability of pressure-loaded CNT-reinforced composite doubly curved panels resting on elastic foundations

AbstractNonlinear stability of nanocomposite spherical and cylindrical panels reinforced by carbon nanotubes (CNTs), resting on elastic foundations and subjected to uniform external pressure in thermal environments is investigated in this paper. CNTs are embedded into matrix phase through uniform distribution (UD) or functionally graded (FG) distribution, and effective properties of CNT-reinforced composite are estimated through an extended rule of mixture. Governing equations are based on classical shell theory taking geometrical nonlinearity, initial geometrical imperfection and panel-foundation interaction into consideration. Approximate solutions of deflection and stress functions are assumed to satisfy simply supported boundary conditions and Galerkin method is applied to obtain nonlinear load-deflection relation. Numerical examples show the effects of volume fraction and distribution type of CNTs, in-plane condition of edges, curvature of panel, thermal environments, elastic foundations and imperfection size on the nonlinear response and snap-through instability of the curved panels. The present study reveals that efficiency of CNT distribution type depends on curvature of panel and in-plane behavior of boundary edges, and bifurcation type buckling response of pressure-loaded panels may occur at elevated temperature.

Postbuckling of doubly curved FG-GRC laminated panels subjected to lateral pressure in thermal environments

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.

Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical shells subjected to external pressure in thermal environments

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.

Postbuckling of nanotube-reinforced composite cylindrical panels resting on elastic foundations subjected to lateral pressure in thermal environments

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.

Postbuckling of functionally graded fiber reinforced composite laminated cylindrical shells, Part I: Theory and solutions

Buckling and postbuckling behavior are presented for fiber reinforced composite (FRC) laminated cylindrical shells subjected to axial compression or a uniform external pressure in thermal environments. 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 with von Kármán-type of kinematic non-linearity and including the extension-twist, extension-flexural and flexural-twist couplings. 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. The non-linear prebuckling deformations and the 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 of FRC laminated cylindrical shells.

Nonlinear buckling behavior of 3D-braided composite cylindrical shells subjected to internal pressure loads in thermal environments

The nonlinear buckling behavior of a 3D-braided composite cylindrical shell of finite length subjected to internal pressure in thermal environments is considered. According to a new micromacromechanical model, a 3D-braided composite may be treated as a cell system where the geometry of each cell strongly depends on its position in the cross section of the cylindrical shell. The material properties of the epoxy matrix are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear deformation theory of shells with a von Karman–Donnell-type kinematic nonlinearity and include thermal effects. The singular perturbation technique is employed to determine the buckling pressure and the postbuckling equilibrium paths of the shell.

Postbuckling of nanotube-reinforced composite cylindrical shells in thermal environments, Part II: Pressure-loaded shells

A postbuckling analysis is presented for nanocomposite cylindrical shells reinforced by single-walled carbon nanotubes (SWCNTs) subjected to lateral or hydrostatic pressure in thermal environments. The multi-scale model for functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shells under external pressure is proposed and a singular perturbation technique is employed to determine the buckling pressure and postbuckling equilibrium path. Numerical results for pressure-loaded, perfect and imperfect, FG-CNTRC cylindrical shells are obtained 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 pressure as well as postbuckling strength of the shell under external pressure. The results reveal that the carbon nanotube volume fraction has a significant effect on the buckling pressure and postbuckling behavior of CNTRC shells.

Buckling and postbuckling of radially loaded microtubules by nonlocal shear deformable shell model

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.

Postbuckling of internal pressure loaded FGM cylindrical shells surrounded by an elastic medium

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 Karman-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.

Nonlinear Buckling and Postbuckling Behavior of 3D Braided Composite Cylindrical Shells Under External Pressure Loads in Thermal Environments

Nonlinear buckling and postbuckling behavior for a 3D braided composite cylindrical shell of finite length subjected to lateral pressure, hydrostatic pressure, or external liquid pressure in thermal environments have been presented in this paper. Based on a new micromacromechanical model, a 3D braided composite may be treated 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 the epoxy are expressed as a linear function of temperature. The governing equations are based on Reddy’s 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 pressure 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 pressures 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 pressure and postbuckling behavior of braided composite cylindrical shells.

Post-buckling of internal-pressure-loaded laminated cylindrical shells surrounded by an elastic medium

This paper presents a study on the post-buckling response of an anisotropic laminated 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 modelled as a tensionless Pasternak foundation reacting in compression only. The governing equations are based on higher-order shear deformation shell theory with von Kármán–Donnell kinematic non-linearity and including extension–twist, extension–flexural, and flexural–twist couplings. The thermal effects are also included, and the material properties are assumed to be temperature dependent. Non-linear prebuckling deformations and the initial geometric imperfections of the shell are both taken into account. A singular perturbation technique is employed to determine the post-buckling response of the shells, and an iterative scheme is developed to obtain numerical results without using any assumption concerning the shape of the contact region between the shell and the elastic medium. Numerical illustrations concern the buckling and post-buckling response of cross-ply and symmetric angle-ply laminated shells surrounded by an elastic medium of tensionless foundation of the Pasternak type, from which results for conventional elastic foundations are obtained as comparators. The results reveal that unilateral constraints have a significant effect on the post-buckling response of shells subjected to internal pressure in thermal environments when the foundation stiffness is sufficiently large.

Postbuckling of a shear-deformable anisotropic laminated cylindrical shell under external pressure in thermal environments

A postbuckling analysis is presented for a shear-deformable anisotropic laminated cylindrical shell of finite length subjected to external pressure in thermal environments. The material properties are expressed as linear functions of temperature. The governing equations are based on Reddy’s higher-order shear-deformation shell theory with the von Karman-Donnell-type kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. The boundary-layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling region, and the initial geometric imperfections of the shell, is extended to the case of shear-deformable anisotropic laminated cylindrical shells under lateral or hydrostatic pressure in thermal environments. The singular perturbation technique is employed to determine the interactive buckling loads and postbuckling equilibrium paths. The results obtained show that the variation in temperature, layer setting, and the geometric parameters of such shells have a significant influence on their buckling load and postbuckling behavior.

Postbuckling of Pressure-Loaded Functionally Graded Cylindrical Panels in Thermal Environments

A postbuckling analysis is presented for a functionally graded cylindrical panel of finite length subjected to lateral pressure in thermal environments. Material properties are assumed to be temperature dependent, and graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations of a functionally graded cylindrical panel are based on Reddy’s higher-order shear deformation shell theory with von Karman–Donnell-type of kinematic nonlinearity and include thermal effects. The two straight edges of the panel are assumed to be simply supported and two curved edges are either simply supported or clamped. The nonlinear prebuckling deformations and initial geometric imperfections of the panel are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflection in the postbuckling range, and initial geometric imperfections of the shell, i...