Anisotropic Hollow Cylinder Research Articles

Research on Longitudinal Thermoelastic Waves in an Orthotropic Anisotropic Hollow Cylinder Based on the Thermoelastic Theory of Green–Naghdi

Research on Longitudinal Thermoelastic Waves in an Orthotropic Anisotropic Hollow Cylinder Based on the Thermoelastic Theory of Green–Naghdi

Theoretical prediction for the torsional stiffness of reinforced thermoplastic pipes (RTPs) based on the strain energy-work equivalence of anisotropic cylinders

Torsional characteristics must be considered in the mechanical analysis of offshore pipelines. However, there is no specific theoretical model for RTPs to predict the torsional behavior due to the multilayered helically winding laminates. To address the problem, a theoretical model using the energy method is constructed, in which the governing equation is based on the strain energy-work equivalence of helically anisotropic hollow cylinders instead of homogenous structures in previous studies on unbonded flexible risers. The strain energy of RTPs is firstly obtained by the stress analysis of helically anisotropic elements, while the work is derived by the torsion-deformation relationship. It gives a concise theoretical expression of torsional stiffness of RTPs for the first time and greatly improves the computation efficiency. Another improvement is that it could consider the coexistence of the isotropic and orthotropic materials due to the symmetry of isotropic materials. To verify the proposed model, quasi-static torsion tests and numerical simulations were conducted on two RTP specimens. The proposed model could give accurate torsional stiffness predictions in both twisting directions. Besides, the stress distributions, the effect of thickness-radius ratios and fiber's winding angles were also investigated, in which the applicability of the proposed model was further discussed.

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.

Finite Element Analysis of Thermoelastic Fiber-Reinforced Anisotropic Hollow Cylinder with Dual-Phase-Lag Model

In the present paper, we have constructed the equations for generalized thermoelasticity of a fiber-reinforced anisotropic hollow cylinder. The formulation is applied in the context of dualphase-lag model. An application of hollow cylinder is investigated for the outer surface is traction free and thermally isolated, while the inner surface is traction free and subjected to thermal shock. The problem is solved numerically using a finite element method. The results of displacement, temperature and radial and hoop stress are obtained and then presented graphically. Finally, the comparisons are made between the results predicted by the coupled theory, Lord and Shulman theory and dual-phase-lag model in presence and absence of reinforcement.

A thermodynamic framework to analyze the thermal shock response in an anisotropic hollow cylinder with energy dissipation

PurposeThe purpose of this paper is to analyze the thermal shock response on the deformation of circular hollow cylinder in a thermodynamically consistent manner.Design/methodology/approachThe investigation is carried out under the light of generalized thermoelasticity theory with energy dissipation. In order to obtain the analytical expressions of the components of stress and strain fields, appropriate integral transform technique is adopted and the salient features are emphasized.FindingsIt has been observed that the existence of energy dissipation can minimize the development of the stress components into the cylindrical wall. Since more amount of heat is propagate into the medium in a short period of time consequently, the medium deformed in a high rate in presence of energy dissipation. Two special phenomena are also revealed in the particular cases.Originality/valueThe numerical simulated results are demonstrated through a numerous diagrams and some important observations are explained. This work may be helpful for those researchers who are devoted on several types of heat or fluid flow into the pipeline made with anisotropic solids.

Transient thermoelastic waves in an anisotropic hollow cylinder due to localized heating

This paper presents a theoretical study of transient ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic hollow circular cylinder. Generalized thermoelastic theory proposed by Lord and Shulman is adopted to model the dynamic thermoelastic behavior of the cylinder. The concentrated heat source model used is to represent heating due to a pulsed laser beam, which is focused on the outer surface of the cylinder. A semi-analytical finite element (SAFE) method is employed to evaluate guided wave modes in the cylinder. Using integral transform techniques, the modal wave forms are obtained in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying inverse Fourier transformation in the time domain. Numerical results showing the dispersion curves for the group velocities of the propagating modes and transient radial displacements are presented. For this purpose it is assumed that the cylinder is made of transversely isotropic silicon nitride (Si 3N 4). Attention is focused on the propagation characteristics of longitudinal and flexural modes separately.

Exact Thermoelastic Analysis of Functionally Graded Anisotropic Hollow Cylinders with Arbitrary Material Gradation

An exact solution is presented for the thermoelastic analysis of functionally graded long hollow cylinders. The functionally graded material is assumed to have temperature-dependent cylindrical monoclinic material properties that vary as a function of the radial coordinate. Thermal and mechanical boundary conditions are specified on the inner and outer surfaces of the cylinder. In addition, the net axial force and torque acting on the cylinder are prescribed. The nonlinear steady-state heat conduction equation is solved using an iterative power-series solution procedure to obtain the temperature field. Subsequently, the three-dimensional thermoelasticity equations are solved using a power-series solution procedure to obtain the displacements and stresses. The solution procedure is applicable to hollow cylinders with an arbitrary variation of material properties in the radial direction. The convergence of the analytical solution is improved by dividing the hollow cylinder into multiple functionally graded concentric layers or sub-cylinders through the introduction of fictitious material interfaces. Results are presented for isotropic tungsten/copper functionally graded cylinders. The homogenized properties of the composite material are evaluated using the self-consistent scheme. The temperature, displacements and stresses are compared with numerical results obtained using the element-free Galerkin method and the effect of material gradation on the response of the cylinder is scrutinized. Results are also presented for a fiber-reinforced titanium/silicon carbide composite cylinder with functionally graded fiber orientation. The silicon carbide fibers are oriented in the axial direction on the inner surface and circumferential direction on the outer surface with a sigmoidal variation in between. The radial variation of temperature, displacements and stresses are investigated for different sigmoid exponents.

G010015 側面に任意の表面荷重が作用する異方性リングの解析([G01001]計算力学部門一般セッション(1):固体力学の基礎的な数値解析)

Analytical solution for anisotropic hollow cylinder subjected any loadings at lateral surfaces has been not derived so far whereas solution in case of an isotropy was obtained. Even in the case of isotropy, antiplane loading is not yet treated. In this study, the general solution for anisotropic hollow cylinder is shown using a complex stress functions based on Lekhnitskii formalism. Stress functions are derived using a constraint release technique, which is a kind of the convergence numeration applied for the problems of solid cylinder and infinite medium with cavity. Any loadings, for example, distributed load such as hydro pressure and concentrated load are taken into account a stress function developed a Laurent series. Example calculation is shown in several graphical representations.

Propagation of elastic waves in an anisotropic functionally graded hollow cylinder in vacuum

As a non-destructive, non-invasive and non-ionizing evaluation technique for heterogeneous media, the ultrasonic method is of major interest in industrial applications but especially in biomedical fields. Among the unidirectionally heterogeneous media, the continuously varying media are a particular but widespread case in natural materials. The first studies on laterally varying media were carried out by geophysicists on the Ocean, the atmosphere or the Earth, but the teeth, the bone, the shells and the insects wings are also functionally graded media. Some of them can be modeled as planar structures but a lot of them are curved media and need to be modeled as cylinders instead of plates. The present paper investigates the influence of the tubular geometry of a waveguide on the propagation of elastic waves. In this paper, the studied structure is an anisotropic hollow cylinder with elastic properties (stiffness coefficients c ij and mass density ρ) functionally varying in the radial direction. An original method is proposed to find the eigenmodes of this waveguide without using a multilayered model for the cylinder. This method is based on the sextic Stroh’s formalism and an analytical solution, the matricant, explicitly expressed under the Peano series expansion form. This approach has already been validated for the study of an anisotropic laterally-graded plate (Baron et al., 2007; Baron and Naili, 2010) [6,5]. The dispersion curves obtained for the radially-graded cylinder are compared to the dispersion curves of a corresponding laterally-graded plate to evaluate the influence of the curvature. Preliminary results are presented for a tube of bone in vacuum modelling the in vitro conditions of bone strength evaluation.

Solution of problems of free torsional vibrations of thick-walled orthotropic inhomogeneous cylinders

With the use of the 3D theory of elasticity, we investigate the problem of free torsional vibrations of an anisotropic hollow cylinder with different boundary conditions at its end faces. We have proposed a numerical-analytic approach for the solution of this problem. The original partial differential equations of the theory of elasticity with the use of spline approximation and collocation are reduced to an eigenvalue problem for a system of ordinary differential equations of high order in the radial coordinate. This system is solved by the stable numerical method of discrete orthogonalization together with the method of step-by-step search. We also present numerical results for the case of orthotropic and inhomogeneous material of the cylinder for some kinds of boundary conditions.

Using spline-approximation to solve problems of axisymmetric free vibration of thick-walled orthotropic cylinders

The three-dimensional theory of elasticity is used to study the free vibrations of an anisotropic hollow cylinder with different boundary conditions at the ends. The relevant problem is solved by a numerical-and-analytic method. Spline approximation and collocation is used to reduce the partial differential equations of elasticity to a boundary-value problem for a system of ordinary differential equations of high order for the radial coordinate, which is solved using the stable discrete-orthogonalization and incremental-search methods. The calculated results for an orthotropic inhomogeneous cylinder with boundary conditions of several types are presented

Porothermoelastic analyses of anisotropic hollow cylinders with applications

It has been known that material anisotropy and thermal stresses affect borehole stability significantly. Aiming at the experimental studies associated with borehole stability in anisotropic (transversely isotropic) poroelastic materials subject to non-isothermal conditions, this paper details and applies an anisotropic porothermoelastic solution to an unjacketed hollow cylinder in a triaxial set-up. Numerical analyses are presented to demonstrate thermal and material anisotropy effects on the pore pressure and the stress concentrations in and around the geometry of a hollow cylinder subjected to thermal and stress perturbations. Copyright © 2004 John Wiley & Sons, Ltd.

Solution of problems on the stress state of rotating anisotropic hollow cylinders that are nonuniform in the circumferential direction

A new approach is proposed to determining the stress-strain state of a rotating cylinder with elastic characteristics that vary in the radial and circumferential directions. Problems of this type are solved by expanding the stresses and the displacements into Fourier series, leading to a resolvent system of ordinary differential equations of a high order. The loads in these equations are given with allowance for the radial displacements. The problems are solved numerically by the method of discrete orthogonalization. As an illustration, specific problems are solved for several variants of nonuniformity of the elastic properties in the circumferential direction.

CONSOLIDATION ANALYSIS OF THE HOLLOW CYLINDER IN CONSIDERATION OF THE RIGIDITY OF SAND COLUMNS AND APPROXIMATION BY ANISOTROPIC HOLLOW CYLINDER

In an improved ground using a sand drain system, the difference in the rigidity between clay and sand causes the stress concentration on the sand columns in consequence of the progress of consolidation, thereby expanding the diameters of sand columns. In this paper, a consolidation theory is developed considering the rigidity of sand columns, on the assumptions that clay skeleton is anisotropic linear elastic, and sand columns are isotropic elastic body. And, the effects of the rigidity of sand columns and the anisotropy of clay acting upon the consolidation behavior are considered.Besides, considerations are also given to the conditions of deformation in which the consolidation of the ground installed the sand columns is approximated by the use of the consolidation theory for the anisotropic hollow cylinder. The results thereof have arrived at the conclusion that the consolidation can be approximated by the use of the anisotropic hollow cylinder with the loading on the top surface, by restraining the displacement of the internal and external circumferential surfaces.

Creep of Single Crystal Nickel-Base Superalloy Tubes Under Biaxial Tension

An analysis of the statically indeterminate problem of the creep of a biaxially loaded, anisotropic hollow cylinder is presented. The anisotropy of the material leads to a nonuniform axial stress distribution which is evaluated by numerical techniques. Single crystal, tubular specimens of a nickel-base alloy were creep-tested at 1400 deg F with an <001> crystallographic axis nearly coincident with the tube axis in order to evaluate the theoretical analysis. Comparison of predicted and measured creep rates shows fair agreement.

Transient Thermoelastic Problem for a Transversely Anisotropic Hollow Cylinder with Temperature-Dependent Properties

This paper is concerned with an axisymmetric transient thermoelastic problem for a transversely anisotropic hollow cylinder, the boundary of internal surface being subjected to a sudden temperature rise. The problem is treated on assumption that the thermal and elastic properties of the cylinder are dependent on temperature. Basic equation is solved with the aid of perturbation method. The particular boundary value problems are carried out, and the corresponding displacements and stresses are clarified. For numerical examples, calculations are performed for the cases of anisotropic cylinders made of grades ATJ and ZTA graphites respectively. In these treatments, the variation of conductivity and thermal expansion is taken to be linear according to the temperature rise, but that of the Young's moduli is taken to be quadratic. The solution for an isotropic cylinder is also derived as a particular case of the present problem.

Thermal Stresses in Anisotropic Hollow Cylinders

The equations of thermal stresses and displacements in anisotropic hollow cylinders subjected to various selected temperature boundary conditions have been derived. The hollow cylinder is assumed to be made of transversely isotropic material. Several numerical examples are treated and the effects of the degree of anisotropy on the magnitudes of the critical stress and maximum permissible gas temperature for various sizes of grades ATJ and ZTA graphite hollow cylinders are examined. The errors which could result from the assumption of isotropic material are calculated.