The flexural characteristic of a cantilever plate, which is heated from a fixed end, is considered and the effects of heat transfer on the plate are examined. The plate is heated with a temperature source while an excitation force is applied at the free end. Size of heat source is varied and temperature dependent properties of the plate are accommodated in the simulations. The finite element method (FEM) is adopted to determine the temperature field in the plate and flexural characteristics due to the applied impulsive load. It is found that the flexural characteristics of the plate change notably with the size of the heat source located at the fixed end of the plate. In this case, increasing the size of the heat source results in the enhancement of the amplitude and time shift in the flexural motion of the plate due to the heating and noheating situations.

This paper is concerned with an axially symmetric frictionless contact between an elastically transversely isptropic functionally graded half-space and a rigid base that has a small axisymmetric surface recess. The graded half-space is modeled as a nonhomogeneous medium. We reduce the problem to solving Fredholm integral equations, solve these equations numerically and establish a relationship between the applied pressure and gap radius. The effects of anisotropy and nonhomogeneity parameter of the graded half-space on the normal pressure as well as on the critical pressure have been shown graphically.

A new method for separation of isochromatic stresses is presented. This method is derived from the series solution of self-equilibrium polynomial stress equations and compatibility equations. The equations are quantified in terms of a stress function as the photoelastic stresses. Those equations are combined with the digital image processing technique and the linear regression curve fitting method to determine the contour equations of isochromictics and isoclinics fields. The solution of those equations provides a relationship between the normal stresses/shear stress and the photoelastic stress (maximum shearing stress). The results are consistent with the results obtained by the finite element method.

The objective of this study is to derive a time dependent effective based constitutive law on the basis of framework of the Modified Cam-Clay model. This model takes into account the anisotropic characteristics and creep behavior, based on the theory of viscoplasticity. The model sets the initial yield surface symmetric to the Ko line for modeling the initial Ko condition. A method is then developed to compute the gyration and expansion of the loading surface to simulate the anisotropic behavior due to the principal stress gyration after shear. The creep or time dependent behavior is considered in the model by adopting Kutter and Sathialingam's model, which was derived from Taylor's secondary consolidation theory and Bjerrum's delayed compression model. Compared with the Modified Cam-Clay model, the model requires five additional parameters to describe the soil behavior. All of the additional parameters can be obtained through conventional soil tests or parametric studies. The model is evaluated through a series of simulation of undrained shear tests and undrained creep tests.

Milling is becoming an increasingly universal machining operation for producing parts used in aerospace, automotive, and life science engineering industries. The characteristics common to such parts are a high level of complexity and structural flexibility, both of which usually necessitate using low radial immersion milling operations. Low radial immersion milling operations involve interrupted cutting which induces chatter vibration under certain cutting conditions. The stability behavior of low immersion helical end milling processes is investigated in this paper. Time Finite Element Analysis (TFEA) is suggested for an approximate solution for delayed differential equations encountered during interrupted milling. An improved TFEA is proposed which includes the effects of helix angle variations on cutting force, cutting time and specific cutting force coefficients for a 2 DOF vibratory system. To verify the proposed method, experimental tests have been conducted which prove that the improved TFEA method accurately predicts the stability behavior of low immersion milling.

This study theoretically and experimentally investigates the velocity distributions of the interface boundary layer region in a porous medium. By combining a quadratic non-Darcy law and a practical eddy viscosity model, an analytical solution is derived and presented. Three additional parameters, i.e., the depth of the interface boundary layer region, the slip velocity, and proportionality constant, are contained in the analytical solution. The measured experimental data show the depth of the interface boundary layer region only depends on the characteristics of the porous medium rather than the relative flow depth, bed slop, or Reynolds number. The values of the slip velocity are found to increase with increasing relative mean clear fluid velocities. The proportionality constant plays an important role in modeling the penetration of turbulence and the associated momentum transfer. The measured experimental velocity distribution is used to evaluate the accuracy of the analytical predicted profile. The analytical results obtained in this study are in agreement with the measured experimental results.

In this paper, an analytical approach for deriving the Green's function of circular and annular plate was presented. Null-field integral equations were employed to solve the plate problems while kernel functions were expanded to degenerate kernels. The unknown boundary data of the displacement, slope, normal moment and effective shear force were expressed in terms of Fourier series. It was noticed that all the improper integrals were avoided when the degenerate kernels were used. After determining the unknown Fourier coefficients, the displacement, slope, normal moment and effective shear force of the plate could be obtained by using the boundary integral equations. The present approach was seen as an “analytical” approach for a series solution. Finally, several analytical solutions were obtained. To see the validity of the present method, FEM solutions using ABAQUS were compared well with our analytical solutions. The displacement, radial moment and shear variations of radial and angular positions were presented.

This paper presents the results of numerical simulations on the characteristics of hydraulic shockwaves in an inclined chute contraction. A two-dimensional numerical hydraulic simulation model is used to simulate the hydraulic shockwaves, based on the finite-volume multi-stage (FMUSTA) scheme proposed by Guo et al. [1]. This numerical model has been proved having good ability in simulating hydraulic shockwaves through the comparison with the exact solution of idealized shockwaves in a horizontal contraction provided by Ippen and Dawson [2], and the comparison with experimental results provided in the companion paper by Jan et al. [3]. The simulated shockwave parameters such as the shock angle, maximum shockwave height and maximum shockwave position for various conditions are compared with those calculated by the empirical relations obtained in the companion paper. The numerical results validate the applicability of these empirical relations and also extend their applicability to higher approach Froude numbers.

The stability and possible chaotic vibrations of a fluid-conveying pipe with additional combined constraints are investigated. The pipe, restrained by motion constraints somewhere along the length of the pipe, is modeled by a beam clamped at the left end and supported by a special device (a rotational elastic constraint plus a Q-apparatus) at the right end. The motion constraints are modeled by both cubic and trilinear models. Based on the Differential Quadrature Method (DQM), the nonlinear dynamical equations of motion for the system are formulated, and then solved via a numerical iterative technique. Calculations of bifurcation diagrams, phase portraits, time responses and Poincare maps of the oscillations establish the existence of chaotic vibrations. The route to chaos is shown to be via period-doubling bifurcations. It is found that the effect of spring constant of the rotational elastic constraint on the dynamics is significant. Moreover, the critical fluid velocity at the Hopf bifurcation point for the cubic model is higher than that for the trilinear model.

The stress state of a magnetized elastic half-plane with a uniformly pressurized crack parallel to the free surface subjected to a uniform magnetic induction Bo is considered. The linear theory for a soft ferromagnetic elastic solid with muti-domain structure, which has been developed by Pao and Yeh [1] is adopted to investigate this problem. A numerical method is developed to determine the magnetoelastic stress intensity factor. The effect of the magnetic field and the boundary conditions on the magnetoelasitc stress intensity factor are shown graphically and numerically.

The cross sections formed by the contact asperities of two rough surfaces at an interference are islandshaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). The contact parameters, including the total contact force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and Ds parameters in these deformation regimes increased with increasing the mean separation (d*). The initial plasticity index before contact deformation (ψ)0 is also a factor of importance to the predictions of the contact load (F*t) and contact area (At*) between the model of variable D and G, non-Gaussian asperity heights and circular contact area and the present model of variable D and G, non-Gaussian asperity heights and fractal contact area.

This paper presents the experimental results of the characteristics of hydraulic shock waves in an inclined chute contraction with consideration of the effects of sidewall deflection angle φ, bottom inclination angle θ and approach Froude number Fr0. Seventeen runs of laboratory experiments were conducted in the range of 27.45° ≤φ ≤ 40.17°, 6.22° ≤ θ ≤ 25.38° and 1.04 ≤ Fr0 ≤ 3.51. Based on the experimental data, three empirical dimensionless relations for the shock angle, maximum shockwave height, and corresponding position of maximum shockwave were obtained by regression analyses, respectively. These empirical relations would be useful for hydraulic engineers in designing chute contraction structures.

The magnetorheological (MR) damper is a new device proposed for structural protection. It is filled with MR fluid that can be changed, when exposed to a magnetic field, regularly from free flowing liquid, linear viscous one to semi-solid. A phenomenological model based on the Bouc-Wen hysteresis model is adopted to predict both the force-displacement behavior and the complex nonlinear force-velocity response. The theory of fuzzy control is adopted here to determine the command voltage of MR dampers, but the applying of fuzzy control rules has always to deal with the classic problem of optimization. And due to the structural responses of analysis results, it can be confirmed that the reducing effects have an obviously improvement after an optimization by genetic algorithm.