Integral transform solution of multi-material structure with finite crack perpendicular to the interface

The plane elasticity problem for layered elastic systems containing a finite crack perpendicular to the interface is considered. To derive the singular integral equations. Fourier transform in conjunction with dislocation is used. The singular integral equation is solved with the Lobatto-Chebyshev method commonly applied to such problems. In order to have an idea about the usefulness of the method described, a two-layer structure which contains a cut parallel toh is considered.     

Free vibration analysis of a plate on foundation with completely free boundary by finite integral transform method

The theoretical solutions of eigenfrequencies and vibration modes of a rectangular thin plate on an elastic foundation with completely free boundary are derived by using a double finite cosine integral transform method. In the analysis procedure, the elastic foundation is regarded as a Winkler elastic foundation model. Because the basic dynamic elasticity equations of the thin plate on elastic foundation are only used, it is not needed to select the deformation function arbitrarily. Therefore, the solution developed in the present paper is more reasonable and more accurate. To prove the correctness of the solutions, numerical results obtained using the present solutions are compared with those in the literatures.     

Modeling the effect of diffusion of the ambient medium on the long-term strength of a hollow cylinder under uniaxial tension

The problem of the long-term strength of an extended thick-walled tube containing a corrosive medium in the internal cavity is solved. The diffusion of this medium into the tube material is analyzed. The diffusion equation is solved approximately by introducing the diffusion front, and the error of the solution is estimated. The dependence of the time of fracture of the tube on the variable tensile stress and the concentration of the medium filling the cavity is obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 88–93, July–August, 2007.     

Application of the scale entropy diffusion model to describe a liquid atomization process

Whatever the situation, liquid atomization processes show a continuous evolution of the liquid system shape. However, such a system is a multiscale object, i.e., its shape cannot be fully described by a single geometrical parameter. The present work makes use of the scale entropy function to describe this multiscale object. This function is found similar to the scale distribution previously introduced to take into account the droplet shape in liquid spray characterization. Time-averaged scale entropy is locally measured on images of atomizing liquid flows issuing from a low injection pressure single-hole triple-disk nozzle. The advantage in using this nozzle is that the atomization process and the spray are inscribed in a plane and can be fully described by 2-D visualizations. The measurements are performed from the nozzle exit down to the spray region. The operating conditions consider varying injection pressure and liquid physical properties. The temporal evolution of the scale entropy is described by the scale entropy diffusion model. Initially developed in turbulence, this model introduces new parameters such as the scale diffusivity and the local scale entropy flux sink, which characterize the diffusion dynamic of the scale entropy in the scale space. For the first time, these parameters are measured and strong correlations between them and the working conditions are evidenced. Furthermore, new parameters are introduced such as a scale viscosity and the total scale entropy flux lose. These results demonstrate the relevance of the scale entropy diffusion model to describe a liquid atomization process. This application is the first of its kind.     

Closed-form solutions of the frictional sliding contact problem for a magneto-electro-elastic half-plane indented by a rigid conducting punch

This paper focuses on the study of a frictional sliding contact problem between a homogeneous magneto-electro-elastic material (MEEM) and a perfectly conducting rigid flat punch subjected to magneto-electro-mechanical loads. The problem is formulated under plane strain conditions. Using Fourier transform, the resulting plane magneto-electro-elasticity equations are converted analytically into three coupled singular integral equations in which the main unknowns are the normal contact stress, the electric displacement and the magnetic induction. An analytical closed-form solution is obtained for the normal contact stress, electric displacement and magnetic induction distributions. The main objective of this paper is to study the effect of the friction coefficient and the elastic, electric and magnetic coefficients on the surface contact pressure, electric displacement and magnetic induction distributions for the case of flat stamp profile.     

Application of a n-Phase Model to the Diffusion Coefficient of Chloride in Mortar

The determination of the chloride diffusion coefficient of a concrete is needed to help the prediction of the service life of concrete structure. In this paper, we propose first a critical review of models for chloride diffusion coefficients already used in literature at different scales and then we develop an analytical model, which takes into account the characteristics of the different phases of concrete. These materials are treated as a three-phase composite, consisting of a cement continuous phase, of an aggregates dispersed phase and of an interface transition zone. Chloride diffusion coefficient using an n-layered inclusion-based micromechanical modeling is predicted. The details of calculations are summarized hereafter and experimental measurements obtained on mortars are compared with predicted results.     

Computer computation of the method of multiple scales—dirichlet problem for a class of system of nonlinear differential equations

The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application of the method of boundary layer with multiple scales. Contributed by Jiang Fu-ru, Original Member of Editorial Committe, AMM Biography: Xie La-bing (1976∼); Jiang Fu-ru(1927∼)     

Application of the two-equation k-ϵ turbulence model to a two-dimensional,steady, free surface flow problem with separation

An application of the depth-integrated k-? turbulence model is presented for separated flow in a wide, shallow, rectangular channel with an abrupt expansion in width. The well-known numerical problems associated with the use of upwind and central finite differences for convection are overcome by the adoption of the spatially third-order accurate QUICK finite difference technique. Results show that modification of the depth-integrated k-? turbulence closure model for streamline curvature leads to significant improvement in the agreement between model predictions and experimental measurements.     

Application of the modified method of multiple scales to solving the problem of a thin clamped circular plate of a very large deflection

In this paper,asymptotic behaviour of the solution to the problem of a thin clamped circular plate under uniform normal pressure at very large deflection is restudied by means of the modified method of multiple scales given in[1?].The result presented herein is in good agreement with the one obtained by professor Chien Wei-zang who first proposed the method of composite expansions to solve this problem in[3].However,by contrast,the advantage of the modified method of multiple scales it seems to be relatively simpler than the method used in[3].It is also shown that the restriction of the method of paper[1-2]pointed out in paper[4]is not essential,and several computation errors in[3]are corrected as well.