Thick Hollow Cylinder Research Articles

Accretion–ablation mechanics

In this paper, we formulate a geometric nonlinear theory of the mechanics of accreting–ablating bodies. This is a generalization of the theory of accretion mechanics of Sozio & Yavari (Sozio & Yavari 2019 J. Nonlinear Sci. 29 , 1813–1863 (doi:10.1007/s00332-019-09531-w)). More specifically, we are interested in large deformation analysis of bodies that undergo a continuous and simultaneous accretion and ablation on their boundaries while under external loads. In this formulation, the natural configuration of an accreting–ablating body is a time-dependent Riemannian 3 -manifold with a metric that is an unknown a priori and is determined after solving the accretion–ablation initial-boundary-value problem. In addition to the time of attachment map, we introduce a time of detachment map that along with the time of attachment map, and the accretion and ablation velocities, describes the time-dependent reference configuration of the body. The kinematics, material manifold, material metric, constitutive equations and the balance laws are discussed in detail. As a concrete example and application of the geometric theory, we analyse a thick hollow circular cylinder made of an arbitrary incompressible isotropic material that is under a finite time-dependent extension while undergoing continuous ablation on its inner cylinder boundary and accretion on its outer cylinder boundary. The state of deformation and stress during the accretion–ablation process, and the residual stretch and stress after the completion of the accretion–ablation process, are computed. This article is part of the theme issue ‘Foundational issues, analysis and geometry in continuum mechanics’.

Thermoelastic impact in a thick hollow cylinder using time-fractional-order theory

The study focuses on thermoelastic behavior of the time-fractional heat conduction equation in a thick hollow cylinder by quasi-static approach. The utilization of the Caputo fractional derivative has been employed. The upper and lower surfaces of the cylinder have been assigned arbitrary temperature values, while the boundaries of the cylinder remain at a constant temperature of zero. The integral transform technique has been utilized to solve the conduction equation. A mathematical model has been prepared for Copper material. The fractional-order thermoelasticity for distinct fractional values of time variable has been discussed and the results are presented graphically.

A two-temperature model and fractional order derivative in a rotating thick hollow cylinder with the magnetic field

A novel multi-phase-lags model with fractional order derivative is introduced to study a thick hollow cylinder with two temperatures under the influence of magnetic field and rotation. The basic non-dimensional equations of the problem are discussed by using harmonic wave analysis. Numerical computations are carried out with the help of Matlab software. Comparisons are made with the results of the refined-phase-lag theory for different values of rotation and magnetic field. Comparisons also are made with the results of the refined-phase-lag theory for different values of the fractional order parameter. Some particular cases of special interest have been deduced from the present investigation.

Semi-Analytical Large Deformation and Three-Dimensional Stress Analyses of Pressurized Finite-Length Thick-Walled Incompressible Hyperelastic Cylinders and Pipes

This research is devoted to semi-analytical stress and large deformation analyses of finite-length thick-walled incompressible Mooney–Rivlin hyperelastic cylindrical pressure vessels/pipes with fixed ends, employing the three-dimensional theory of hyperelasticity. The formulation accounts for the thickness reduction in both radial and axial directions. The governing system of equations and the boundary conditions are assembled using a large-weights penalty method, after utilizing central, forward, and backward second-order point collocation expressions for the discretization of the thick hollow cylinder in both longitudinal and radial directions. The resulting coupled highly nonlinear two-dimensional equations are solved by the Newton–Raphson iterative updating technique. The results include the radial, axial, and three-dimensional distributions of the deformations and all the stress components. Comprehensive parametric studies are accomplished to evaluate the effects of the hyperelasticity parameters, boundary conditions, and thickness and length-to-radius ratios of the pressure vessel/pipe. Results reveal that the sections located in the vicinity of the fixed edges and the mid-section of the cylinder undergo the highest stresses, at low and high pressures, respectively. Moreover, while the pipe undergoes an overall expansion due to the internal pressure, it experiences a bending moment that induces compressive stresses at the outer boundary, due to the fixed edge. The magnitudes of the radial deformation and the circumferential stress significantly grow by increasing the cylinder length and the nonlinearities in the cylinder responses and behaviors increase by increasing the cylinder length.

On the natural frequency investigation of the thick hollow cylinder with 2D-FGM Mori-Tanaka scheme

ABSTRACT In this paper, we conduct the natural frequency analysis for a 2D-FGM (functionally graded material) finite-length, thick-walled cylinder by the graded finite element method. The material properties gradations are considered along with the thickness and the longitudinal axis of the cylinder according to the Mori-Tanaka scheme and power-law volume fraction distributions. Therefore, the graded properties are implemented by user subroutine UMAT in ABAQUS/Standard™. The eigenvalue problem is solved using three-dimensional elasticity equations, and the current technique has been confirmed by earlier research. The major purpose of this study is to see how FGM configurations affect the vibration behaviour of the cylinder. The variation of the cylinder's first natural frequencies for various thickness-to-outer-radius and length-to-outer-radius ratios is presented, taking into account varied material distributions. According to the findings, raising the power exponents, particularly the radial one, increases the natural frequencies.

A deep learning approach based on the physics-informed neural networks for Gaussian thermal shock-induced thermoelastic wave propagation analysis in a thick hollow cylinder with energy dissipation

This paper proposes a novel approach based on the physics-informed neural networks (PINNs) as an efficient deep learning approach to solve a broad range of the coupled partial differential equations (PDEs). For the first time, the PINN methodology is successfully applied to the thermoelastic wave propagation analysis with energy dissipation in a thick hollow cylinder based on the Green-Naghdi (GN) theory of coupled thermoelasticity. The assumed thick hollow cylinder is subjected to Gaussian thermal shock loading applied on the inner bounding surface. This research presents a PINN architecture with self-adaptive weights, which does not suffer from the curse of dimensionality as opposed to the numerical methods. An in-depth discussion is provided on the method and its capabilities to address PDE-related issues. Moreover, the PINN-based parametric studies are performed to show the effects of the materials coefficients on the thermoelastic wave propagation and dynamic behaviors of the fields’ variables. Numerous examples of thermoelastic wave propagation analysis with and without energy dissipation are solved via this approach. The framework generates satisfactory results in terms of accuracy and stability, as summarized in the paper.

Thermally nonlinear generalized thermoelasticity investigation of a functionally graded thick hollow cylinder based on the finite difference method

In the present paper, the propagation and reflection of the transient displacement, temperature, and stress waves are numerically explored in a functionally graded thick-walled hollow cylinder, based on the Lord–Shulman generalized thermoelectricity theory and using the finite difference method. The motion and thermoelastic energy balance equations are first established based on the dimensionless radial displacement and temperature fields. It is assumed that the elasticity modulus, Poisson’s ratio, mass density, thermal expansion coefficient, thermal conductivity coefficient, and specific heat follow power functions of the dimensionless radius while the relaxation time is assumed to be constant within the FGM cylinder. Unlike many previous studies in which the energy balance equation was linearized by assuming small temperature rises, the present research accounts for the significant temperature variations and employs a nonlinear energy balance equation. Nondimensional forms of energy balance and motion equations are derived by introducing dimensionless quantities and discretized via the finite difference method. The Newmark method with constant average acceleration was employed to solve the highly nonlinear equations found from the finite difference method. Two different boundary conditions were used to investigate the propagation and reflection of the displacement, temperature, and stress transient waves in the radial direction of the cylinder. The results revealed the variable speed of the displacement wave and the significant role of the changes in the properties along the radius of the cylinder and the boundary conditions in altering the results.

Electron-LO-phonon intrasubband scattering rates in a hollow cylinder under the influence of a uniform axial applied magnetic field

Scattering rates arising from the interactions of electrons with bulk longitudinal optical (LO) phonon modes in a hollow cylinder are calculated as functions of the inner radius and the uniform axial applied magnetic field. Now, the specific nature of electron-phonon interactions mainly depends on the character of the energy spectrum of electrons. As is well known, in cylindrical quantum wires, the application of a parallel magnetic field lifts the double degeneracy of the non-zero azimuthal quantum number states; \(m \not = 0\); irrespective of all electron’s radial quantum number l states. In fact, this Zeeman splitting is such that the \(m < 0\) electron’s energy subbands initially decrease with the increase of the parallel applied magnetic field. In a solid cylinder, the lowest-order; {\(l = 1;\,m = 0\)} subband is always the ground state. In a hollow cylinder, however, as the axial applied magnetic field is increased, the electron’s energy subbands take turns at becoming the ground state; following the sequence \(\lbrace m=0,-1,-2...~ -N\rbrace\) of azimuthal quantum numbers. Furthermore, in a hollow cylinder, in general, the electron’s energy separations between any two subbands are less than the LO phonon energy except for exceptionally high magnetic fields, and some highest-order quantum number states. In view of this, the discussion of the energy relaxation here is focused mainly on intrasubband scattering of electrons and only within the lowest-order {\(l = 1;\,m = 0\)} electron’s energy subband. The intrasubband scattering rates are found to be characterized by shallow minima in their variations with the inner radius, again, for a fixed outer radius. This feature is a consequence of a balance between two seemingly conflicting effects of the electron’s confinement by the inner and outer walls of the hollow cylinder. First; increased confinement of the charge carriers generally leads to the enhancement of the rates. Second; the presence of a hole in a hollow cylinder leads to a significant suppression of the scattering rates. The intrasubband scattering rates also show a somewhat parabolic increase in their variations with the applied magnetic field; an increase which is more pronounced in a relatively thick hollow cylinder.

Time fractional heat transfer analysis in thermally sensitive functionally graded thick hollow cylinder with internal heat source and its thermal stresses

The aim of this work is to investigate the time fractional thermoelastic state of a thermally sensitive functionally graded thick hollow cylinder subjected to internal heat source. Convection boundary conditions are applied on the curved surface of cylinder also sectional heating is assumed on the lower surface. The material properties except density and Poisson’s ratio are assumed to be dependent on temperature. Kirchhoff’s variable transformation is used to reduce the nonlinear heat conduction with temperature dependent thermal conductivity and specific heat capacity to linear form. Further the solution of linear form is obtained by using integral transform technique in the form of Bessel’s and trigonometric functions. All physical and mechanical quantities are taken as dimensional for the theoretical analysis whereas for numerical computations non-dimensional parameters are assumed. Numerical results of temperature change and stress distribution are illustrated graphically for ceramic-metal-based functionally graded materials and shown in figures with the help of Mathematica software.

Hybrid integral transform and p-version FEM for thermo-mechanical analysis of a functionally graded piezoelectric hollow cylinder subjected to asymmetric loads

As the first endeavor, a combination of fast Fourier transform and p-version of finite element method is proposed for electro-thermo-elastic analysis of a thick hollow cylinder under asymmetric thermal loadings. Especially in shells of revolution, the proposed FFT-pFE method is accompanied by a significant decrease in the computational costs. Due to the problem periodicity in such structures, the fast Fourier transform technique is used to discretize the governing equations into a set of harmonics in circumferential direction. Each harmonic is then partitioned using higher order finite elements. Hierarchical finite elements based on Legendre polynomial interpolation functions are utilized to discretize 2D governing equations of a functionally graded piezoelectric (FGP) cylinder. 3D governing equations of a FGP hollow cylinder are then discretized by using the higher-order Lagrangian finite elements. The effects of FFT grid-size as well as the order of the interpolation functions are investigated on convergence behavior of the proposed mixed FFT-pFE method. The piezoelectric material properties, with the exception of the Poisson’s ratio, are considered to vary along the radius of the cylinder and pursue the power function. The governing equations are derived using the principle of virtual displacements. For a 3D FGP hollow cylinder, the influence of ...

Active broadband sound transmission loss control through an arbitrary thick smart Piezo-laminated cylinder

The feedback control strategy is utilized for the enhancement of the sound transmission loss (STL) through an infinite thick hollow Piezo-laminated cylinder of arbitrary thickness insonified by an oblique progressive incident plane wave. The close form formulation is accomplished by utilizing the sound wave equation, the three-dimensional (3D) exact theory of elasticity and piezoelasticity. The active control strategy is achieved by sending a control signal from the distributed piezoelectric sensor layer through a controller with certain feedback gain to drive the external piezoelectric actuators. The mechanical stress generated by the piezo-actuator layer cancels the parts of the input incident wave to enhance the STL. Comprehensive numerical studies are carried out to investigate the poling direction and feedback gain effects on the STL. The results show that in the case of radially polarized piezoelectric materials, the feedback control provides significant sound enhancement especially, when the angle of the incident wave is close to normal, however, in the case of axially polarized piezoelectric materials, the control feedback strategy reduces the unfavorable oscillatory motion of the cylinder in addition to providing a superior sound isolation enhancement, particularly for near-grazing incident angles. The accuracy of the proposed solution is confirmed by comparing the presented results with the ones from the simplified models in the literature as well as the commercial finite element package Comsol Multiphysics.

Transient thermal stress analysis for a short thick hollow FGM cylinder with nonlinear temperature-dependent material properties

In this study, nonlinear transient thermo-elastic analysis for a thick hollow 1D-FGM (functionally graded material) axisymmetric cylinder with finite length is investigated using higher-order graded finite element method. The material property gradations are along the radial direction and the power-law volume fraction and simple rule of mixture scheme are utilized to perform the effective material properties. As the cylinder exposed to high temperature, the temperature dependency of material properties is considered. So it led to nonlinear thermal conduction equation and in spite of the material distribution along one-direction by changing the temperature, the material properties are varied along two-direction with time. The nonlinear heat equation leads to 2D-temperature distribution for an axisymmetric cylinder. Also the thermal stress field would be different from an infinite cylinder which has been studied before. The temperatures, displacements and stresses for different values of volume fraction exponents along radial direction are investigated. It is revealed that the stresses and temperature in FGM cylinder are lower than the ceramic rich one. In other words, functionally graded cylinder wall gives better results in both stress and temperature cases than non-FGM cylinder.

Time fractional thermoelastic problem of a thick cylinder with non homogeneous material properties

In this article, we assume a two dimensional thermoelastic problem of nonhomogeneous thick hollow cylinder within the context of fractional order derivative of order 0 < α ≤ 2. Convective heat exchange boundary conditions are applied at the curved surface, whereas the lower surface and the upper surface of the cylinder are considered at zero temperature. Furthermore cylinder is subjected to a sectional heating at the outer curved surface of cylinder. Let the material properties of the cylinder except Poisson’s ratio and density are considered to be expresses by a simple power law in axial direction. The solution of the thermoelastic problem is obtained in terms of trigonometric and Bessel’s functions. Both the thermal and mechanical behavior is analyzed by the influence of inhomogeneity. Numerical computations are carried out for a mixture of copper and tin metals for both homogeneous and nonhomogeneous cases. Results of numerical solutions are illustrated graphically for temperature distribution and thermal stresses for all the different values of the fractional-order parameter α with the help of Mathematica software.

Time fractional heat transfer analysis in nonhomogeneous thick hollow cylinder with internal heat generation and its thermal stresses

In this article, we assume a two dimensional thermoelastic problem of a nonhomogeneous thick hollow cylinder within the context of fractional order derivative . Convection boundary conditions are applied on the curved surface of cylinder with internal heat generation. Let the material properties other then Poisson’s ratio and density are assumed to be expresses by a simple power law in axial direction. Lower and upper surface are assumed to be thermally insulated. The affect of inhomogeneity on the both thermal and mechanical behavior is examined. Numerical computations are carried out for both homogeneous and nonhomogeneous cylinders and are illustrated graphically are shown in figures with the help of Mathematica software.

A Comparative Numerical Study on Conjugate Natural Convection From Vertical Hollow Cylinder With Finite Thickness Placed on Ground and in Air

Abstract The present work reports a comparative analysis of natural convection heat transfer from a thick hollow vertical cylinder either placed on the ground or suspended in the air. The numerical simulations have been performed by varying the cylinder length to its outer diameter (L/Do) in the range of 0.2–20, the thickness ratio (Di/Do) in a range of 0.5–0.9, and Rayleigh number (Ra) from 104 to 108. The flow and heat transfer characteristics have been delineated precisely with the presentation of the thermal plume and flow field in the vicinity of the cylinder. The variation of average Nusselt number (Nu), local Nu, and contribution to total heat loss from different surfaces with the pertinent parameters have been elucidated graphically. The average Nu is always more for the cylinder in the air compared with the case when it is on the ground. However, the difference between the Nu for these two cases diminishes, as the L/Do increases. It has also been found that the contribution to total heat loss from the inner surface of the hollow cylinder suspended in air increases with L/Do, attains a peak, and decreases sharply. Cooling time curves for the cylinder placed in air or on the ground have been described precisely. Finally, a correlation for the average Nusselt number as a function of all the pertinent parameters has been proposed that can be useful for industrial and academic purposes.

Natural convection heat transfer and fluid flow around a thick hollow vertical cylinder suspended in air: A numerical approach

The present study reports numerical investigation on natural convection heat transfer and fluid flow from a thick hollow vertical cylinder suspended in air within laminar regime for a Rayleigh number (Ra) of 104 to 108. Numerical simulations have been performed by changing the length to outer diameter ratio (L/Do) of the cylinder from 0.2 to 20 and thickness ratio (Di/Do) from 0.5 to 0.9. Variation of average Nusselt number (Nu) and local Nusselt number with the above parameters has been elucidated graphically. Subsequently, the influences of Ra, L/Do, Di/Do on mass-flow rate and velocity profile inside the cylinder has also been investigated. Temperature contour and velocity vector plot around the cylinder have been represented pictorially to describe the thermal and velocity field around the vertical thick hollow cylinder. It has been observed that the average Nu of a thick hollow cylinder increases with L/Do, attains a peak and then decreases to a minimum and then again increases with L/Do. This phenomenon is very well observed at high Ra of 106 compared to lower Ra of 104. The Nu of the inner surface is found to be always lower compared to the outer surface and as L/Do increases beyond 8 the inner surface Nu falls drastically at high Ra compared to lower Ra. It has also been observed that the non-dimensional mass-flow rate due to buoyancy driven flow inside the thick hollow cylinder increases with L/Do, attains a peak and then decreases for all Ra. Cooling curve and a correlation for Nusselt number as a function of geometrical and thermal parameter have been presented which are useful for industrial purposes.

Numerical simulation of elastoplastic problems by Brezis–Ekeland–Nayroles non-incremental variational principle

This paper is concerned with the energy-dissipation Brezis–Ekeland–Nayroles variational principle (BEN principle) for the numerical study of quasi-static elastoplastic and viscoplastic problems in small strains. This principle is based on the dissipation potential and its Fenchel transform and allows to have a consistent view of the whole evolution by computing the nonlinear response along the whole time history as a solution of a suitable minimization problem. In the present work, the BEN principle is applied to address the elastic perfectly plastic and viscoplastic thick hollow cylinder subjected to internal pressure. It turns out that the BEN variational formulation is based on a two-field functional, that leads naturally to discretize the displacement and stress fields. We present the detailing of the discretization and the numerical implementation of the minimization problem by using the mixed finite element method which is more efficient to enforce the yield condition. Computational accuracy and efficiency of the BEN principle is assessed by comparing the numerical results with the analytical ones and the simulations derived by the classical step-by-step finite element procedure.

3D numerical study of natural convection heat transfer from a hollow horizontal cylinder placed on the ground

In the present work, natural convection heat transfer from a thick hollow horizontal cylinder placed on ground is studied numerically. 3D numerical simulations have been performed by varying the Rayleigh number (Ra) from 104 to 108 (preferably within laminar regime). All the simulations have been carried out by varying length to outer diameter ratio (L/D) and thickness ratio (d/D) in the range of 0.2–20 and 0.4–0.9 respectively. Nusselt number, heat transfer rate and contribution to total heat transfer rate from different surfaces have been calculated and their variation with the above parameter is represented graphically. Similarly, thermal plume and velocity vector are shown pictorially at different sections of the cylinder and physical phenomenon of fluid flow and heat transfer could be described from such pictures. Later on effect of above parameters on cooling time is also discussed. It has been observed that with increase in thickness, Nu decreases at low L/D (L/D ≤ 2), whereas at higher L/D a reverse trend is observed. Heat transfer rate from the inner surface increases initially with increase in L/D and after a particular L/D, it attains constant value whereas for outer surface, it increases continuously. It has been also observed that at a particular L/D and d/D, contribution of heat transfer rate from inner surface increases with Ra, whereas reverse trend is observed for outer and side flat surface. A correlation for Nusselt number as a function of Rayleigh number, L/D and d/D has been developed which may be useful for industrial purposes.

Stress distributions in nanocomposite sandwich cylinders reinforced by aggregated carbon nanotube

In order to improve the static response of thick hollow cylinders, a sandwich cylinder with two carbon nanotube (CNT)‐reinforced nanocomposite face sheets are proposed in this article. Moreover, due to the use of optimum amount of high cost CNTs, the CNT distribution is suggested to be functionally graded (FG) along the thickness of cylinder. The stress and deflection profiles of the proposed sandwich cylinders subjected to internal and external pressures have been investigated using a finite element method (FEM) based on an axisymmetric model. The significant effect of formation of CNT agglomerations in the surrounded matrix is considered and the material properties of the resulted nanocomposite are estimated by Eshelby‐Mori‐Tanaka approach. Using the developed axisymmetric FEM model, the effects of CNT aggregation state, volume fraction, and distribution as well as geometrical dimension and loading condition on the stress and deflection distributions of the nanocomposite sandwich cylinders have been characterized. The extensive simulations have revealed that instead of adding higher volume fraction of CNT, the selection of suitable distribution for CNTs can lead to a nanocomposite sandwich cylinder with less deflection. POLYM. COMPOS., 40:E1918–E1927, 2019. © 2019 Society of Plastics Engineers

Mathematical Modeling of Thermoelastic State of a Functionally Graded Thermally Sensitive Thick Hollow Cylinder With Internal Heat Generation

In this paper, the effect of internal heat generation has been studied in a functionally graded thick hollow cylinder in context with thermosensitive thermoelastic properties. Initially, the cylinder is kept at reference temperature and the radial boundary surface under consideration dissipates heat by convection according to Newton’s law of cooling, heat flux is applied at the lower surface, while the upper surface is insulated. The heat conduction equation due to internal heat generation is solved by integral transform technique and Kirchhoff’s variable transformation is used to deal with the nonlinearity of the heat conduction equation. A mathematical model has been constructed for a nonhomogenous material in which the material properties are assumed to be dependent on both temperature and spatial variable z. A ceramic-metal-based FGM is considered in which alumina is selected as ceramic and nickel as metal. The results obtained are illustrated graphically.