Cylindrical interface crack in a hollow layered functionally graded cylinder under static torsion

A hollow functionally graded composite cylinder under static torsion, which consists of an inner and outer elastic circular tube with a cylindrical interface crack, is studied in this work. By utilizing Fourier integral transform method, the mixed boundary value problem is reduced to a Cauchy singular integral equation, from which the numerical results of the stress intensity factor are obtained by the Lobatto–Chebyshev quadrature technique. Numerical results demonstrate the coupled effects of geometrical, physical, and functionally graded parameters on the interfacial fracture behavior.     

Effect of friction on subsurface stresses in sliding line contact of multilayered elastic solids

A numerical integral scheme based on Fourier transformation approach is employed to investigate the effect of friction on subsurface stresses arising from the two-dimensional sliding contact of two multilayered elastic solids. The analysis incorporates bonded and unbonded interface boundary conditions between the coating layers. Two line contact problems are presented. The first one is the contact problem between a rigid cylinder and a two-layer half space and the second one is the indentation of a multilayered elastic half-space by a flat rigid punch. The effects of the surface coating on the contact pressure distribution and subsurface stress field are presented and discussed.     

The influence of Murnaghan constants on the propagation of a torsional wave in pre-stretched compound circular cylinders

The propagation of torsional waves in prestressed compound circular cylinders is investigated modeling them by a piecewise-homogeneous body and using the three-dimensional linearized theory of elastic waves in prestressed body. It is assumed that the elastic relations for the components of the cylinders include the Murnaghan potential. The numerical investigations are performed for bronze (Br) or brass (Pr) (for the solid cylinder) and steel (St) (for the hollow cylinder). The effect of the variation of the geometric (the ratio of the thickness of the outer cylinder to the radius of the inner cylinder) and mechanical parameters on the dispersion curves are analyzed using the numerical results obtained     

非理想界面弹性层/压电柱结构中SH波的传播特性

研究了各向同性弹性层与压电柱之间非理想连接时沿周向传播的SH波的频散特性.弹性层表面力学自由;弹性层与压电柱之间应力连续、位移间断.通过求解控制方程,将问题的解用Bessel函数表示,利用界面条件和边界条件得到频散方程,然后对其进行数值求解,分析了界面性态、材料常数和几何尺寸对SH波传播特性的影响.     

Exact solutions for radial deformations of a functionally graded isotropic and incompressible second-order elastic cylinder

We find closed-form solutions for axisymmetric plane strain deformations of a functionally graded circular cylinder comprised of an isotropic and incompressible second-order elastic material with moduli varying only in the radial direction. Cylinder's inner and outer surfaces are loaded by hydrostatic pressures. These solutions are specialized to cases where only one of the two surfaces is loaded. It is found that for a linear through-the-thickness variation of the elastic moduli, the hoop stress for the first-order solution (or in a cylinder comprised of a linear elastic material) is a constant but that for the second-order solution varies through the thickness. The radial displacement, the radial stress and the hoop stress do not depend upon the second-order elastic constant but the hydrostatic pressure and hence the axial stress depends upon it. When the two elastic moduli vary as the radius raised to the power two or four, the radial and the hoop stresses in an infinite space with a pressurized cylindrical cavity equal the pressure in the cavity. For an affine variation of the elastic moduli, the hoop stress in an internally loaded cylinder made of a linear elastic isotropic and incompressible material at the point is the same as that in a homogeneous cylinder. Here R_in and R_ou equal, respectively, the inner and the outer radius of the undeformed cylinder and R the radial coordinate of a point in the unstressed reference configuration.     

一种散体材料SHPB被动围压试验体应力修正方法

本文利用有限元仿真给出了一种修正方法，并用数值仿真和试验验证了该方法的可靠性。研究表明:散体材料SHPB被动围压试验中，试样厚度远小于厚壁圆筒长度时，端部效应会导致厚壁圆筒不均匀凸出变形，计算材料的体应力-应变关系不能将厚壁圆筒应力状态简化为平面应力问题；厚壁圆筒处于弹性状态下，通过厚壁圆筒理论计算出的径向力与真实径向力存在一定比例关系，在一定范围内，折算系数与试样实时厚度呈二次函数关系。     

Stress intensity factors around a cylindrical crack in an interfacial zone in composite materials

Axisymmetric stresses around a cylindrical crack in an interfacial cylindrical layer between an infinite elastic medium with a cylindrical cavity and a circular elastic cylinder made of another material have been determined. The material constants of the layer vary continuously from those of the infinite medium to those of the cylinder. Tension surrounding the cylinder and perpendicular to the axis of the cylinder is applied to the composite materials. To solve this problem, the interfacial layer is divided into several layers with different material properties. The boundary conditions are reduced to dual integral equations. The differences in the crack faces are expanded in a series so as to satisfy the conditions outside the crack. The unknown coefficients in the series are solved using the conditions inside the crack. Numerical calculations are performed for several thicknesses of the interfacial layer. Using these numerical results, the stress intensity factors are evaluated for infinitesimal thickness of the layer.     

Elastic field due to an edge dislocation in a multilayered composite

A numerical procedure is presented for the analysis of the elastic field due to an edge dislocation in a multilayered composite. The multilayered composite consists of n perfectly bonded layers having different material properties and thickness, and two half-planes adhere to the top and bottom layers. The stiffness matrices for each layer and the half-planes are first derived in the Fourier transform domain, then a set of global stiffness equations is assembled to solve for the transformed components of the elastic field. Since the singular part of the elastic field corresponding to the dislocation in the full-plane has been extracted from the transformed components, regular numerical integration is needed only to evaluate the inverse Fourier transform. Numerical results for the elastic field due to an edge dislocation in a bimaterial medium are shown in fairly good agreement with analytical solutions. The elastic field and the Peach–Kohler image force are also presented for an edge dislocation in a single layered half-plane, a two-layered half-plane and a multilayered composite made of alternating layers of two different materials.     

Magneto-thermoelastic problem in non-homogeneous isotropic cylinder

The present paper concerns the investigation of the stress, temperature and magnetic fields in an isotropic elastic cylinder in a primary magenetic field when the curved surface of the cylinder subject to certain boundary conditions.The system of fundamental equations is solved by means of a finite difference method and the numerical calculations are carried out for the temperature, the components of displacement and the components of stresses with time and through the thickness of the cylinder. The results indicate that the effects of inhomogeneity and magnetic field are very pronounced.     

Electroelastic response of a piezoelectric cylinder with D∞ symmetry under axisymmetric mechanical loading

To understand the electroelastic field in fibers made of biodegradable polymers such as poly-l-lactic acid, we theoretically analyze the axisymmetric electroelastic field in a solid and infinitely long cylinder with D_∞ symmetry, when subjected to a combined pressure and torsional shear stress. By introducing two kinds of displacement potential functions and an electric potential function and applying a Fourier transform technique, we derive the formulae for the electroelastic field quantities inside the body. Moreover, by performing numerical calculations, we elucidate the field both qualitatively and quantitatively, and investigate the possibility of using fibers made of poly-l-lactic acid for medical engineering applications.     

A Solution for the Stress Distribution in a Granular Medium

We propose an example of an incremental elastic problem for a granular material. The mechanical behavior of this material is sensitive to the confining pressure that typically is applied before any loading. Experiments, numerical simulations, and theoretical models show that the effective elastic moduli of a granular medium are function of the confining pressure in non-linear way. Therefore, if we consider a reference state where the pressure is not constant the material behaves differently in each point and, for example, the stress associated to a subsequently loading should be obtained as solution of a non-homogeneous material. We focus our attention on this kind of problem for a granular material that fills an hollow cylinder first isotropically compressed and then sheared under a rotatory motion. Next a small perturbation is applied on the boundaries of the specimen and we evaluate the corresponding stress distribution in the plane perpendicular to the axis of the cylinder.     

Poromechanical response of a finite elastic cylinder under axisymmetric loading

Drained or undrained cylindrical specimens under axisymmetric loading are commonly used in laboratory testing of soils and rocks. Poroelastic cylindrical elements are also encountered in applications related to bioengineering and advanced materials. This paper presents an analytical solution for an axisymmetrically-loaded solid poroelastic cylinder of finite length with permeable (drained) or impermeable (undrained) hydraulic boundary conditions. The general solutions are derived by first applying Laplace transforms with respect to the time and then solving the resulting governing equations in terms of Fourier–Bessel series, which involve trigonometric and hyperbolic functions with respect to the z-coordinate and Bessel functions with respect to the r-coordinate. Several time-dependent boundary-value problems are solved to demonstrate the application of the general solution to practical situations. Accuracy of the numerical solution is confirmed by comparing with the existing solutions for the limiting cases of a finite elastic cylinder and a poroelastic cylinder under plane strain conditions. Selected numerical results are presented for different cylinder aspect ratios, loading and hydraulic boundary conditions to demonstrate the key features of the coupled poroelastic response.     

自平衡端头载荷问题衰减率的分析与计算

给出了自平衡端头载荷问题应力衰减率分析的一种方法．用边界单元法求得了在端面自平衡载荷作用下，具有椭圆截面和矩形截面的弹性柱体内应力场的最小衰减率。计算结果表明：当椭圆截面的长短轴之比和矩形截面的长宽之比变化时，最小衰减率变化很小．     

Complementary energy variational approach for plane elastic problems with singularities

Presented is the numerical analysis of plane elastic problems involving stress concentrations and/or singularities using a physically meaningful complementary energy variational approach. The continuum body is modeled by a non-conventional truss structure. Stress distributions in laminated composite bodies and orthotropic sheets with a through crack are obtained. The present results are compared with the analytical solutions for different numerical methods.     

Surface tension-induced stress concentration around a nanosized hole of arbitrary shape in an elastic half-plane

This paper studies surface tension-induced stress concentration around a nanosized hole of arbitrary shape inside an elastic half-plane. Of particular interest is the maximum hoop stress on the hole’s boundary with relation to the point of maximum curvature and the distance between the hole and the free surface of the half-plane. The shape of the hole is characterized by a conformal mapping which maps the exterior of the hole onto the exterior of the unit circle in the image plane. On using the technique of conformal mapping and analytic continuation, the complex potentials of the half-plane are expressed in a series form with unknown coefficients to be determined by Fourier expansion method. Detailed numerical results are shown for elliptical, triangular, square and rectangular holes. Two basic conclusions are that the hoop stress increases with decreasing hole size and the maximum hoop stress generally appears nearby but not exactly at the point of maximum curvature. In addition, it is shown that the hoop stress nearby the point of maximum curvature on the hole’s boundary increases rapidly with decreasing distance between the hole and the free surface of the half-plane. On the other hand, if the distance between the hole and the free surface is more than three times the hole size, the effect of the free surface on the stress concentration around the hole is ignorable and the elastic half-plane can be treated approximately as an elastic whole plane.     

Propagation of discontinuities in electromagneto generalized thermoelasticity in cylindrical regions

In this work we study wave propagation for a problem of an infinitely long solid conducting circular cylinder whose lateral surface is traction free and subjected to known surrounding temperatures in the presence of a uniform magnetic field in the direction of the axis. The problem is in the context of generalized magneto-thermo-elasticity theory with one relaxation time. Laplace transform techniques are used to derive the solution in the Laplace transform domain. The inversion process is carried out using a numerical method based on Fourier series expansions. Wave propagation in the elastic medium and in the free space, bounding it, is investigated.     

Finite and transversely isotropic elastic cylinders under compression with end constraint induced by friction

This paper derives an exact solution for the non-uniform stress and displacement fields within a finite, transversely isotropic, and linear elastic cylinder under compression with a kind of radial constraint induced by friction between the end surfaces of the cylinder and the loading platens. The main feature of the present work is the introduction of a general solution form for Lekhnitskii’s stress function such that the governing equation and all end and curved boundary conditions of the cylinder are satisfied exactly. Two different solutions were obtained corresponding to the real or complex characteristic roots of the governing equation, depending on the combination of the elastic material constants. The solution by Watanabe [Watanabe, S., 1996. Elastic analysis of axi-symmetric finite cylinder constrained radial displacement on the loading end. Structural Engineering/Earthquake Engineering JSCE 13, 175s–185s] for isotropic cylinders under compression test can be recovered as a special case. Our numerical results show that both the non-uniform stress distribution and the difference between the apparent and the true Young’s moduli of the cylinder are very sensitive to the anisotropy of Young’s moduli, Poisson’s ratios and shear moduli. A more distinct bulging shape of the cylinder is expected when anisotropy in shear modulus is strong, the cylinder is relatively short, and the end constraint is large. The bulging shape, however, does not depend strongly on anisotropy of either Poisson’s ratio or Young’s modulus.     

An explicit formulation for the evolution of nonlinear surface waves interacting with a submerged body

An explicit formulation to study nonlinear waves interacting with a submerged body in an ideal fluid of infinite depth is presented. The formulation allows one to decompose the nonlinear wave–body interaction problem into body and free‐surface problems. After the decomposition, the body problem satisfies a modified body boundary condition in an unbounded fluid domain, while the free‐surface problem satisfies modified nonlinear free‐surface boundary conditions. It is then shown that the nonlinear free‐surface problem can be further reduced to a closed system of two nonlinear evolution equations expanded in infinite series for the free‐surface elevation and the velocity potential at the free surface. For numerical experiments, the body problem is solved using a distribution of singularities along the body surface and the system of evolution equations, truncated at third order in wave steepness, is then solved using a pseudo‐spectral method based on the fast Fourier transform. A circular cylinder translating steadily near the free surface is considered and it is found that our numerical solutions show excellent agreement with the fully nonlinear solution using a boundary integral method. We further validate our solutions for a submerged circular cylinder oscillating vertically or fixed under incoming nonlinear waves with other analytical and numerical results. Copyright © 2007 John Wiley & Sons, Ltd.     

Application of the angular superposition method to the contact problem on the compression of an elastic cylinder

The angular superposition method is used to construct an approximate solution of the contact problem on the compression of an elastic cylinder by two rigid plates. The solution thus obtained has a closed-form analytic expression and can be used in the entire domain of the cylinder cross-section. We analyze the absolute error, which takes the largest value near the points of contact between the plates and the cylinder, where the boundary conditions are discontinuous. According to the von Mises criterion, when moving into the depth of the cylinder from the contact site along the symmetry axis, the second invariant J ₂ of the stress deviator tensor first decreases and then, after attaining a minimum, increases and attains the largest value at a small depth, which agrees with Johnson’s photoelastic experiments and Dinnik’s computations. We present the graphs of the displacement and normal stress distributions over the contact site, the dependence of the compressing force on the displacements of rigid plates, and the dependence of the invariant J ₂ on the coordinate along the symmetry axis. If 640 computation points are chosen on the cylinder boundary and the Hertz law for the normal pressure on the contact site is used, then the error in the approximate solution near the endpoint of the contact site is approximately 55%, and if the proposed two-parameter normal law is used, then the error is of the order of 4%. On the free lateral surface of the cylinder boundary, we find the critical pointM*, which separates the cylinder contraction and extension parts.The contact problems are the most difficult problems, and their solution is complicated by the discontinuous boundary conditions [1–5]. In [6], the contact problem is solved by the Fourier method, which can be used only for bodies of classical shapes. In such cases, the problem can be reduced to solving coupled integral equations [7]. The interaction between the bandage and a cylindrical body is considered in [2, 6, 7]. In [8], the possibility of using the finite element method is investigated in the case of contact problems for a differential wheel with roughness of the contacting surfaces taken into account. In [9, 10], the method of homogeneous solutions is used to consider contact problems for a finite-dimensional elastic cylinder loaded on its end surfaces. Note that only error estimates are given in the literature cited above; the absolute error over the entire domain of the elastic body is not studied, although this is one of the important characteristics of the obtained approximate solution. A sufficiently complete survey of the literature in the field of contact interactions of elastic bodies is given in [3–5].In what follows, we propose to solve contact problems by the angular superposition method [11]. This method can be used for bodies of nonclassical shapes, which can be multiply connected, and the friction on the contact site can be taken into account. In the present paper, as a first example of applied character, we show how this method can be used in the simplest case. The multiple connectedness and the curvilinearity of the shape of the body, as well as taking into account the friction on the boundary, do not create new essential difficulties in this method.     

Diffraction of an elastic wave in a disc

A numerical solution is constructed for the axisymmetric problem of the diffraction of a plane longitudinal wave in a rigid disc (cylinder) of finite thickness. The disc is enclosed in an unbounded elastic medium; at the contact surface, the tangential stresses are limited by some constant. The incident wave moves along the axis of the cylinder and has the form of a semiinfinite washed-out step. At the same time, a solution is obtained to the corresponding static problem. A study was made of the dependence of the rate of motion of the cylinder and the stress field on the parameters of the problem. In particular, it is shown that the contact conditions have a considerable effect on the stress field only near the lateral surface. The results obtained can be useful for evaluating the errors in measurement of the stresses and velocities in an elastic medium, and possibly also in certain other cases.Deceased.Translated from Zhurnal Prikladnoi Mekhaniki i Teknicheskoi Fiziki, No. 3, pp. 139–150, May–June, 1972.