A Green's function approach to the deflection of a FGM plate under transient thermal loading

Summary  Green's function approach is adopted for analyzing the deflection and the transient temperature distribution of a plate made of functionally graded materials (FGMs). The governing equations for the deflection and the transient temperature are formulated into eigenvalue problems by using the eigenfunction expansion theory. Green's functions for solving the deflection and the transient temperature are obtained by using the Galerkin method and the laminate theory, respectively. The eigenfunctions of Green's function for the deflection are approximated in terms of a series of admissible functions that satisfy the homogeneous boundary conditions of the plate. The eigenfunctions of Green's function for the temperature are determined from the continuity conditions of the temperature and the heat flux at interfaces. Received 9 October 2000; accepted for publication 3 April 2001     

Singular perturbation analysis of dynamic fields in a thermoelastic solid with a small surface-breaking crack

An asymptotic analysis is presented for a dynamic problem of a semi-infinite isotropic thermoelastic solid with a small surface breaking crack. The exterior surface of the solid is subjected to a series of short thermal pulses. The crack surface is traction free and an ideal thermal contact is assumed across the crack. The stress intensity factor is asymptotically evaluated as a function of the crack depth and time. The effect of a boundary layer associated with the diffusive term is identified. The theoretical model is supplied with numerical simulations.     

The effect of initial stress and inhomogeneity on the thermoelastic stresses in a rotating anisotropic solid

The present paper presents a general treatment of the transient thermoelastic stresses in a rotating nonhomogeneous anisotropic solid under compressive initial stress. The system of fundamental equations is solved by means of a boundary element method (BEM) and the numerical calculations are carried out for the temperature, displacement components and stress components. The results indicate that the effects of inhomogeneity and initial stress are very pronounced.     

Crack initiation at the rectangular step notch surface under combined loading

Summary  Under external forces acting on the face of a notch, cracks originate at corners, and the system is liable to fail. An analysis is presented of the stress field in the neighborhood of the notch tips, based on the integral representation of the biharmonic solution and on numerical methods. Computations were performed for constant loading or constant displacement distributed along one face of the notch. The coefficients in the principal terms of the asymptotic formulae for the circumferential and shear stresses depend on the angle and height of the notch face and on the boundary conditions. The maximal values of these coefficients determine the stress intensity factors for the opening and shear modes. The angles corresponding to the maximal values of the intensity factors indicate the directions of initiation of opening and sliding cracks. Received 30 May 2000; accepted for publication 3 April 2001     

The analysis of thermal stresses in thermopiezoelastic semi-infinite body with an edge crack

Summary  Thermopiezoelastic materials have recently attracted considerable attention because of their potential use in intelligent or smart structural systems. The governing equations of a thermopiezoelastic medium are more complex due to the intrinsic coupling effects that take place among mechanical, electrical and thermal fields. In this analysis, we deal with the problem of a crack in a semi-infinite, transversely isotropic, thermopiezoelastic material by means of potential functions and Fourier transforms under steady heat-flux loading conditions. The problem is reduced to a singular integral equation that is solved. The thermal stress intensity factor for a crack situated in a cadmium selenide material is calculated. Received 20 March 2001; accepted for publication 18 October 2001     

Small edge crack in a semi-infinite solid subjected to thermal stratification

The mode I stress intensity factor for a small edge crack in an elastic half-space is found when the space is in contact with two stratified fluids of different temperatures, the boundary between the fluids oscillating sinusoidally over the solid surface. The variation in the stress intensity factor, which may lead to thermal fatigue crack growth, is examined as a function of time, crack depth, amplitude and temporal frequency of oscillation, surface heat transfer coefficient and material properties of the half-space. It is shown how this ‘boundary layer’ solution may be applied to problems involving finite geometries.     

Wrinkling of thick orthotropic sandwich plates under general loading conditions

Summary  This contribution presents an efficient analytical model as well as a FE computation of the critical load, which leads to local stability failure (wrinkling) in sandwich structures. The analytical model assumes an orthotropic face layer and a thick transversely isotropic core. In the last section, a more general core material model is considered. Common core materials (foams and honeycombs) can be described with good accuracy within this model. The main advantage of the solution is the consideration of general loading conditions for the orthotropic face layer as well as in-plane deformations of the core. The results of the FE calculations and the analytical model are in good agreement with each other. Received 7 January 1999; accepted for publication 15 June 1999     

Transient dislocation emission from a crack tip under dynamic mode III loading

Summary  Transient dislocation emission from a crack tip under dynamic mode III loading is analyzed. By taking into account the dynamic interaction between the crack and dislocation, the governing equation for the dislocation motion is derived under the quasi-steady assumption. The behavior of dislocation emission is explored in detail by solving this equation numerically. A critical initial speed can be determined, which must be exceeded by dislocations to escape from the crack tip. The dislocation emission process is found to be completed in such a short time period that the applied load may be approximately treated as constant during dislocation emission. Based on this fact, an asymptotic criterion for transient dislocation emission is developed, from which the critical initial speed can be evaluated. In the case that the dislocation is emitted from rest, we recover the quasi-static criterion of dislocation emission. Received 22 November 2000; accepted for publication 20 March 2001     

A piezoelectric-elastic body with inhomogeneities and a crack under plane electrical and anti-plane mechanical loads

Summary  In this paper, we study a two-dimensional electroelastic problem of an infinite piezoelectric body with two circular piezoelectric inhomogeneities, one of which contains a crack. We formulate the stress intensity factor (SIF) analytically and investigate it numerically. The problem is solved based on Bueckner's principle, and is reduced to a problem of a singular integral equation of the first kind with respect to the distribution function of screw dislocation. The effect of interaction between the two inhomogeneities and the crack on the electroelastic field as well as the control of the SIF by electrical loads is investigated. Received 18 April 2000; accepted for publication 24 October 2000     

Dynamic response of a crack in a functionally graded interface of two dissimilar piezoelectric half-planes

Summary  In this paper, the dynamic anti-plane crack problem of two dissimilar homogeneous piezoelectric materials bonded through a functionally graded interfacial region is considered. Integral transforms are employed to reduce the problem to Cauchy singular integral equations. Numerical results illustrate the effect of the loading combination parameter λ, material property distribution and crack configuration on the dynamic stress and electric displacement intensity factors. It is found that the presence of the dynamic electric field could impede of enhance the crack propagation depending on the time elapsed and the direction of applied electric impact. Received 4 December 2001; accepted for publication 9 July 2002 This work is supported by the National Natural Science Foundation of China through Grant No. 10132010.     

Effects of dynamic viscoelastic properties on acoustic diffraction by a solid sphere submerged in a viscous fluid

Summary  This study provides a general analysis for scattering of a planar monochromatic compressional sound wave by a homogeneous, isotropic, viscoelastic, solid sphere immersed in an unbounded viscous, heat-nonconducting, compressible fluid. The dynamic viscoelastic properties of the spherical scatterer and the viscosity of the surrounding fluid are rigorously taken into account in the solution of the acoustic-scattering problem. Havriliak–Negami model for viscoelastic material behaviour along with the appropriate wave-harmonic field expansions and the pertinent boundary conditions are employed to develop a closed-form solution in form of infinite series. Subsequently, the associated acoustic quantities such as the scattered far-field pressure directivity pattern, scattered intensity distribution, differential scattering cross section, and the acoustic radiation force are evaluated for given sets of viscoelastic material properties. Numerical results clearly indicate that, in addition to the traditional fluid viscosity-related mechanisms, the dynamic viscoelastic properties of the solid obstacle can be of major significance in sound scattering. Limiting cases are examined and fair agreements with well-known solutions are established. Received 15 January 2002; accepted for publication 2 July 2002 The authors wish to sincerely thank professors Daniel Levesque, Roderic Lakes, Yves Berthelot, S. Temkin, and Andrei Dukhin for valuable and productive consultations on dynamic theory of viscoelasticity and acoustics of (thermo)viscous media.     

M-integral analysis for a two-dimensional metal/ceramic bimaterial solid with extending subinterface microcracks

Summary  The problem of the extension of subinterface microcracks in an infinite metal/ceramic bimaterial solid is studied. For the microcrack growth, the values of the M-integral are calculated under the assumption of a self-similar growth. First, the role that the M-integral plays in a metal/ceramic bimaterial solid with growing subinterface cracks is analyzed. It is concluded that an inherent relation exists between the value of the M-integral and the decrease of the effective elastic moduli for a bimaterial solid with growing subinterface microcracks. Second, it is concluded that mutual amplification and shielding effects exist during the microcrack extension, while they are substantially dependent on the increment of the microcrack length as well as the geometry of the microcrack arrangement under given loads. This strong mutual shielding effect of interacting microcracks makes the microcrack extension become increasingly difficult, and may stop the growth of the microcracks even under constant loads. Also, it is concluded that for a certain microcrack growth, the value of the M-integral in metal/ceramic bimaterial solid is always larger than that in homogeneous brittle solid for the same crack configuration. This means that the same microcrack growth in the former case shows lower stability than that in the latter one, due to the existence of a ductile phase. Received 3 May 2001; accepted for publication 27 June 2002 This work was supported by the Chinese National Nature Science Foundation (Grant 19472053) and supported by the Doctorate Foundation of Xi'an Jiaotong University (Grant DFXJU2000-15).     

Measurement of instantaneous velocity and surface topography in the wake of a cylinder at low Reynolds number

A technique capable of simultaneous measurement of free-surface topography and velocity vector field data is presented. This technique offers substantial benefits of both reduced complexity and enhanced accuracy over all other techniques known to offer the same measurements. The flow behind a circular cylinder at low Reynolds numbers is measured using this technique. The velocity and vorticity fields as well as Strouhal number closely match the expected results. The free-surface topography, which can be related to the pressure field, exhibits an intimate relationship to the vorticity field.     

Electro-mechanical analysis of an interfacial crack between a piezoelectric and two orthotropic layers

Summary  The problem of an interfacially cracked three-layered structure constructed of a piezoelectric and two orthotropic materials is analyzed using the theory of linear piezoelectricity and fracture mechanics. Anti-plane shear loading is considered, and the integral transform technique is used to determine the stress intensity factor. Numerical examples show the electro-mechanical effects of various material combinations and layer thicknesses on the stress intensity factor. Interesting results are obtained in comparison with earlier solutions for interfacially cracked piezoelectric structures. Received 29 December 2000; accepted for publication 3 May 2001     

An analysis of the plane-strain compression of a three-layer strip

Summary  The problem considered here is that of the plane-strain compression of a long symmetric strip of a three-layered material between rigid, parallel, rough plates. Two combinations of layers are examined: (a) a viscoplastic material placed between two layers of a rigid/perfectly plastic material, and (b) a rigid/perfectly plastic material placed between two layers of a viscoplastic material. Closed-form solutions are presented for each combination, and qualitative differences between these solutions and solutions obtained for homogeneous materials are discussed. A possible effect of asymptotic behaviour of the solution in the vicinity of maximum-friction surfaces on the general structure of the solution is mentioned. Received 24 July 2000; accepted for publication 6 February 2001     

Variation of the stress intensity factor along the front of a 3-D rectangular crack subjected to mixed-mode load

Summary  The singular integral equation method is applied to the calculation of the stress intensity factor at the front of a rectangular crack subjected to mixed-mode load. The stress field induced by a body force doublet is used as a fundamental solution. The problem is formulated as a system of integral equations with r ⁻³-singularities. In solving the integral equations, unknown functions of body-force densities are approximated by the product of polynomial and fundamental densities. The fundamental densities are chosen to express two-dimensional cracks in an infinite body for the limiting cases of the aspect ratio of the rectangle. The present method yields rapidly converging numerical results and satisfies boundary conditions all over the crack boundary. A smooth distribution of the stress intensity factor along the crack front is presented for various crack shapes and different Poisson's ratio. Received 5 March 2002; accepted for publication 2 July 2002     

The nonlinear response of Cattaneo-type thermal loading of a laser pulse on a medium using the generalized thermoelastic model

The nonlinear thermoelastic responses of an elastic medium exposed to laser generated shortpulse heating are investigated in this article. The thermal wave propagation of generalized thermoelastic medium under the impact of thermal loading with energy dissipation is the focus of this research. To model the thermal boundary condition(in the form of thermal conduction),generalized Cattaneo model(GCM) is employed. In the reference configuration, a nonlinear coupled Lord-Shulman-type generalized thermoelasticity formulation using finite strain theory(FST) is developed and the temperature dependency of the thermal conductivity is considered to derive the equations. In order to solve the time-dependent and nonlinear equations, Newmark's numerical time integration technique and an updated finite element algorithm is applied and to ensure achieving accurate continuity of the results, the Hermitian elements are used instead of Lagrangian's. The numerical responses for different factors such as input heat flux and nonlinear terms are expressed graphically and their impacts on the system's reaction are discussed in detail.The results of the study are presented for Green–Lindsay model and the findings are compared with Lord-Shulman model especially with regards to heat wave propagation. It is shown that the nature of the laser's thermal shock and its geometry are particularly determinative in the final stage of deformation. The research also concluded that employing FST leads to achieving more accuracy in terms of elastic deformations; however, the thermally nonlinear analysis does not change the results markedly. For this reason, the nonlinear theory of deformation is required in laser related reviews, while it is reasonable to ignore the temperature changes compared to the reference temperature in deriving governing equations.     

Antiplane stress singularities in a bonded bimaterial piezoelectric wedge

Summary  In this paper, the eigen-equations governing antiplane stress singularities in a bonded piezoelectric wedge are derived analytically. Boundary conditions are set as various combinations of traction-free, clamped, electrically open and electrically closed ones. Application of the Mellin transform to the stress/electric displacement function or displacement/electric potential function and particular boundary and continuity conditions yields identical eigen-equations. All of the analytical results are tabulated. It is found that the singularity orders of a bonded bimaterial piezoelectric wedge may be complex, as opposed to those of the antiplane elastic bonded wedge, which are always real. For a single piezoelectric wedge, the eigen-equations are independent of material constants, and the eigenvalues are all real, except in the case of the combination C–D. In this special case, C–D, the real part of the complex eigenvalues is not dependent on material constants, while the imaginary part is. Received 26 March 2002; accepted for publication 2 July 2002     

3D electroelastic fields in a functionally graded piezoceramic hollow sphere under mechanical and electric loadings

Summary  The problem of a piezoceramic hollow sphere is investigated analytically based on the 3D equations of piezoelasticity. The functionally graded property of the material along the radial direction can be taken arbitrarily in the paper. Displacement and stress functions are introduced, and two independent state equations with variable coefficients are derived. By employing the laminate model, the two state equations are transformed into ones with constant variables from which the state variable solution is easily obtained. Two linear relationships between the state variables at the inner and outer spherical surfaces are established. Numerical calculations are performed for different boundary conditions imposed on the spherical surfaces. Received 28 February 2001; accepted for publication 26 June 2001     

Impact response of an interface crack in a hybrid piezoelectric laminate

Summary  In a hybrid laminate containing an interfacial crack between piezoelectric and orthotropic layers, the dynamic field intensity factors and energy release rates are obtained for electro-mechanical impact loading. The analysis is performed within the framework of linear piezoelectricity. By using integral transform techniques, the problem is reduced to the solution of a Fredholm integral equation of the second kind, which is obtained from one pair of dual integral equations. Numerical results for the dynamic stress intensity factor show the influence of the geometry and electric field. Received 29 June 2001; accepted for publication 3 December 2001