Non-homogeneous Cylinder Research Articles

Saint-Venant torsion of non-homogeneous orthotropic circular cylinder

The object of this paper is the Saint-Venant torsion of a radially non-homogeneous, hollow and solid circular cylinder made of orthotropic piezoelectric material. The elastic stiffness coefficients, piezoelectric constants and dielectric constants have only radial dependence. This paper gives the solution of the Saint-Venant torsion problem for torsion function, electric potential function, Prandtl’s stress function and electric displacement potential function.

Analysis of axisymmetric problem from the theory of elasticity for an isotropic cylinder of small thickness with alternating elasticity modules

Asymptotic methods play an important role in solving three-dimensional elasticity problems. The method of asymptotic integration of three-dimensional equations of elasticity theory takes an important place in solving the problems of the limited transition from three-dimensional problems to two-dimensional for elastic membranes. Based on the method of asymptotic integration of equations of the elasticity theory, the axisymmetric problem of elasticity theory for radially non-homogeneous cylinder of small thickness is explored. The case when elasticity modules change by the radius according to the linear law is considered. It is expected that the lateral part of the cylinder is free from stresses and boundary conditions, leaving a cylinder in equilibrium, are assigned at the ends of a cylinder. The stated boundary-value problem is reduced to the spectral problem. The behavior of solutions to the spectral problem both in the inner part of a cylinder, and near the ends of a cylinder if the parameter of thinness of cylinder’s walls tends to zero, is studied. Three groups of solutions were obtained and the nature of the constructed homogeneous solutions was explained. The solution corresponding to the first iterative process determines the penetrating stressed-strained state of a cylinder. The solution corresponding to the second iterative process represents edge effects in the applied theory of shells. The third iterative process determines the solution which has the character of a boundary layer. The solution corresponding to the first and second iterative processes determines the internal stressed-strained state of the cylinder. In the first term of asymptotics, they can be regarded as a solution on the applied theory of shells. It was shown that the stressed-strained state, similar to the case of a homogeneous cylinder of small thickness, consists of three types: penetrating stressed state, simple edge effect and a boundary layer. The problem of meeting the boundary conditions on the ends of a radially non-homogeneous cylinder using the Lagrangian variation principle was considered.

Stress intensity factor of radial cracks in isotropic functionally graded solid cylinders

This paper estimates stress intensity factors of rotating solid disks or cylinders with a radial crack subjected to a uniform tension at their outer surface and a uniform temperature change through the body. Material properties of the cylinder are assumed to obey from the power law through the radius of the cylinder. The cracks are assumed to be small and located radially at center, inside or edge of the body. The stress intensity factors are obtained applying an approximate method and using the proper geometric functions for combination of the thermomechanical stresses. The method proposed in this paper is imposed to isotropic FG plates with an edge slanted crack to quantify the difference between present method and numerical methods given in the literature review. Also, the SIFs obtained for the non-homogeneous cylinder are reduced to the homogeneous one and are compared with the corresponding exact solution of isotropic materials.

Hygro-thermo-electro-elastic response of a functionally graded piezoelectric cylinder resting on an elastic foundation subjected to non-axisymmetric loads

In this paper, the general theoretical analysis of a thick-walled cylinder made of functionally graded piezoelectric materials subjected to a non-axisymmetric hygro-thermo-electro-mechanical loading is presented. The transversely isotropic and non-homogeneous cylinder is rested on a Winkler-type elastic foundation on the outer surface. All mechanical, hygrothermal and electrical properties are assumed to obey a power-law function in the radial direction with different non-homogeneity constants. Non-axisymmetric moisture concentration and temperature distributions are assumed to be a function of radial and circumferential directions and are obtained by solving two-dimensional and steady-state Fourier heat conduction and Fickian moisture diffusion equations. By substituting constitutive equations into electrical and mechanical equilibrium equations, three second-order non-homogeneous partial differential equations in terms of electric potential and mechanical displacements are derived. The separation of variables and complex Fourier series method are employed to solve heat conduction, moisture diffusion and Navier equations. Numerical results clearly illustrate the effects of hygrothermal loading, elastic foundation and non-homogeneity constants on hygro-thermo-electro-elastic behavior of the functionally graded piezoelectric cylinder. It is observed that non-homogeneity constant, hygrothermal loading and elastic foundation have considerable effects on displacements, stresses and electric potential distributions.

Effect of the Rotation on a Non-Homogeneous Infinite Elastic Cylinder of Orthotropic Material with Magnetic Field

Effect of the Rotation on a Non-Homogeneous Infinite Elastic Cylinder of Orthotropic Material with Magnetic Field

On the Rotation and Axial Magnetic Field Effects of a Non-Homogeneous Composite Infinite Cylinder of Orthotropic Material

On the Rotation and Axial Magnetic Field Effects of a Non-Homogeneous Composite Infinite Cylinder of Orthotropic Material

Thermoelastic analysis of non-uniform pressurized functionally graded cylinder with variable thickness using first order shear deformation theory(FSDT) and perturbation method

Recently application of functionally graded materials(FGMs) have attracted a great deal of interest. These materials are composed of various materials with different micro-structures which can vary spatially in FGMs. Such composites with varying thickness and non-uniform pressure can be used in the aerospace engineering. Therefore, analysis of such composite is of high importance in engineering problems. Thermoelastic analysis of functionally graded cylinder with variable thickness under non-uniform pressure is considered. First order shear deformation theory and total potential energy approach is applied to obtain the governing equations of non-homogeneous cylinder. Considering the inner and outer solutions, perturbation series are applied to solve the governing equations. Outer solution for out of boundaries and more sensitive variable in inner solution at the boundaries are considered. Combining of inner and outer solution for near and far points from boundaries leads to high accurate displacement field distribution. The main aim of this paper is to show the capability of matched asymptotic solution for different non-homogeneous cylinders with different shapes and different non-uniform pressures. The results can be used to design the optimum thickness of the cylinder and also some properties such as high temperature residence by applying non-homogeneous material.

Stress Characterization of Nonisothermal Elastodynamics for Nonhomogeneous Anisotropic Body under Plane Strain Conditions

Stress characterization of non-isothermal elastodynamics for an anisotropic nonhomogeneous infinite cylinder under plane strain conditions is presented. The cylinder is referred to the Cartesian coordinates x i (i = 1, 2, 3) in which the axis of the cylinder is parallel to the x 3-axis and a cross-section of the cylinder at x 3 = 0, denoted by C, is a domain of the time-dependent stresses S ij = S ij (x α, t), [i, j = 1, 2, 3; α = 1, 2; x α ∈ C; t ≥ 0]. The density of the cylinder ρ, the compliance tensor K ijkl [i, j, k, l = 1, 2, 3], and the stress-temperature tensor M ij depend on x 2 only, while a thermomechanical load that complies with the plane strain conditions, depends on (x 1, x 2) ∈ C and time t ≥ 0 only. It is shown that S ij = S ij (x α, t) is generated by a unique solution S αβ = S αβ(x γ, t), [α, β, γ = 1, 2; t ≥ 0] to a pure stress initial-boundary value problem of nonisothermal elastodynamics on C × [0, ∞), and the in-plane stress components generate the out-of plane stress components provided the inner product of a compliance dependent tensor field and the tensor does not vanish; here, ; t ≥ 0] represents the actuation tensor field. Also, a body-force analogy for S αβ = S αβ(x γ, t) is formulated from which it follows that S αβ = S αβ(x γ, t) can be identified with a solution to a pure stress initial-boundary value problem of isothermal elastodynamics. The stress characterization presented here should prove useful in a study of stress waves in an infinite cylinder made of an anisotropic functionally graded material within both the isothermal and non-isothermal elastodynamics.

Collapse Pressure Analysis in Torsion of a Functionally Graded Thick-walled Circular Cylinder under External Pressure

Abstract A hollow thick-walled cylinder made of functionally graded material subjected to twist has been analyzed. The objective of this paper is to provide the guidance to design the torsion of thick-walled cylinder made of functionally graded material so that collapse of cylinder due to external pressure can be avoided. The concept of transition theory based on the concept of Lebesgue strain measure has been used to simplify the constitutive equations. Results have been analyzed theoretically and discussed numerically. From the discussion, we can conclude that highly non-homogeneous cylinder is on the safer side of the design as compared to lesser non-homogeneous cylinder. This is because of the reason that percentage increase in pressure required for initial yielding to become fully plastic is very high for non-homogeneous cylinder whose non-homogeneity increases radially as compared to lesser non-homogeneous cylinder. Also, non-homogeneous cylinder whose thickness is very high is on the safer side of the design as compared to less thick-walled cylinders because percentage increase in pressure required for initial yielding to become fully plastic is very high for highly thick-walled cylinders as compared to other cases.

Safety analysis of thermal creep non-homogeneous thick-walled circular cylinder under internal and external pressure using Lebesgue strain measure

Purpose – Safety analysis has been done for thermal non-homogeneous thick-walled circular cylinder under internal and external pressure. The paper aims to discuss these issues. Design/methodology/approach – Transition theory based on the concept of generalized principal Lebesgue strain measure has been used which simplifies the constitutive equations by prescribing a priory the order of the measure of deformation and helps to achieve better agreement between the theoretical and experimental results. Findings – From the analysis, the paper can conclude that by introducing a suitably chosen temperature gradient, non-homogeneous compressible circular cylinder with internal and external pressure for non-linear measure is on the safer side of the design as compared to the cylinder without temperature because circumferential stresses are less for cylinder with temperature as compared to cylinder without temperature. Practical implications – Introduction of temperature gradient leads to the idea of “Stress Savin...

Transient Hyperbolic Heat Conduction in a Functionally Graded Hollow Cylinder

DOI: 10.2514/1.41368 Hyperbolic heat conduction in a functionally graded hollow cylinder is investigated in this paper. Except for uniform thermal relaxation time, all other material properties of the cylinder are assumed to vary along the radial direction following a power-law form with arbitrary exponents known as the nonhomogeneity indices. When the cylinder is infinitely long, end effects can be ignored, and the one-dimensional heat conduction problem in the radial directionissolvedanalyticallyintheLaplacedomain.The finaltransientsolutionoftheprobleminthetimedomainis obtained by numerical inversion of the Laplace transformed temperature and heat flux. The exact speed of the thermalwave in the nonhomogeneous cylinder isalso obtained.Moreover, the effects of the nonhomogeneity indices and thermal relaxation time on the results are shown graphically by some illustrative examples. The current results are corroborated by the steady-state results for the homogeneous cylinder in the literature.

Finite element method of thermal shock problem in a non-homogeneous isotropic hollow cylinder with two relaxation times

A solution of thermal shock problem of generalized thermoelasticity of a non-homogeneous isotropic hollow cylinder using finite element method is developed. Lord–Shulman and Green–Lindsay for the generalized thermoelasticity model are selected for that purpose which reduces to the classical model by appropriate choice of the parameters. The problem has been solved numerically using a finite element method (FEM). Numerical results for the temperature distribution, displacement, radial stress and hoop stress are represented graphically. The results indicate that the effects of nonhomogeneity are very pronounced. The effects of nonhomogeneity is presented with the three theories.

Effect of the non-homogenity on the composite infinite cylinder of orthotropic material

In this Letter, the solution of non-homogeneous orthotropic elastic cylinder for plane strain problems is developed. The dynamical problem of an orthotropic cylinder containing: (i) an isotropic core and (ii) a rigid core are considered. The elastic constants and density are taken as a power function of the radial coordinate. Analytical expressions for the component of the displacement and the components of the stresses in different cases are obtained. The numerical calculations are carried out for the component of displacement and the components of the stresses through the radial of the cylinder. The results indicate that the effect of inhomogeneity is very pronounced. Those cases have been illustrated and discussed by figures.

Magnetothermodynamic stress and perturbation of magnetic field vector in a non-homogeneous thermoelastic cylinder

This paper presents a theoretical method for analyzing magnetothermoelastic responses and perturbation of the magnetic field vector in a conducting non-homogeneous thermoelastic cylinder subjected to thermal shock. By making use of finite Hankle integral transforms the analytical expressions for magnetothermodynamic stress and perturbation response of an axial magnetic field vector in the non-homogeneous cylinder are obtained. From sample numerical calculations both magnetothermostress and perturbation of the axial magnetic field vector in a non-homogeneous cylinder is revealed and discussed.

Thermo-electro-elastic transient responses in piezoelectric hollow structures

The paper presents an analytical method to solve thermo-electro-elastic transient response in piezoelectric hollow structures subjected to arbitrary thermal shock, sudden mechanical load and electric excitation. Volterra integral equation of the second kind caused by interaction between elastic deformation and electric field is solved by using an interpolation method. Thus, the exact expressions for the transient responses of displacement, stresses, electric displacement and electric potential in the piezoelectric hollow structures are obtained by means of Hankel transform, Laplace transform, and their inverse transforms. In Section 2, based on spherical coordinates, the governing equation of thermo-electro-elastic transient responses in a piezoelectric hollow sphere is found and the associated numerical results are carried out. In Section 3, based on cylindrical coordinates, the governing equation of thermo-electro-elastic transient responses in a non-homogeneous piezoelectric hollow cylinder is found and the corresponding numerical results are carried out. The results carried out may be used as a reference to solve other transient coupled problems of thermo-electro-elasticity in piezoelectric structures.

Elastic-plastic Transition of a Non-homogeneous Thick-walled Circular Cylinder under Internal Pressure

Elastic-plastic stresses have been derived for a cylinder under internal pressure using Seth's transition theory. The effect of non-homogeneity has been discu ssed numerically and depicted graphically. It has been observed that a cylinder made of non-homogeneous material with nohomogeneity increasing radially requires a higher percentage increase in pressure to become fully plastic than to its initial yielding as compared to a homogeneous cylinder and is on the safer side of the design.

Analytical solution of a special non-homogeneous pyroelectric hollow cylinder for piezothermoelastic axisymmetric plane strain dynamic problems

By virtue of the introduction of a dependant variable and the separation of variables technique, the piezothermoelastic axisymmetric plane strain dynamic problem of a special non-homogeneous pyroelectric hollow cylinder is transformed to a Volterra integral equation of the second kind about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solutions of displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a non-homogeneous pyroelectric hollow cylinder with an arbitrary thickness subjected to arbitrary axisymmetric thermal loads. Numerical results are presented graphically.

Analytical solution for the axisymmetric plane strain electroelastic dynamics of a special non-homogeneous piezoelectric hollow cylinder

By virtue of the introduction of a dependent variable and the separation of variables technique, the axisymmetric plane strain electroelastic dynamic problem of a special non-homogeneous piezoelectric hollow cylinder is transformed to a Volterra integral equation of the second kind about a function with respect to time, which can be solved successfully by means of the interpolation method. Then the solutions of displacements, stresses, electric displacements and electric potential are obtained. The present method is suitable for a piezoelectric hollow cylinder with an arbitrary thickness subjected to arbitrary mechanical and electrical loads. Numerical results are finally presented.

Exact solution of a Stefan problem in a nonhomogeneous cylinder

The exact solution is found for the Stefan problem of inwards freezing of a nonhomogeneous cylinder whose specific heat and latent heat depend upon the inverse square of the radial distance. The freezing time for the corresponding annular cylinder is found exactly. The validity of the pseudo-steady-state approximation for the solvable cylinder problem is verified explicitly. It is argued that the exact solution for the solvable cylinder problem may be used as a small-time start-up solution for numerical procedures for general axi-symmetric cylinder problems and for general Stefan numbers.

K-0605 不均質円筒の非軸対称等温弾性解析(S05-2 複合材料システムの弾性数理モデリング(2))(S05 複合材料システムの弾性数理モデリング)

K-0605 不均質円筒の非軸対称等温弾性解析(S05-2 複合材料システムの弾性数理モデリング(2))(S05 複合材料システムの弾性数理モデリング)