Influence of Anisotropy on the Response Characteristics of Finite Cylinders Under Free Vibrations

A numerical–analytical approach is proposed to solve a problem on the free vibrations of cylindrical bodies. The approach is based on three-dimensional elastic theory and the semianalytic finite-element method. The free vibrations of isotropic and anisotropic solid cylinders of finite length are examined. It is studied how boundary conditions and mechanical and geometrical parameters affect the distribution of dynamic properties. The efficiency of the approach proposed is tested by comparing results produced by different approaches     

Reaction of an anisotropic cylindrical shell to a moving load

A method is proposed to determine the stress-strain state of inhomogeneous anisotropic viscoelastic cylindrical shells subject to a load moving along the circumference with a given velocity. The effect of localization of the load on the dynamic stress and displacement amplification factors is examined for cylinders of different lengths __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 80–88, April 2007.     

Homogenized equations for steady heat conduction in composite materials with dilutely-distributed impurities

In this paper.by using the two-space method,homogenizedequations for steady heat conduction in the composite ma-terial cylinders with dilutely-distributed elliptic cylin-ders of impurities are derived.and the ezplicit ezpres-sions for the corresponding effective heat conductivity ofthose which are concerned are obtained.It is also shownthat the macroscopic heat conduction is anisotropic whenthe cross-sections of the impurity cylinders are unidirec-tionally oriented and isotropic when the angular distribu-tion of the cross-sections is uniform.     

Elliptic cross section without warping under torsion

The object of this paper is the pure torsion of the nonhomogeneous anisotropic elastic beam. The results of Saint-Venant’s theory of uniform torsion are used to prove a nonwarping property of elliptic cylinders.     

Semi-inverse solution for Saint-Venant's problem in the theory of porous elastic materials

The purpose of this research is to study the Saint-Venant's problem for right cylinders with general cross-section made of inhomogeneous anisotropic elastic materials with voids. We reformulate the quasi-static equilibrium equations with the axial variable playing the role of a parameter. Two classes of semi-inverse solutions to Saint-Venant's problem are described in terms of five generalized plane strain problems. These classes are used in order to obtain a semi-inverse solution for the relaxed Saint-Venant's problem. An application of this results in the study of extension, bending, torsion and flexure of right circular cylinders in the case of isotropic materials is presented.     

Buckling of geometrically imperfect cylindrical shells — definition of a buckling load

On the basis of extensive buckling tests and analytical and numerical buckling analyses for composite cylinders it became desirable to provide a recommendation for the most reliable evaluation of stability limits for imperfect CFRP cylinders subjected to axial compression. This paper reports on different approaches including linear, non-linear and dynamic non-linear FE analysis results and discusses the related effects and potential difficulties.     

Propagation of Harmonic Waves in Anisotropic Piezoelectric Cylinders. Compound Waveguides

Waves in anisotropic homogeneous and piecewise-homogeneous piezoelectric cylinders are investigated for various types of anisotropy, boundary conditions, and interaction with the ambient acoustic medium and electromagnetic field     

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.     

Elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders by analytical method

An elastodynamic solution for plane-strain response of functionally graded thick hollow cylinders subjected to uniformly-distributed dynamic pressures at boundary surfaces is presented. The material properties, except Poisson’s ratio, are assumed to vary through the thickness according to a power law function. To achieve an exact solution, the dynamic radial displacement is divided into two quasi-static and dynamic parts, and for each part, an analytical solution is derived. The quasi-static solution is obtained by means of Euler’s equation, and the dynamic solution is derived using the method of the separation of variables and the orthogonal expansion technique. The radial displacement and stress distributions are plotted for various functionally graded material (FGM) hollow cylinders under different dynamic loads, and the advantages of the presented method are discussed. The proposed analytical solution is suitable for analyzing various arrangements of hollow FGM cylinders with arbitrary thickness and arbitrary initial conditions, which are subjected to arbitrary forms of dynamic pressures distributed uniformly on their boundary surfaces.     

Dynamic crack tip fields and dynamic crack propagation characteristics of anisotropic material

Based on mechanics of anisotropic material, the dynamic crack propagation problem of I/II mixed mode crack in an infinite anisotropic body is investigated. Expressions of dynamic stress intensity factors for modes I and II crack are obtained. Components of dynamic stress and dynamic displacements around the crack tip are derived. The strain energy density theory is used to predict the dynamic crack extension angle. The critical strain energy density is determined by the strength parameters of anisotropic materials. The obtained dynamic crack tip fields are unified and applicable to the analysis of the crack tip fields of anisotropic material, orthotropic material and isotropic material under dynamic or static load. The obtained results show Crack propagation characteristics are represented by the mechanical properties of anisotropic material, i.e., crack propagation velocity M and fiber direction α. In particular, the fiber direction α and the crack propagation velocity M give greater influence on the variations of the stress fields and displacement fields. Fracture angle is found to depend not only on the crack propagation but also on the anisotropic character of the material.     

Experimental determination of stiffness properties of thin-shell composite cylinders

An experimental determination is made of the in-plane stiffness properties of 11 composite cylinders constructed by filament winding. All the cylinders have in-plane and bending stiffness matrices of orthotropic form. Also, five of the cylinders exhibit an anisotropic coupling between stretching and shear of the form described by Reissner and Stavsky. In-plane stiffness matrices are determined by the classical procedure of using three simple tests: internal pressure, axial tension or compression, and torsion. They provide the data from which to extract composite orthotropic moduli for filament-wound construction. Moduli thus determined are compared with those predicted by the recent theory of S. W. Tsai. Agreement is good when a value of 0.3 is assigned to his contiguity factor.J. Tasi was formerly Associate Research Scientist, Martin Co.; is now Post-Doctoral Fellow in Mechanics, The Johns Hopkins University, Baltimore, Md.Paper was presented at 1965 SESA Spring Meeting held in Denver, Colo., on May 5–7.     

各向异性介质的弹性波散射问题的边界元方法

本文引用加权残数法建立了各向异性介质内含任意形式异质夹杂时的散射问题的边界积分方程式,导出了相应的辐射条件,计算了内含圆柱体,椭圆柱体、界面裂纹情形下对SH 波的散射位移场、应力场以及散射横截面.数值结果表明本方法用于解答各向异性介质的弹性波散射问题具有良好的精度和应用前景.     

Stress state of rotating inhomogeneous anisotropic cylinders

The stress-strain state of anisotropic cylinders under the action of centrifugal loads is considered, adopting a new approach, in the case where the elastic properties of the cylinders vary arbitrarily over the thickness. The system of resolving differential equations, in which the load is expressed as a function of the radius change, is solved. The changes of the radius of the boundary surfaces and the interlayer contact surfaces are taken into account by successive approximation. The problem is solved numerically. Specific examples of the solution are presented. S. P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Prikladnaya Mekhanika, Vol. 35, No. 8, pp. 29–34, August, 1999.     

A meshfree method for transverse vibrations of anisotropic plates

A meshfree approach, called displacement boundary method, for anisotropic Kirchhoff plate dynamic analysis is presented. This method is deduced from a variational principle, which uses a modified hybrid functional involving the generalized displacements and generalized tractions on the boundary and the lateral deflection in the domain as independent variables. The discretization process is based on the employment of the fundamental solutions of the static problem operator for the expression of the variables involved in the functional. The stiffness and mass matrices obtained for the dynamic model are frequency-independent, symmetric and positive definite and their computation involves boundary integrals of regular kernels only. Due to its features, the final resolving system can be solved with the classical approaches by using standard numerical procedures. To assess the formulation, the free vibrations of some anisotropic plates were calculated and the results compared with those obtained using other solution techniques. The present results are in good agreement with those found in the literature showing the accuracy and effectiveness of the proposed approach.     

Nonaxisymmetric Electroelastic Vibrations of a Hollow Cylinder with Radial Axis of Physicomechanical Symmetry

An approach is proposed to calculate the natural frequencies and modes of vibrations of cylindrically anisotropic piezoelectric cylinders. The frequency equation is derived, and the frequency spectrum is analyzed __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 7, pp. 68–72, July 2005.     

各向异性双材料界面裂纹扩展裂尖场

应用界面断裂力学理论和Stroh方法,研究了广义平面变形下动态裂纹沿着各向异性双材料界面扩展时的裂尖奇异应力及动态应力强度因子.双材料界面的动态裂尖区域特性主要由两个实矩阵W和D确定,且裂尖奇异应力和动态应力强度因子可以由包含这两个矩阵的柯西奇异积分方程确定,同时给出了动态应力强度因子和能量释放率的显示表达式.算例得出当裂纹以小速度扩展时,裂尖振荡因子ε与静态时几乎相同,当界面裂纹扩展速度接近瑞利波速时,ε趋于无穷大;同时得出应力强度因子及能量释放率随裂纹扩展速度的变化关系.     

Dynamic stress intensity factor K III and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.     

Torsion of Incompressible Fiber-Reinforced Nonlinearly Elastic Circular Cylinders

Torsion of solid cylinders in the context of nonlinear elasticity theory has been widely investigated with application to the behavior of rubber-like materials. More recently, this problem has attracted attention in investigations of the biomechanics of soft tissues and has been applied, for example, to examine the mechanical behavior of passive papillary muscles of the heart. A recent study in nonlinear elasticity was concerned specifically with the effects of strain-stiffening on the torsional response of solid circular cylinders. The cylinders are composed of incompressible isotropic nonlinearly elastic materials that undergo severe strain-stiffening in the stress-stretch response. Here we investigate similar issues for fiber-reinforced transversely-isotropic circular cylinders. We consider a class of incompressible anisotropic materials with strain-energy densities that are of logarithmic form in the anisotropic invariant. These models reflect stretch induced strain-stiffening of collagen fibers on loading and have been shown to model the mechanical behavior of many fibrous soft biological tissues. The consideration of anisotropy leads to a more elaborate mechanical response than was found for isotropic strain-stiffening materials. The classic Poynting effect found for rubber-like materials where torsion induces elongation of the cylinder is shown to be significantly different for the transversely-isotropic materials considered here. For sufficiently large anisotropy and under certain conditions on the amount of twist, a reverse-Poynting effect is demonstrated where the cylinder tends to shorten on twisting The results obtained here have important implications for the development of accurate torsion test protocols for determination of material properties of soft tissues.     

Some Approaches to the Solution of Problems on Thin Shells with Variable Geometrical and Mechanical Parameters

A number of approaches to the solution of stress problems for anisotropic inhomogeneous shells in the classical formulation are discussed. A review is made of approaches to the solution of one- and two-dimensional static problems for thin shells with variable parameters and to the solution of stress–strain problems for anisotropic shells of revolution under axisymmetric and non-axisymmetric loading, shallow convexo-convex shells, noncircular cylindrical shells, plates of various shapes, and shells of complex geometry     

Strain-history effect on isotropic and anisotropic plastic behavior

An experimental investigation was performed to evaluate the effect of strain history on an initially isotropic material. A hot-rolled 2.5-in.-diam bar of SAE 1045 steel provided all the test specimens. Axial and circumferential compression data indicated that the steel was isotropic. Additional tension and torsion data indicated that the steel was an isotropic-hardening von Mises material; this was also confirmed by proportionate loading of thin-walled cylinders such that the ratio of axial to circumferential stresses was either 0, 1/2, 1, 2 or ∞. Two additional sets of cylinders were preloaded either in simple axial tension or as closed-ended cylinders to an effective plastic strain of 0.006 before they were proportionately loaded. The preloading had a pronounced effect on yield surfaces for reloading if the effective plastic strain on reloading was only slightly greater than that for the preloading. The effect of preloading on the yield surfaces was small when the effective plastic strain was three to four times that for the preloading. Hill's anisotropic theory was used to predict stress-strain relations for several of the reloaded cylinders. Good agreement was obtained between theory and experiment.