Orthotropic Hollow Cylinder Research Articles

Dynamic behavior of the orthotropic hollow cylinder under a magnetic field: a thermoelastic analysis

The present article focuses on the complete analytical solution of an orthotropic hollow cylinder using a proposed magneto-thermoelastic model and finite Hankel transformation. The study considers the Lord–Shulman and Green–Lindsay models of hyperbolic generalized thermoelasticity within the context of thermoelasticity theory. The analytical expressions of the field variables of the cylinder in a magnetic field were obtained under thermo-mechanical loadings. The study also offered closed-form field functions and measured the thermoelastic behavior concerning the magnetic field intensity of the cylinder based on thermoelastic theories involving a second sound. The inclusion of hyperbolic-type heat conduction models enhanced the visualization of the reflection of thermal waves into the cylinder. The study also investigated the impacts of orthotropic material properties on the considered medium and compared the results with the existing literature.

Analytical solutions and material tailoring for combined radial expansion and twisting of functionally graded orthotropic hollow cylinders

Assuming that material properties are described by the same function of the radius, we first analytically find the displacement field in a functionally graded, orthotropic and linearly elastic hollow cylinder undergoing combined radial expansion and twisting. Subsequently, either for a desired axisymmetric displacement field or a stress distribution, we determine the required variations of the material properties to produce them in an inhomogeneous orthotropic cylinder. Numerical results presented for four example problems reveal the possibility of suitably varying material properties in the radial direction to simultaneously minimize the structural mass and the maximum circumferential stress on the inner surface of a hollow cylinder. It is found that out of the three heterogeneous cylinders of the same geometric and material parameters, the one having the least mass also has the smallest value of the maximum circumferential stress on the cylinder's inner surface. It occurs when the material moduli essentially vary affinely through the cylinder thickness. The analytical solutions presented here can serve as benchmarks for others to verify their numerical algorithms.

Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories

Magneto–thermoelastic behavior of an orthotropic hollow cylinder based on Lord–Shulman and Green–Lindsay theories

Stress state modeling of non-circular orthotropic hollow cylinders under different types of loading

Based on a spatial model of the linear theory of elasticity, using an unconventional approach of the reduction of the original three-dimensional boundary value problem described by a system of partial differential equations with variable coefficients to a one-dimensional boundary value problem for a system of ordinary differential equations with constant coefficients, the problem of finding the dimensional stress of hollow elliptic orthotropic cylinders under the influence of various types of loading has been solved under certain boundary conditions at the orientation plane. Reducing the dimensionality of the original problem is carried out using analytical methods of separating variables in two coordinate directions in combination with the method of approximating functions by discrete Fourier series. The one-dimensional boundary value problem is solved by the stable numerical method of discrete orthogonalization.

A novel solution to thermo-elasto-dynamic response for inhomogeneous orthotropic hollow cylinders

This paper proposes a novel solution for the radially FGM cylinder subjected to thermo-mechanical shock. By discretizing the state space equation in the spatial domain and applying the time marching technique based on central difference, a semi-analytical solution to the thermoelastic dynamic behavior of cylinders is developed. The proposed solution technique has two advantages, one is suitable for the arbitrariness of material properties varying in the radial direction, and the other is applicable to different boundary conditions. Numerical examples for the cylinders with different graded material properties and two different boundary conditions are examined. The obtained results not only verify the correctness and effectiveness of the present solution, but also demonstrate the flexibility of the present method. The influences of gradient functions and boundary conditions on dynamic behavior are clearly displayed. The solution method is convenient and practical, which may help to freely select the gradient function for the design of FGM cylinders under various conditions.

Dynamic response of an orthotropic hollow cylinder under thermal shock based on Green–Lindsay theory

This research deals with the thermoelastic response of an orthotropic hollow cylinder under thermal shock, based on generalized thermoelasticity. In order to consider both Lord–Shulman and Green–Lindsay theories of generalized thermoelasticity, a unified formulation is considered for governing equations. The heat conduction equation and the equation of motion for the orthotropic cylinder are derived based on this unified formulation, and an analytical solution using Finite Hankel transformation is presented. A thermal shock in the form of heat flux is applied on the inner surface of the orthotropic cylinder, and then the temperature distribution and the history of stress components are plotted for the classical dynamic, Lord–Shulman and Green–Lindsay theories. The effects of considering different values for the relaxation times in the Green–Lindsay theory and considering orthotropic material properties for the cylinder are shown in the figures. The results are validated by comparing with the known data in the literature, which show good agreement.

Several cracks in an orthotropic hollow cylinder coated by an MEE layer under torsion

This paper performs such fracture analysis for an orthotropic hollow cylinder coated by a magneto-electro-elastic (MEE) layer under torsion. The orthotropic hollow cylinder contains several arbitrarily shaped cracks. A uniform electric displacement and magnetic induction are applied on the outer boundary of the MEE coating. At first, the displacement and stress components of the coated hollow cylinder weakened by a Volterra-type screw dislocation are found as a function of the dislocation density through Fourier transform. Next, distributed dislocation technique (DDT) is used to simplify the stress components corresponding to the screw dislocation to a set of Cauchy singular integral equations. The singular integral equations are subsequently solved through a numerical procedure to obtain the unknown dislocation density. Next, the stress intensity factors (SIFs) and the torsional rigidity in the cracked hollow cylinder with its MEE coating are found in terms of the dislocation density function. Several numerical results of the SIFs and torsional rigidity are provided to reveal the effects of the geometrical and physical parameters on fracture behavior. It is concluded that the SIFs can be minimized using suitable values of the electric displacement and magnetic induction.

Analytical Solution for Thermoelastic Stress Wave Propagation in an Orthotropic Hollow Cylinder

The problem of thermoelastic stress wave propagation in an orthotropic hollow cylinder is investigated using analytical methods. The fully coupled classical theory of thermoelasticity is used to extract the equations for an orthotropic cylinder. To solve the boundary value problem, heat conduction equation and equation of motion are divided into two different sets of equations, the first set consists of uncoupled equations with considering boundary conditions and the second set comprises coupled ones with initial conditions. Finite Hankel transform (Fourier-Bessel expansion) is utilized to solve the problem with respect to radial variable. Two different cases, pure mechanical load and pure thermal load, were studied numerically to show the effect of considering the thermomechanical coupling term in the heat conduction equation. To show the effect of considering the coupling term in the heat conduction equation, the temperature history is plotted for the pure mechanical load case, where the temperature rises without applying any thermal load. By applying boundary conditions on the inner surface of the cylinder, initiation of the stress waves from the inner surface of the cylinder, propagation through the thickness in the radial direction and reflection from the outer surface were observed in the plotted figures.

Fractional Moore-Gibson-Thompson heat transfer model with nonlocal and nonsingular kernels of a rotating viscoelastic annular cylinder with changeable thermal properties

Long hollow cylinders are commonly utilized in various technological applications, including liquid and gas transmission. As a result, its value is growing, becoming increasingly important to many research efforts. Compared with thermal isotropic homogeneous cylinders, thermo-viscoelastic orthotropic cylinders have less relevant data. In this paper, a thermoelastic fractional heat conduction model was developed based on the Moore-Gibson-Thompson equation to examine the axial symmetry problem of a viscoelastic orthotropic hollow cylinder. Atangana and Baleanu derivative operators with nonsingular and nonlocal kernels were used in constructing the fractional model. The thermal properties of the cylinder materials are assumed to be temperature-dependent. The Laplace transform is applied to solve the system of governing equations. The numerical calculations for temperature, displacement, and stress components are performed by the effect of fractional order, rotation, and changing thermal properties of the cylinder. The results showed that due to the presence of fractional derivatives, some properties of the physical fields of the medium change according to the value of the fractional order.

Thermo‐viscoelastic behavior in an infinitely thin orthotropic hollow cylinder with variable properties under the non‐Fourier MGT thermoelastic model

AbstractThe purpose of this work is to investigate the influences of viscosity and the variation of thermal conductivity on the thermoelastic vibrations in a very thin hollow cylinder. The generalized thermal model has been developed using the Moore Gibson‐Thompson (MGT) equation by adding relaxation time in the developed Fourier law according to Green‐Naghdi theories. In addition to the initial conditions, some boundary conditions have been taken into consideration on the inner and external surface of the hollow solid cylinder. Unlike many problems in which the coefficient of thermal conductivity is assumed to be constant, it has been taken into account that it is variable and depends on the change of temperature. By applying the Laplace transform method, the numerical solutions are assigned to the studied physical quantities. The studied quantities have been presented graphically and in tabular form to compare the outcomes for various models of thermoelasticity and to illustrate the influences of changing thermal properties and viscosity on the physical fields.

Study of surface wave vibration in rotating human long bones of cylindrical shape under the magnetic field influence

ABSTRACT Internal remodeling of Bone models describes the process by which bone adapts its histological structure to change in the long duration of mechanical load areas. In orthopedics, wave propagation over bone is used in monitoring the rate of fracture healing. The present problem studies the effect of initial stress, rotation and magnetic field on wave propagation in long dry bones. A dry long bone has been considered as an orthotropic hollow cylinder. The equation of motion is solved in terms of displacements. Bisection method has been used to calculate the phase velocity of harmonic wave and frequencies of vibration in anisotropic long bone. Peculiar effects of rotation, initial stress, surface span and magnetic field on vibrations in long bone medium have been investigated and presented through graphs. The present study finds its applications in wave propagation and vibration test to determine the vivo properties of long bones. As an outcome, there is a significant effect of initial stress on long bone structure as compared to rotation and magnetic parameter. Findings may also be useful for theoretical development of orthopedic studies related to cylindrical poroelastic long bones.

Mixed analytic/energetic approach for a sliding orthotropic hollow cylinder. Application to coil sagging

This paper deals with the numerical simulation of coil sagging. This problem arises within the framework of the steel making industry where strips are wound on themselves for storage. Coil sagging is a major defect that can occur for recent grades undergoing phase transitions during the coiling process. The detailed mechanisms leading to coil sagging are still not well understood, making this phenomenon very difficult to prevent. The coil is a multilayer hollow cylinder where sliding takes place at each interface and significantly contributes to the overall deformation. However, a detailed numerical simulation addressing the contact problem, considering both pressure and sliding is difficult to perform under non-axisymmetric conditions. This paper presents a simplified approach considering an orthotropic hollow cylinder instead of a multilayer coil. The anisotropy is due to contact roughness that tends to decrease the radial stiffness. The hollow cylinder is subjected to gravity and an eigenstrain representing thermal expansion, phase transitions and transformation induced plasticity. Sliding at each interface is taken into account through a continuous plastic-like shear strain that is determined through an energetic principle. The proposed solution relies on analytical developments so that computation time is compatible with parametric studies. Results are addressed in order to give a better understanding of mechanisms and conditions under which coil sagging occur.

Guided waves propagation in anisotropic hollow cylinders by Legendre polynomial solution based on state-vector formalism

A spectral approach was presented in the computation of dispersion curves for the general anisotropic hollow cylinders. The derivation is based on the hybrid method of the state-vector formalism and Legendre polynomials expansion, which was previously adopted for the anisotropic plates. This method will lead to an eigenvalue/eigenvector problem for the calculation of wavenumbers and displacement profiles. This hybrid method avoids solving the transcendental dispersion equation. A closed-form solution for the hollow cylinder, involving multiple integral expressions, is demonstrated. A stable scheme for the integration expansion was established by re-expanding the expansion operators from the first round Legendre polynomial expansion versus the displacements. Usually, the traditional matrix methods are based on root-finding algorithms, which is difficult to implement in anisotropic tubes. In this research, the hybrid approach we proposed provides a reliable mathematical solution of wave propagations in an anisotropic hollow cylinder. Applications will be illustrated using isotropic and orthotropic hollow cylinders, in which the isotropic case agrees well with the results by global matrix method. The dispersion curves of orthotropic hollow cylinders, when the out radius set to approximate infinity, are compared to its corresponding anisotropic plate, which is obtained from our previous work. Furthermore, the displacement and stress profiles will be given and analyzed for an orthotropic tube, which has 10 mm thickness with an out radius of 50 mm.

Determination of the thermal stress wave propagation in orthotropic hollow cylinder based on classical theory of thermoelasticity

The thermoelasticity problem in a thick-walled orthotropic hollow cylinder is solved analytically using finite Hankel transform and Laplace transform. Time-dependent thermal and mechanical boundary conditions are applied on the inner and the outer surfaces of the cylinder. For solving the energy equation, the temperature itself is considered as boundary condition to be applied on both the inner and the outer surfaces of the orthotropic cylinder. Two different cases are assumed for solving the equation of motion: traction–traction problem (tractions are prescribed on both the inner and the outer surfaces) and traction–displacement (traction is prescribed on the inner surface and displacement is prescribed on the outer surface of the hollow orthotropic cylinder). Due to considering uncoupled theory, after obtaining temperature distribution, the dynamical structural problem is solved and closed-form relations are derived for radial displacement, radial and hoop stress. As a case study, exponentially decaying temperature with respect to time is prescribed on the inner surface of the cylinder and the temperature of the outer surface is considered to be zero. Owing to solving dynamical problem, the stress wave propagation and its reflections were observed after plotting the results in both cases.

A New Approach to Thermal Analysis of a Multilayered Cylindrical Structure With Imperfect Bonds and Internal Heat Source

In the present research, a new and straightforward mathematical model, named augmented state-space method, is introduced to solve the heat conduction equation for a multilayered orthotropic hollow cylinder with bonding imperfection in the presence of heat source. Since such problems including heat source are inherently inhomogeneous and complex, augmented state-space method converts these inhomogeneous equations into homogeneous ones. The transient solution will be achieved by present method based on laminate approximation theory in the Laplace domain, and then the solutions obtained are retrieved into the time domain by applying the numerical Laplace transform inversion. All material properties can be considered to vary continuously within the cylinder along the radial direction with arbitrary grading pattern. Based on the proposed method, the solution of heat conduction problem can be also obtained for general boundary conditions which may be included various combinations of arbitrary temperature, flux, or convection. Due to lack of any data on the transient thermal analysis corresponding to problems with imperfect bonds in the cylindrical coordinate system (r,θ), comparison is carried out with the available results for the three-layer semi-circular annular region with perfect bonds in the literature. Finally, the influence of orthotropy and interface imperfection on the distribution of the temperature field for three-layer hollow cylinder, in which the second layer is made of orthotropic functionally graded material (FGM), will be visualized.

Effect of Orthotropy on the Stress State of Longitudinally Corrugated Hollow Cylinders

The effect of orthotropy on the stress state of longitudinally corrugated orthotropic hollow cylinders is analyzed using a three-dimensional problem formulation, the analytical variable-separation and Fourier-series methods, and the numerical discrete-orthogonalization method. The results obtained are presented in the form of graphs of displacement and stress fields

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method.

Homogenization and Stress Analysis of Multilayered Composite Offshore Production Risers

An approach for stress analysis of multilayered composite cylinders is proposed for the analysis of new composite risers used in deep-water oil production of offshore petroleum industries. Risers essentially comprise long cylindrical sections connected end-to-end. In the formulation, only stresses and strains that are continuous through the thickness of the multilayered composite risers are taken to be equal to reported solutions for homogenous orthotropic hollow cylinders using homogenized material properties. These stress and strain solutions are then used to calculate the remaining discontinuous stresses and strains from the material properties of individual layers of materials. The homogenized elastic constants of cylindrically orthotropic composite risers are derived from force-deformation equivalence, taking into account the stress and strain distributions in each layer. Four typical loading conditions are considered in the stress analysis, namely, internal and external pressures, axial loading, bending, and torsion. Examples of homogenized elastic constants and stress analyses of composite cylindrical structures with different layups and materials are presented to demonstrate the application of the proposed method. The results compared very favorably with those from other solutions. This method provides practical benefits for the design and analysis of composite risers. Because there is no requirement to explicitly enforce interfacial continuity in this method, stress analyses of composite cylinders with many layers of different fiber angles or materials can be carried out efficiently. The homogenized elastic constants can greatly expedite the analysis of entire composite riser systems by replacing complex models of riser sections with homogenized riser sections.

Effect of Rotation on a Non-Homogenous Orthotropic Hollow Elastic Cylinder

Effect of Rotation on a Non-Homogenous Orthotropic Hollow Elastic Cylinder

Piezoelectric Behavior of an Inhomogeneous Hollow Cylinder with Thermal Gradient

An analytical solution to the axisymmetric problem of a radially polarized, radially orthotropic piezoelectric hollow cylinder with a thermal gradient and subjected to various boundary conditions is developed. The elastic coefficients, piezoelectric coefficients, stress-temperature moduli, dielectric coefficient, pyroelectric coefficients, thermal conductivity coefficient, and thermal expansion coefficients of the hollow cylinder are assumed to be graded in the radial direction according to a simple power-law distribution. The governing second-order differential equations are derived from the equilibrium equation, the charge equation of electrostatics, and steady state heat transfer equation through the radial direction of the inhomogeneous hollow cylinder. The displacement, stresses, and potential field distributions in the cylinder are examined. The influence of the inhomogeneity parameter on the numerical results is investigated.