Static response of a layered magneto-electro-elastic half-space structure under circular surface loading

A cylindrical system of vector functions, the stiffness matrix method and the corresponding recursive algorithm are proposed to investigate the static response of transversely isotropic,layered magneto-electro-elastic(MEE) structures over a homogeneous half-space substrate subjected to circular surface loading. In terms of the system of vector functions, we expand the extended displacements and stresses, and deduce two sets of ordinary differential equations, which are related to the expansion coeficients. The solution to one of the two sets of these ordinary differential equations can be evaluated by using the stiffness matrix method and the corresponding recursive algorithm. These expansion coeficients are then integrated by adaptive Gaussian quadrature to obtain the displacements and stresses in the physical domain. Two types of surface loads, mechanical pressure and electric loading,are considered in the numerical examples. The calculated results show that the proposed technique is stable and effective in analyzing the layered half-space MEE structures under surface loading.     

Transient responses of a multilayered spherically isotropic piezoelectric hollow sphere

The dynamic solution of a multilayered spherically isotropic piezoelectric hollow sphere subjected to radial dynamic loads is obtained. By the method of superposition, the solution is divided into two parts: one is quasi-static and the other is dynamic. The quasi-static part is derived by the state-space method, and the dynamic part is obtained by the method of separation of variables coupled with the initial parameter method as well as the orthogonal expansion technique. By using the quasi-static and dynamic parts, the electric boundary conditions as well as the electric continuity conditions, a Volterra integral equation of the second kind with respect to a function of time is derived, which can be solved successfully by means of the interpolation method. The displacements, stresses and electric potentials are finally obtained. The present method is suitable for a multilayered spherically isotropic piezoelectric hollow sphere consisting of arbitrary layers and subjected to arbitrary spherically symmetric dynamic loads. Finally, numerical results are presented and discussed.     

Perturbation analysis of an undulating free surface in a multi-layered structure

This paper presents an analysis of the effect of an undulating free surface on the stress state in a multi-layered structure with an arbitrary number of layers. We present a simple procedure to derive in terms of stress functions the first-order perturbation solution for a multi-layered structure subjected to residual stresses and to external edge loads. The solution is valid for undulation amplitudes that are small compared to undulation wavelength, and it reproduces results reported earlier for homogeneous materials and bi-layers. Using this perturbation solution, the stability of a stressed undulating surface with a given surface energy is evaluated. This analysis leads naturally to the definition of a critical undulation wavelength above which undulations are preferred energetically over a flat surface. The results obtained in the perturbation analysis can be applied to surface diffusion/etching problems in multi-layered structures and to a range of other engineering problems related to undulating surfaces and surface stability.     

Flexural Stress Concentration Near a Hyperboloidal Neck in a Transversely Isotropic Piezoceramic Cylinder

The general solution of the electroelastic problem for a transversely isotropic hyperboloid of revolution is used to find the stress concentration near a hyperboloidal neck in a piezoceramic body subjected to bending. The solution is a sum of four partial solutions for the case where the forces and the normal component of the induction vector on the neck surface are equal to zero. Numerical examples are given for specific external loads and properties of the body. The stress components and normal component of the induction vector near the neck vertex are plotted as a function of the external load and neck curvature     

Stresses in a transversely isotropic,short hollow cylinder subjected to an outer band load

Summary An axi-symmetric stress analysis of a transversely isotropic, short hollow cylinder subjected to an outer band load is presented in a series form. The generalized Elliott's solution is used for the analysis. The solution consists of five independent potential functions which yield two kinds of elasticity solution. The boundary conditions for the shearing stress on the four surfaces are exactly satisfied. Other boundary conditions are numerically satisfied with the aid of a Fourier series expansion or a Fourier-Bessel series expansion. Numerical results for stresses in magnesium and cadmium crystals, as examples of transversely isotropic materials, and in an isotropic material are illustrated. The effect of anisotropy on the stresses is investigated by comparison with the stresses in the isotropic material.

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Spannungen in einem transversal-isotropen, kurzen Hohlzylinder unter einer äußeren Bandlast

Übersicht Vorgestellt wird eine axialsymmetrische Spannungsanalyse mittels Reihen für einen transversalisotropen, kurzen Hohlzylinder unter einer äußeren Bandlast. Für die Analyse wird die verallgemeinerte Elliottsche Lösung benutzt. Die Lösung besteht aus fünf unabhängigen Potentialen, welche zwei Arten der Elastizitätslösung abgeben. Die Randbedingungen der Schubspannung auf den vier Flächen werden genau erfüllt. Die anderen Randbedingungen werden durch eine Fouriersche Reihenentwicklung oder eine Fourier-Besselsche Reihenentwicklung numerisch erfüllt. Die numerischen Resultate der Spannungen in einem Magnesiumkristall und einem Kadmiumkristall als Beispiele transversal-isotroper Materialien und in einem isotropen Material werden illustriert. Der Einfluß der Anisotropie auf die Spannungen wird durch Vergleich mit den Spannungen im isotropen Material untersucht.

     

Measurement of Applied Stresses and Residual Stresses on a Residual Stress Model by Applying Two Different Loads

Applied stresses on a residual stress model have previously been obtained by measuring the residual stresses and the resultant stresses generated by applying a load. The present paper reports that the applied stresses and the residual stresses on the residual stress model can be obtained by measuring two resultant stresses generated by applying loads of two different magnitudes. In the proposed method, the residual stresses need not be obtained from the residual stress model before applying a load. The residual stress model used to test the proposed method is a circular disk with frozen stresses that is subjected to a diametral compressive load at a certain angle. The applied stresses and the residual stresses on a residual stress model were experimentally and precisely obtained by digital photoelasticity using linearly polarized light.     

Pointwise errors in the classical and in Reissner's linear theory of plates,especially for concentrated loads

An infinite, horizontal, elastically isotropic plate is subjected to a distributed vertical, axisymmetric load, part of which is a body force and part of which is a surface traction. The resulting 3-dimensional stresses and displacements are found with the aid of Love's stress function and Hankel transforms. From these, the sum of the principal stress couples, the average rotation of radial fibers, and the average vertical deflection are computed and compared against the predictions of classical and Reissner's shear-deformation plate theory. Remarkably, the elasticity and plate theory predictions for the stress couples and the rotation agree if Poisson's ratio is zero. In general, for smoothly varying loads, the predictions of Reissner's theory are closer than those of classical theory to the predictions of elasticity theory. However, if a part of the load is (nearly) concentrated, then it is shown that the singularities in the sum of the principal stress couples and in the rotation predicted by Reissner's theory are too strong (because his theory accounts for normal stress effects based on smoothly varying loads). Moreover, if the concentrated part of the external load is a uniformly distributed line load through the thickness, then classical theory predicts the correct singularity in these variables, although with an erroneous strength. On the other hand, Reissner's theory correctly predicts the logarithmic singularity in the average vertical deflection (for any type of concentrated load), although with an erroneous strength.     

Thermal Stress Measurement in Continuous Welded Rails Using the Hole-Drilling Method

The absence of expansion joints in Continuous Welded Rail has created the need for the railroad industry to determine the in-situ thermal stress levels for rail buckling and breakage prevention. This paper explores the hole-drilling method as a possible solution to this problem. A new set of calibration coefficients to compute the stress field relieved by fine hole depth increments required by the high strength steel was determined. The new calibration coefficients were experimentally validated on an aluminum plate subjected to a known uniaxial load. The thermal stress levels of constrained rails were estimated after compensation for the residual stress components, based on statistical relationships developed experimentally between the longitudinal and the vertical residual stresses. The results showed that the hole-drilling procedure, with appropriate calibration coefficients and residual stress compensation, can estimate the in-situ rail thermal stresses with an expected accuracy that is within the industry acceptable levels.     

An analytical solution of an axisymmetric problem of deforming an isotropic half-space with an elastic fixed boundary under the action of a distributed load

An analytical solution to the axisymmetric problem on the action of a distributed load on an isotropic half-space when the load is given by a function dependent on the radial coordinate is obtained. The surface of the half-space is elastically fixed outside the circular domain of load application, the shear stresses are absent along the entire boundary, and the stresses vanish at infinity. At the boundary and inside the elastic half-space, the solutions are represented by the formulas for the stress tensor components and for the displacement vector components.     

Oblique edge crack in an anisotropic material under antiplane shear

An oblique edge crack in an anisotropic material under antiplane shear loadings is investigated. The antiplane problems are formulated based on a linear transformation method. An anisotropic solid containing an edge crack subjected to concentrated forces is first considered. The stress intensity factor for the edge crack with concentrated forces is obtained from the solution of the transformed edge crack in an isotropic material which is solved by using conformal mapping technique and complex function theory. The solution of the edge crack under concentrated loads is used to construct the stress intensity factor for the oblique edge crack in the anisotropic material subjected to antiplane distributed loads. Some numerical computations are carried out to calculate the stress intensity factors for the edge crack in inclined orthotropic materials subjected to point forces as well as distributed tractions.     

Orthotropic semi-infinite medium with a crack under thermal shock

A cracked orthotropic semi-infinite plate under thermal shock is investigated. The thermal stresses are generated due to sudden cooling of the boundary by ramp function temperature change. The superposition technique is used to solve the problem. The crack problem is formulated by applying the thermal stresses obtained from the uncracked plate with opposite sign to be the only external loads on the crack surfaces as the crack surface tractions. The Fourier transform technique is used to solve the problem leading to a singular equation of the Cauchy type. The singular integral equation is solved numerically using the expansion method. The influence of the material orthotropy on the stress intensity factors is shown by comparing the results obtained for different orthotropic materials and isotropic materials in the case of plane stress. The numerical results of the stress intensity factors are demonstrated as a function of time, crack length, location of the crack and the duration of the cooling rate.     

Thermomagnetic viscoelastic responses in a functionally graded hollow structure

This paper presents an analytical solution for the interaction of electric potentials,electric displacements,elastic deformations,and thermoelasticity,and describes electromagnetoelastic responses and perturbation of the magnetic field vector in hollow structures(cylinder or sphere),subjected to mechanical load and electric potential.The material properties,thermal expansion coefficient and magnetic permeability of the structure are assumed to be graded in the radial direction by a power law distribution.In the present model we consider the solution for the case of a hollow structure made of viscoelastic isotropic material,reinforced by elastic isotropic fibers,this material is considered as structurally anisotropic material.The exact solutions for stresses and perturbations of the magnetic field vector in FGM hollow structures are determined using the infinitesimal theory of magnetothermoelasticity,and then the hollow structure model with viscoelastic material is solved using the correspondence principle and Illyushin’s approximation method.Finally,numerical results are carried out and discussed.     

Solids containing spherical nano-inclusions with interface stresses: Effective properties and thermal–mechanical connections

This work examines the overall thermoelastic behavior of solids containing spherical inclusions with surface effects. Elastic response is evaluated as a superposition of separate solutions for isotropic and deviatoric overall loads. Using a variational approach, we construct the Euler–Lagrange equation together with the natural transition (jump) conditions at the interface. The overall bulk modulus is derived in a simple form, based on the construction of neutral composite sphere. The transverse shear modulus estimate is derived using the generalized self-consistent method. Further, we show that there exists an exact connection between effective thermal expansion and bulk modulus. This connection is valid not only for a composite sphere, but also for a matrix-based composite reinforced by many randomly distributed spheres of the same size, and can be viewed as an analog of Levin’s formula for composites with surface effects.     

Influence of elastic properties on the stress state of a nonthin transversely isotropic plate with a circular hole

The paper outlines a method for constructing the general analytic solution to the system of equilibrium equations of nonthin transversely isotropic plates. The method uses the Fourier–Legendre series expansion of the unknown functions with respect to the thickness coordinate. The stress state near a circular hole in a nonthin plate subject to tensile and shear stresses at infinity is analyzed     

Full-Field Thermoelastic Stress Analysis of a Finite Structure Containing an Irregularly-Shaped Hole

An assessment of the structural integrity of members containing irregularly-shaped cutouts necessitates knowing the associated stresses. Stress analysis of such structures can be challenging as theoretical solutions are seldom available for finite geometries having non-simple shaped discontinuities and, like numerical methods, they require accurate knowledge of external loads. The latter are often unavailable in practice. This paper describes the ability to process load induced temperature information with an Airy stress function in real polar coordinates to determine the stresses in an isotropic linear elastic finite tensile plate containing an irregularly-shaped hole. Using polar coordinates is significant in that while a relatively simple general solution to the governing biharmonic equation is available in polar coordinates, this is seemingly not so with orthogonal curvilinear coordinates. Compared with displacement-based experimental or finite element techniques, important advantages of the present technique include not having to differentiate recorded data, or know constitutive properties or external loads.     

Thermal stresses and shakedown in wheel/rail contact

Summary  Sliding friction between railway wheels and rails results in considerable contact temperatures and gives rise to severe thermal stresses at the surfaces of the wheels and rails. An approximate analytical solution is presented for a line contact model. The increased bulk temperature of the wheel after a long period of constant operating conditions is also taken into account. The thermal stresses have to be superimposed on the mechanical contact stresses. They reduce the elastic limit of the wheel and rail, and yielding begins at lower mechanical loads. When residual stresses build up during the initial cycles of plastic deformation, the structure can carry higher loads with a purely elastic response in subsequent load cycles. This phenomenon is referred to as shakedown. Due to the distribution of temperature, the rail surface is generally subjected to higher stresses than the wheel surface. This can cause structural changes in the rail material and hence rail damage. Received 7 May 2002; accepted for publication 3 September 2002     

Spherically isotropic,elastic spheres subject to diametral point load strength test

This paper presents an analytic solution for the stress concentrations within a spherically isotropic, elastic sphere of radius R subject to diametral point load strength test. The method of solution uses the displacement potential approach together with the Fourier–Legendre expansion for the boundary loads. For the case of isotropic sphere, our solution reduces to the solution by Hiramatsu and Oka, 1966 and agrees well with the published experimental observations by Frocht and Guernsey (1953) . A zone of higher tensile stress concentration is developed near the point loads, and the difference between this maximum tensile stress and the uniform tensile stress in the central part of the sphere increases with E/E′ (where E and E′ are the Youngs moduli governing axial deformations along directions parallel and normal to the planes of isotropy, respectively) , G′/G (where G and G′ are the moduli governing shear deformations in the planes of isotropy and the planes parallel to the radial direction) , and ν̄/ν′ (where ν̄ and ν′ are the Poissons ratios characterizing transverse reduction in the planes of isotropy under tension in the same plane and under radial tension, respectively) . This stress difference, in general, decreases with the size of loading area and the Poissons ratio.     

Rotationally Symmetric Deformations of Partially Loaded Annular Elastic Membranes Without Wrinkling

This paper investigates axisymmetric deformations of curved annular membranes subjected to a partially vanishing vertical surface load and to radial edge loads or displacements. The frame of the membrane model we deal with is the nonlinear small-strain theory. The determination of the principal stresses reduces to the solution of a single nonlinear second order ODE. Analysis becomes explicit on the unloaded membrane part while the loaded part is treated by methods which have been previously developed. In particular, the ranges of those stress and displacement boundary data are determined which admit for wrinkle-free solutions only, i.e. for solutions governed by a nonnegative radial and circumferential stress component. For such a tensile state, a curved membrane flattens out on the unloaded portions. This revised version was published online in August 2006 with corrections to the Cover Date.     

Thermal stresses in infinite circular cylinder subjected to rotation

The present investigation is concerned with the effect of rotation on an infinite circular cylinder subjected to certain boundary conditions.An analytical procedure for evaluation of thermal stresses,displacements,and temperature in rotating cylinder subjected to thermal load along the radius is presented.The dynamic thermal stresses in an infinite elastic cylinder of radius a due to a constant temperature applied to a variable portion of the curved surface while the rest of surface is maintained at zero temperature are discussed.Such situation can arise due to melting of insulating material deposited on the surface cylinder.A solution and numerical results are obtained for the stress components,displacement components,and temperature.The results obtained from the present semi-analytical method are in good agreement with those obtained by using the previously developed methods.     

Three-dimensional solution for a hybrid cylindrical shell under axisymmetric thermoelectric load

Summary An exact axisymmetric piezothermoelastic solution is presented for a simply-supported hybrid cylindrical shell made of cross-ply composite laminate and piezoelectric layers. Numerical results for hybrid shells are presented for sinusoidal and central band thermal and electrical loads. The effect of the loading, the radius-to-thickness ratio, the span-to-radius ratio and the number of layers of the substrate on the response is investigated. The interface between the substrate and the actuated piezoelectric layer has been found to be subjected to high shear stress. It has been shown that the maximum values of the deflection and the stresses, due to thermal load, can be appreciably reduced by appropriate application of actuation potential. Accepted for publication 13 October 1996