Anisotropic Cylinder Research Articles

Thermal Effects in Anisotropic Porous Elastic Rods

This research is concerned with the thermoelastic deformation of a porous anisotropic right cylinder subjected to a thermal field independent of the axial coordinate. The case of a material with a plane of elastic symmetry which contains the axis of cylinder is considered. The solution of the problem is expressed in terms of solutions of some generalized plane strain problems. It is shown that the temperature field produces extension, torsion, and a plane strain. For this kind of anisotropy, an infinitesimal twist produces a variation of volume fraction field. The method is used to study the deformation of an inhomogeneous circular cylinder.

Differential theory for anisotropic cylindrical objects with an arbitrary cross section

We extend the differential theory to anisotropic cylindrical structures with an arbitrary cross section. Two cases have to be distinguished. When the anisotropic cylinders do not contain the origin, the scattering matrix of the device is calculated from the extended differential theory with the help of the scattering matrix propagation algorithm. The fields outside the cylinders are described by Fourier-Bessel expansions. When the origin is located in one cylinder, the fields inside the cylinder are expressed from a semi-analytical theory related to a homogeneous anisotropic medium. In this second case, the formalism of the scattering matrix propagation algorithm is not exactly the same and requires suitable change. The numerical results are in good agreement with the ones obtained for the diffraction by one circular cylinder. The theory is then applied on the diffraction by an elliptical cylinder.

Methods and Findings of Stress–strain State and Strength Analyses of Multilayer Thick-Walled Anisotropic Cylinders under Dynamic Loading (Review). Part 2. Theoretical Methods

The authors review the known (from available publications) methods and results of theoretical (analytical and numerical) investigations of stress–strain state and strength of multilayer thickwalled anisotropic cylinders under dynamic loading.

Stability of anisotropic cylinder with zero expansion

We study the dynamical instability of anisotropic collapsing cylinder with the expansion-free condition, which generates vacuum cavity within fluid distribution. The perturbation scheme is applied to distinguish Newtonian, post-Newtonian and post-post Newtonian terms, which are used for constructing dynamical equation at Newtonian and post-Newtonian regimes. We analyze the role of pressure anisotropy and energy density inhomogeneity on the stability of collapsing cylinder. It turns out that stability of the cylinder depends upon these physical properties of the fluid, not on the stiffness of the fluid.

Thin and Moderately Thick Anisotropic Cylinders under Torsion, Axial Compression and Combined Load

Thin and Moderately Thick Anisotropic Cylinders under Torsion, Axial Compression and Combined Load

Methods and findings of stress-strain and strength analyses of multilayer thick-walled anisotropic cylinders under dynamic loading (review). Part 1. Experimental studies

The paper provides a review of the known (from available publications) methods and findings of experimental studies of stress-strain state and strength of multilayer thick-walled anisotropic cylinders under dynamic loading.

Microwave power absorbed by and scattered from a multilayered zero-index anisotropic metamaterial-semiconductor cylinder

We present here dependencies of scattered and absorbed powers of incident perpendicularly and parallel polarized microwaves by a multilayered cylinder. We consider here the normal (angle θ=90∘) and oblique (angles θ=60∘,30∘,5∘) incidence of microwave on the cylinder. The one consists of a glass core that is coated by the six anisotropic metamaterial and lossy n-Si semiconductor alternative layers. Characteristics of a cylinder with the semiconductor external layer are presented. The dispersion dependency of n-Si losses was taken into account. The metamaterial is a uniaxial anisotropic medium with the electric and magnetic plasma resonances in the frequency range from 1 until 4 GHz. The anisotropic metamaterial can include the constitutive parameters equal to zero. The multilayered cylinder has the external radius equal to 2 mm. The glass core has a radius equal to 0.5 mm. The thickness of all layers is the same. We have compared the scattered and absorbed power dependencies on the microwave polarization, the angle of microwave incidence (the normal and oblique directions of the incidence to the z-axis), and the n-Si specific resistivity. We discovered specific dependencies of scattered and absorbed powers on the parameters.

Statistical Knockdown Factors of Buckling Anisotropic Cylinders Under Axial Compression

Statistical knockdown factors for the axial buckling of anisotropic cylinders were derived for practical design purposes. The solution with the least amount of simplification in the linear bifurcation theory was chosen from the previously published solutions, and it was compared with more than 100 experimental results from the open literature. A-basis values (99% probability with 95% confidence level) and B-basis values (90% probability with 95% confidence level) of knockdown factors were obtained by using inferential statistics, i.e., inference concerning unknown aspects of a population by using a small sample.

Propagation properties of an elliptical anisotropic metamaterial cylinder

The propagation characteristics were investigated of an open elliptical cylinder comprising a uniaxial anisotropic metamaterial. The dispersion relation for hybrid modes in this cylinder was examined theoretically. It is shown that forward and backward waves can be supported by such a metamaterial cylinder. Even and odd modes have different losses in a realistic anisotropic elliptical cylinder. The forward wave can propagate longer distances than the backward wave because of its lower loss. The light can propagate backward on the cylinder without the limit of structure size. The odd modes have higher operating wavelengths than the even modes. The extraordinary properties in this structure are identified as multilayer plasmons. The validity of the effective medium approximation of this structure is examined.

On the torsion of inhomogeneous and anisotropic bars

This paper is concerned with the torsion of anisotropic, linearly elastic cylindrical bars. The solution of the problem in the case where the medium has a plane of elastic symmetry which contains the axis of the cylinder is established. We consider the case of inhomogeneous cylinders where the elastic coefficients are independent of the axial coordinate. We prove that, in general, the torsion induces extension and bending. The solution is new even for homogeneous bodies. The results are used to study the torsion of an anisotropic circular cylinder.

側面に任意荷重を受ける異方性だ円柱の解析

This paper presents general solutions for anisotropic cylinder using complex stress functions based on Lekhnitskii formalism. Up to now, an analytical solution of isotropic cylinder has been widely used whereas solutions of anisotropic elliptic cylinders subject to arbitrary surface loads have not been derived. The proposed complex stress functions, which are developed by Laurent series, enable to solve conditions under distributed loads like hydro pressures and concentrated loads. The function can also analyze a shear load parallel to longitudinal axis of a cylinder. Analyzed stress distributions are graphically represented.

Simple Closed-Form Solution for the Buckling of Moderately Thick Anisotropic Cylinders

Simple Closed-Form Solution for the Buckling of Moderately Thick Anisotropic Cylinders

Cylinder with charged anisotropic source

We take charged anisotropic fluid cylinder when there is no external pressure acting on the fluid. This is a cylindrical version of the Krori and Barua's method to explore the field equations with anisotropic fluid. We discuss models with positive matter density and pressure that satisfy all the energy and stability conditions. It is found that charge does not vanish at the center of the cylinder. The equilibrium condition as well as physical conditions are discussed. Further, we highlight the connection between our solutions and the charged strange quark stars as well as with dark matter including charged massive particles. The graphical analysis of the matter variables versus charge is given which indicates a physically reasonable matter distribution.

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.

Tunable phononic crystals with anisotropic inclusions

We present a theoretical study on the tunability of phononic band gaps in two-dimensional phononic crystals consisting of various anisotropic cylinders in an isotropic host. A two-dimensional plane-wave expansion method was used to analyze the band diagrams of the phononic crystals; the anisotropic materials used in this work include cubic, hexagonal, trigonal, and tetragonal crystal systems. By reorienting the anisotropic cylinders, we show that phononic band gaps for bulk acoustic waves propagating in the phononic crystal can be opened, modulated, and closed. The methodology presented here enables enhanced control over acoustic metamaterials which have applications in ultrasonic imaging, acoustic therapy, and nondestructive evaluation.

Relationships between the Torsions of Anisotropic Circular and of Isotropic Elliptical Elastic Cylinders

Relationships between the solutions to the Saint-Venant torsion of an anisotropic circular cylinder and of an isotropic elliptical cylinder are proven. It is shown that if the geometrical data describing an isotropic elliptical cylinder are certain functions of the shear rigidities of an anisotropic circular cylinder, then the torsional functions and torsional rigidities of the considered cross-sections are the same. The material of both cylinders is homogeneous. The class of anisotropy taken into account has at least one plane of elastic symmetry normal to the axis of the circular cylinder.

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.

Buckling of thin and moderately thick anisotropic cylinders under combined torsion and axial compression

The effects of anisotropy, transverse shear stiffness, length, and their interactions on buckling under pure torsion and under combined axial compression and torsion were investigated using a previously derived analytical model based on deep shell theory including anisotropy and transverse shear stiffness. The model was verified only for buckling under pure axial compression, hence results for buckling under torsion have now been compared with the results of previous analyses, and the comparison showed that the model has good accuracy for buckling under torsion. Investigation showed that the buckling loads of a cylindrical shell are affected not only by anisotropy and transverse shear stiffness but also by shell length. This means that the shallow shell theory (Donnell-type theory) is not appropriate and deep shell theory including anisotropy and transverse shear stiffness must be used.

Effect of anisotropy on steady state creep in functionally graded cylinder

The steady state creep in transversely isotropic functionally graded cylinder, operating under internal and external pressures, has been investigated. The cylinder is composed of functionally graded material (FGM) containing silicon carbide whiskers in a matrix of 6061Al. The creep behavior of the FGM has been described by a threshold stress based creep law. The effect of anisotropy on creep stresses and creep rates in the FGM cylinder has been analysed and compared with an isotropic FGM cylinder. The anisotropy is represented by a parameter α, defined as the ratio of radial (or axial) and tangential yield strength. The study reveals that in an anisotropic FGM cylinder i.e. when α deviates from unity, radial and tangential stresses are marginally affected whereas axial and effective stresses are significantly affected as compared to those in an isotropic FGM cylinder. The strain rates as well as inhomogeneity in strain rates in the FGM cylinder decrease significantly when α reduces from 1.3 to 0.7. The magnitude of stresses, strain rates and inhomogenity in strain rates in the FGM cylinder, subjected to internal pressure alone, could be significantly reduced by subjecting it to both internal and external pressures though the stress inhomogenity in the FGM cylinder increases.