Cylindrical Shells In Thermal Environments Research Articles

Analyzing the nonlinear torsional buckling and post-buckling of ES-FG porous cylindrical shells in thermal environment using FSDT in terms of the displacement components

The main aim of this paper is to investigate the nonlinear buckling and post-buckling of eccentrically stiffened sandwich functionally graded porous (FGP) cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach in terms of the displacement components. The shells are reinforced by eccentric rings and stringers attached to the inside and material properties of face sheets and stiffeners are assumed to be continuously graded in the thickness direction. The sandwich cylindrical shell is composed of FG porous core and two FG layer coating. Based on the first order shear deformation theory (FSDT) with von Kármán geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived. Using Galerkin method, the closed form to find critical torsional load and post-buckling load-deflection curves are obtained. The effects of porosity parameters, the thickness of the porous core, temperature, stiffener, foundation, material and dimensional parameters are analyzed.

Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment

Based on Love’s thin shell theory, an effort is made to investigate the nonlinear primary resonance response of axially moving functionally graded materials (FGM) cylindrical shells subjected to external excitations in thermal environment. Two kinds of temperature fields, namely, uniform temperature rise and heat conduction, are considered. The effective material properties of the FGM cylindrical shells are temperature-dependent. The equations of motion are derived using Euler-Lagrange principle and solved by multiple scale method, in which the cylindrical shell with four clamped edges is considered. Finally, the effects of different influencing factors on the nonlinear resonance response are discussed.

Free and forced vibration analysis of thin-walled cylindrical shells with arbitrary boundaries in steady thermal environment

This paper presents a method for predicting the free and forced vibration behavior of open and closed cylindrical shells in the steady-state thermal environment. The vibration characteristics of cylindrical shells in thermal environment are studied by considering the changes of the thermal strain in the cylindrical shell and the material properties caused by temperature rise. Based on Spectral-Geometry Method (SGM), the displacement functions of cylindrical shell are expressed as the improved Fourier series. The potential energy and kinetic energy of the cylindrical shell are obtained based on the first-order shear deformation theory (FSDT). Three sets of linear springs and one set of rotating springs are used to simulate arbitrary boundaries of the cylindrical shell, and the circumferential coupling springs are used to ensure the continuity of circumferential boundaries of the shell. The accuracy of the present method is verified by comparing with results derived by the finite element method (FEM), and a comprehensive parametric analysis was performed.

Nonlinear parametric vibration of imperfect SSMFG cylindrical shells in thermal environment including internal and subharmonic resonances

The nonlinear vibration behavior of the spiral stiffened multilayer functionally graded (SSMFG) cylindrical shells with initial imperfection exposed to axial parametric and external excitation in the thermal environment is presented in this paper using a semi-analytical method. The distribution of temperature and material constitutive of the stiffeners along the direction of thickness is assumed. The cylindrical shell consists of three layers, the interior and exterior layer is respectively rich metal and ceramic, and the middle layer is functionally graded material (FGM). Using the smeared stiffeners technique, von Kármán equations, and the Galerkin method, the nonlinear vibration problem has been solved. Then, utilizing the multiple scales method, the nonlinear vibration behavior of the system is examined. The resonant case, including internal parametric resonance among three modes and subharmonic resonance of order one-half, is considered. The results show that although the trend of all figures is approximately like together, but the maximum amplitude vibration of the internal SSMFG cylindrical shell with the angle of stiffeners and the external SSMFG cylindrical shell with the angle of stiffeners is more than others.

Nonlinear vibration characteristics of fibre reinforced composite cylindrical shells in thermal environment

In this paper, an analytical model for fiber reinforced polymer composite cylindrical shells (FRPCCSs) accounting for material and geometric nonlinearities and thermal effect is proposed, which is capable of predicting natural frequencies, damping ratios, and resonant responses under different excitation amplitudes and temperatures. Firstly, the nonlinear Young's and shear moduli and loss factors of fiber reinforced polymer composites considering amplitude and temperature dependent properties are represented based on the Jones-Nelson nonlinear material theory, complex modulus principle, together with polynomial fitting technique. Then, the equations of motion for FRPCCSs are derived accounting for nonlinear strain–displacement relations of the von Kármán type. The procedure of determining fitting coefficients for nonlinear Young's and shear moduli and loss factors is also presented in details. Following theoretical studies, a series of thermal vibration experiments on two shell specimens made of CF120 carbon/epoxy composites are carried out to validate the proposed modeling approach as well as evaluating nonlinear vibrations of FRPCCSs experimentally. It has been found that the first three natural frequencies of composite shell specimens are initially decreased and then increased along with the increase of excitation amplitude. This variation trend becomes more significant at high temperature with the maximum variation degree of 8.2%. Meanwhile, the corresponding damping ratios and resonant responses of FRPCCSs show upward trends as the excitation amplitude and environmental temperature increase. Compared to excitation amplitude, environmental temperature has more significant effect on the damping performance of FRPCCSs, of which the relative variation degree is up to 300.5% as the temperature raises from 20 to 200 °C.

Nonlinear Torsional Buckling of Functionally Graded Carbon Nanotube Orthogonally Reinforced Composite Cylindrical Shells in Thermal Environment

This paper deals with the nonlinear large deflection torsional buckling of functionally graded carbon nanotube (CNT) orthogonally reinforced composite cylindrical shells surrounded by Pasternak’s elastic foundations with the thermal effect. The shell is made by two layers where the polymeric matrix is reinforced by the CNTs in longitudinal and circumferential directions for outer and inner layers, respectively. The stability equation system is obtained by combining the Donnell’s shell theory, von Kármán nonlinearity terms, the circumferential condition in average sense and three-state solution form of deflection. The critical torsional buckling load, postbuckling load-deflection and the load-end shortening expressions are obtained by applying the Galerkin procedure. The effects of temperature change, foundation parameters, geometrical properties and CNT distribution law on the nonlinear behavior of cylindrical shell are numerically predicted. Especially, the effect of orthogonal reinforcement in comparison with longitudinal and circumferential reinforcement on the torsional buckling behavior of shells is observed.

Application of the hybrid DQ- Heaviside-NURBS method for dynamic analysis of FG-GPLRC cylindrical shells subjected to impulse load

Abstract In this paper, dynamic response of multilayer functionally graded graphene platelets reinforced composite (FG-GPLRC) cylindrical shells in thermal environment under an impulse load is studied based on the first order shear deformation theory (FSDT) of shells. The cylindrical shells under consideration are made up of multiple graphene platelet reinforced composite (GPLRC) layers with uniformly distributed and randomly oriented graphene platelets (GPLs) in each layer. GPL concentration is assumed to be graded in thickness direction. A new differential quadrature method based on direct projection of the Heaviside function is utilized to spatially discretize the governing equations. To solve the resulting system of ordinary differential equations (ODE) in temporal domain, a recently developed multi-step time integration technique, introduced based on the non-uniform rational B-spline (NURBS), is employed. After validating the approach, the effects of the different GPLs distribution patterns, the weight fraction and dimension ratios of the GPLs, temperature change, time durations and types of impulse loading on the dynamic responses of the FG-GPLRC shells are investigated and discussed. It is shown that the addition of only little GPLs to polymer matrix considerably decreases the period of oscillatory portions of the center deflection.

Analytical solution of low-velocity impact of graphene-reinforced composite functionally graded cylindrical shells

In this paper, low-velocity impact behavior of graphene-reinforced composite functionally graded (GRC-FG) cylindrical shells in thermal environments ia investigated analytically. The effective temperature-dependent material properties of the GRC-FG cylindrical shells are evaluated based on the extended Halpin–Tsai micromechanical model. The contact process follows a linearized contact law which is used to obtain a linearized contact coefficient, and Fourier series expansion and Laplace transforms are utilized during the solving process. The analytical expression of transverse displacement of GRC-FG cylindrical shells is furnished. The motion equations of the GRC-FG cylindrical shells are established based on Reddy’s third-order shear deformation theory (HSDT). The numerical results illustrate the influences of graphene distribution, temperature variation, geometric parameters, impactor mass and different impactor velocities on the central deflection of the GRC-FG cylindrical shells as well as the contact force between the GRC-FG cylindrical shells and the impactor.

Thermal-mechanical coupling analysis of functionally graded cylindrical shells

Functionally graded materials is a new material for thermal protection in the aerospace field. It is extremely important to study the temperature and stress changes in the thermal environment to ensure the normal operation of the spacecraft and the safety of crews. In this paper, ABAQUS is used to perform sequential thermal coupling and full thermal coupling analysis. The temperature variation and mechanical properties of functionally graded cylindrical shells in thermal environment under temperature and force field and temperature field interacts with force field are studied. Based on the first law of thermoelasticity and thermodynamics, the three-dimensional stress and energy equations of functionally graded cylindrical shells in thermal environment are derived. The example shows that the temperature variation law and mechanical characteristics of the two types of thermo-mechanical coupling analysis are almost the same. The temperature value results of the sequential thermal-mechanical coupling analysis are the same as the results of the full thermal coupling, but the stress value results are lower than the results of the full thermal coupling.

Semi-analytical solutions of free and force vibration behaviors of GRC-FG cylindrical shells

In this paper, free and force vibration behaviors of graphene-reinforced composite functionally graded (GRC-FG) cylindrical shells in thermal environments are investigated based on Reddy's third-order shear deformation theory (HSDT). The GRC-FG cylindrical shells are composed of piece-wise pattern graphene-reinforced layers which have different volume fraction. Based on the extended Halpin-Tsai micromechanical model, the effective material properties of the resulting nanocomposites are evaluated. Using the Hamilton's principle and the assumed mode method, the motion equation of the GRC-FG cylindrical shells is formulated. Using the time- and frequency-domain methods, free and force vibration properties of the GRC-FG cylindrical shell are analyzed. Numerical cases are provided to study the effects of distribution of graphene, shell radius-to-thickness ratio and temperature changes on the free and force vibration responses of GRC-FG cylindrical shells.

Torsional postbuckling behavior of FG-GRC laminated cylindrical shells in thermal environments

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.

Effect of Porosity on Flexural Vibration of CNT-Reinforced Cylindrical Shells in Thermal Environment Using GDQM

This article investigates the flexural vibration of temperature-dependent and carbon nanotube-reinforced (CNTR) cylindrical shells made of functionally graded (FG) porous materials under various kinds of thermal loadings. The equivalent material properties of the cylindrical shell of concern are estimated using the rule of mixture. Both the cases of uniform distribution (UD) and FG distribution patterns of reinforcements are considered. Thermo-mechanical properties of the cylindrical shell are supposed to vary through the thickness and are estimated using the modified power-law rule, by which the porosities with even and uneven types are approximated. As the porosities occur inside the FG materials during the manufacturing process, it is necessary to consider their impact on the vibration behavior of shells. The present study is featured by consideration of different types of porosities in various CNT reinforcements under various boundary conditions in a single model. The governing equations and boundary conditions are developed using Hamilton's principle and solved by the generalized differential quadrature method. The accuracy of the present results is verified by comparison with existing ones and those by Navier's method. The results show that the length to radius ratio and temperature, as well as CNT reinforcement, porosity, thermal loading, and boundary conditions, play an important role on the natural frequency of the cylindrical shell of concern in thermal environment.

Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments

This paper presents an investigation on the nonlinear vibration behavior of graphene-reinforced composite (GRC) laminated cylindrical shells in thermal environments. The material properties of the GRCs are temperature-dependent and the functionally graded (FG) materials concept is adopted which allows a piece-wise variation of the volume fraction of graphene reinforcement in the thickness direction of the shell. An extended Halpin-Tsaia micromechanical model is employed to estimate the GRC material properties. The motion equations for the nonlinear vibration of FG-GRC laminated cylindrical shells are based on the Reddy’s third order shear deformation theory and the von Kármán-type kinematic nonlinearity, and the effects of thermal conditions are included. The nonlinear vibration solutions for the FG-GRC laminated cylindrical shells can be obtained by applying a two-step perturbation technique. The results reveal that the nonlinear vibration characteristics of the shells are significantly influenced by the GRC material property gradient, the stacking sequence of the plies, the temperature variation, the shell geometric parameter and the shell end conditions.

Numerical simulation of the fluid-solid interaction for CNT reinforced functionally graded cylindrical shells in thermal environments

Spacecraft and satellite are susceptible to aerothermoelastic flutter instability, which may jeopardize the mission of the spacecraft and satellite. This kind of instability may result from the coupling of the thermal radiation from the sun and the elastic deformations of aeronautical components. As a first endeavor, the aerothermoelastic flutter and buckling instabilities of functionally graded carbon nanotube reinforced composite (FG-CNTRC) cylindrical shell under simultaneous actions of aerodynamic loading and elevated temperature conditions are investigated. The formulations are derived according to the first-order shear deformation theory, Donnell shell theory in conjunction with von Karman geometrical nonlinearity. Thermomechanical properties are assumed to be temperature-dependent and modified rule of mixture is used to determine the equivalent material properties of the FG-CNTRC cylindrical shell. The quasi-steady Krumhaar's modified piston theory by taking into account the effect of panel curvature, is used to determine the aerodynamic pressure. The nonlinear dynamic equations are discretized in the circumferential and longitudinal directions using the trigonometric expression and the harmonic differential quadrature method, respectively. Effects of various influential factors, including CNT volume fraction and distribution, boundary conditions, geometrical parameters, thermal environments, freestream static pressure and Mach number on the aerothermoelastic instabilities of the FG-CNTRC cylindrical shell are studied in details. It is found that temperature rise has a significant effect on the aerothermoelastic flutter characteristics of the FG-CNTRC cylindrical shell. It is revealed that cylindrical shells with intermediate CNT volume fraction have intermediate critical dynamic pressure, while do not have, necessarily, intermediate critical buckling temperature. It is concluded that the critical circumferential mode number (mCr) corresponding to the minimum critical dynamic pressure, depends not only on the radius-to-thickness ratio but also on the distribution of the CNTs.

Nonlinear stability of eccentrically stiffened S-FGM elliptical cylindrical shells in thermal environment

This paper has studied on the nonlinear buckling and postbuckling of a eccentrically stiffened functionally graded thin elliptical cylindrical shells surrounded on elastic foundations in thermal environment. Material properties are graded in the thickness direction according to a Sigmoid power law distribution (s-FGM) in terms of the volume fractions of constituents with metal - ceramic - metal layers. The elliptical cylindrical shells have stiffeners in two directions (longitudinal and transversal) on the external surface and inside surface surrounded on elastic foundations. The typical point in the study is both elliptical cylindrical shells and stiffeners having temperature-dependent properties are deformed under temperature simultaneously, leading to the equation to determine buckling thermal loads with both sides that are dependent on temperature, so the iterative algorithms are proposed to numerical technique in this case. The equilibrium and compatibility equations for the moderately elliptical cylindrical shells are derived by using the classical shell theory (CST) taking into account both geometrical nonlinearity in von Karman sense and initial geometrical imperfection. By applying the Galerkin method and using a stress function, the effects of material and geometrical properties, temperature-dependent material properties, elastic foundations and stiffeners on the buckling and postbuckling loading capacity of eccentrically stiffened FGM elliptical cylindrical shells in thermal environments are studied simultaneously for first time.

Vibration analysis of CNT-reinforced functionally graded composite cylindrical shells in thermal environments

Vibration characteristics of CNT-reinforced functionally graded composite closed cylindrical shells are studied. Thermal effect is taken into account. In the structural modeling, Reddy's high-order shear deformation theory is applied. Hamilton's principle and the assumed mode method are used to formulate the equation of motion of the CNT-reinforced functionally graded cylindrical shell. Vibration properties of the cylindrical shell are analyzed through the time- and frequency-domain methods. Influences of temperature change, CNTs distribution as well as CNTs volume fractions on the natural frequency of the CNT-reinforced cylindrical shell are investigated. Vibration responses of the cylindrical shell computed by the FSDT and TSDT are compared to verify the necessity of the high-order shear deformation theory in the vibration analysis for thick CNT-reinforced structures. The effects of CNTs volume and distribution on the free and forced vibration of the cylindrical shell are studied. The influences of thermal effect on the vibration responses of the CNT-reinforced cylindrical shell are also investigated.

Nonlinear low‐velocity impact analysis of functionally graded nanotube‐reinforced composite cylindrical shells in thermal environments

This paper presents a nonlinear analysis of impact response of nanocomposites cylindrical shells reinforced by single‐walled carbon nanotubes (SWCNTs) in thermal environments. The nanotube reinforcement distributions are either uniform or functionally graded in the shell thickness direction. Micromechanical models are employed to estimate the material properties of nanotube reinforced composites. A higher‐order shear deformation theory with a von Kármán‐type of kinematic nonlinearity yields the equations of motion. By considering the nanotube reinforced composites as temperature‐dependent, the thermal effects are included. A two‐step perturbation technique is used to solve the equations of motion. A parametric study is carried out, and the effects of nanotube distribution and its volume fraction, impactor initial velocity, temperature change, geometric parameter of shell, and edge boundary condition on the impact response of the shell are discussed. The numerical results show that the central deflection of the shell subjected to impact is sinusoidal. It is found that the nanotube distribution through the thickness can alter the amplitude and the frequency of the central deflection and also the energy absorption significantly. POLYM. COMPOS., 39:730–745, 2018. © 2016 Society of Plastics Engineers

Experimental study on bistable behaviour of anti-symmetric laminated cylindrical shells in thermal environments

Anti-symmetric laminated [+α/−α]n cylindrical shell (ALCS) is a type of bistable composite structures that can deform between two stable shapes under an external loading. The maximum snap loads and shape deformations in varying thermal environments play a significant role in their bistable characteristic. This paper presents an experimental study on the bistable behaviour of ALCSs at 20°C, 40°C, 60°C, and 80°C. The load–displacement curves are obtained by using a testing machine with a thermal chamber. The effect of the temperature variation on the shell’s curvatures is also investigated by digital image processing technique. The obtained experimental results show the same trend as the analytical and numerical results. The thermal influence on the bistable behaviour in a local temperature field is also studied in detail. The experimental investigations presented in this paper is of great importance in the engineering design and applications of morphing structures manufactured from ALCSs.

Nonlinear internal resonance of functionally graded cylindrical shells using the Hamiltonian dynamics

Internal resonance in nonlinear vibration of functionally graded (FG) circular cylindrical shells in thermal environment is studied using the Hamiltonian dynamics formulation. The material properties are considered to be temperature-dependent. Based on the Kármán-Donnell's nonlinear shell theory, the kinetic and potential energy of FG cylindrical thin shells are formulated. The primary target is to investigate the two-mode internal resonance, which is triggered by geometric and material parameters of shells. Following a secular perturbation procedure, the underlying dynamic characteristics of the two-mode interactions in both exact and near resonance cases are fully discussed. It is revealed that the system will undergo a bifurcation in near resonance case, which induces the dynamic response at high energy level being distinct from the motion at low energy level. The effects of temperature and volume fractions of composition on the exact resonance condition and bifurcation characteristics of FG cylindrical shells are also investigated.

Nonlinear torsional buckling and postbuckling of eccentrically stiffened FGM cylindrical shells in thermal environment

The main aim of this paper is to investigate the nonlinear buckling and post-buckling of functionally graded stiffened thin circular cylindrical shells surrounded by elastic foundations in thermal environments and under torsional load by analytical approach. Shells are reinforced by closely spaced rings and stringers in which material properties of shell and the stiffeners are assumed to be continuously graded in the thickness direction. The elastic medium is assumed as two-parameter elastic foundation model proposed by Pasternak. Based on the classical shell theory with von Karman geometrical nonlinearity and smeared stiffeners technique, the governing equations are derived. Using Galerkin method with three-term solution of deflection, the closed form to find critical torsional load and post-buckling load–deflection curves are obtained. The effects of temperature, stiffener, foundation, material and dimensional parameters are analyzed.