A differential equation for a macroscopic total strain of a material containing many aligned elliptic cracks with respect to the crack density of cracks is derived by adopting the concept of the differential scheme to the micromechanical model of the material based on the Mori-Tanaka theorem. By solving the differential equation, the macroscopic total strain and the average interaction stress, and hence the macroscopic elastic moduli are formulated as a function of the crack density of cracks. On the contrary to the results obtained by the ordinary Mori-Tanaka theorem, the resulting macroscopic elastic moduli asymptotically tend to zero as the crack density of the crack increases. The present solution is in good agreement both with the numerical results obtained by Huang et al. [Int. J. Solids Struc. 33(1996), pp.1575-1586] for an aligned slit-like cracked solid and with the results calculated by the self-consistent method for an aligned penny-shaped cracked solid.

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The paper presents an axisymmetric solution for the stresses and displaements in an elastic thick plate containing an oblate spheroidal inclusion under circular bending. The interface of the inclusion is assumed perfect bonding. The related spherical cavity and inclusion problems were solved by Tsuchida et al. in 1975 by using Papcovich-Neuber displacement potentials. We extended the method to a spheroidal inclusion problem. Numerical results are given for different values of size, aspect ratio and stiffness ratio. The stress distributions around inclusion are shown graphically.

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This paper considers the elastic contact problem of a transversely isotropic half-space indented by an axisymmetrically concave or convex rigid punch. The problem is reduced to the solution of an infinite system of simultaneous equations by the expression for the contact stress under the punch as appropriate series. The displacement and stress distributions on the half-space are shown graphically for various magnitude of the contact radius.

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Balancing Domain Decomposition (BDD) proposed by J. Mandel is an effective preconditioning technique for reducing the number of iterations of iterative Domain Decomposition Method(DDM). Until now many researches have been done on the implementation of BDD in different areas including elasticity problems and semiconductor simulation. In this paper, we implement BDD in another area that is 3-dimensional(3-D) heat conductive analysis in solid. We construct the BDD preconditioner in parallel based on Hierarchical Domain Decomposition Method (HDDM). We report the comparative performance of BDD with diagonal scaling and original DDM without preconditioning to analyse heat conductive problems with about 2 million degrees of freedom and over 11 million degrees of freedom. With BDD the convergence rates are reduced effectively and become independent of the number of subdomains.

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In Large Eddy Simulation (LES) using the dynamic Smagorinsky model¹⁾, the test filtering operation is important because the model constant is dependent on the operation.In order to precisely evaluate the numerical results using the dynamic Smagorinsky model, it is necessary to have a clear grasp of the operation. In the present study, we examine the characteristics of the test filtering operation descritized with Finite Element Method (FEM).In order to clarify this characteristics, we apply the FiniteDifference Method ( FDM ) to only the test filtering operation and compare the results obtained respectively by FEM and FDM.The numerical model is a turbulent channel flow, which is a benchmark problem. Based on the numerical results, we clarify the difference in the discretization of the test filtering operation and reveal the influence of different discretization method.

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We present three-dimensional results of flows around two circular cylinders in tandem arrangement, which are located in a uniform flow, and show features of aerodynamic characteristics of the cylinders at some spacing between two circular cylinders. In this computation, the finite element approximation is applied to the Navier-Stokes equations, and the Euler implicit scheme is used for numerical time integration. The Reynolds number is set as 1000. The computed results are compared with other experimental data.

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The combined compact difference (CCD) scheme proposed by the authors has high accuracy with comparatively low computational cost and it is promising for large scale computation with high accuracy. The parallelization of CCD schemes with a block tridiagonal matrix is developed, which is based on that of the tridiagonal matrix problem proposed by Mattor et al., and is suitable for the domain decomposition technique. The parallel efficiency of this algorithm is measured. The results show that the parallelization of CCD schemes is highly effective.

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The author reported numerical computation results of turbulent shear flows in ducts of rectangular cross-section using the algebraic stress model and the harmonic mixing length model, in Volume 51 of Theoretical and Applied Mechanics. A time marching method was adopted as a calculation method and the validity of the harmonic mixing length model was confirmed. In this report, more detailed examinations are carried out: characteristics of turbulent shear flows with all smooth walls, all rough walls, and smooth-rough mixed walls are investigated in square duct flows, and characteristics of the mutual convergence process of axial and secondary flows are investigated in rectangular duct flows.

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Studies on the flow past a cavity region in an otherwise homogeneous granular material are made. In the case of a circular cylindrical cavity placed laterally to a uniform flow at infinity, the volume flux into this region increases as much as 2 times, whereas the velocity at the center of the void amounts to 3 times of those without that hole. The interaction of two cavities is also examined, which reveals the presence of a configuration with maximum flow rate. Due to the enhancement of fluid flow into cavity regions, the latter boundaries are destroyed even below the critical velocity, which further reinforces the flow around those cavities. This slowly progressing micro-scale interaction is repeated and develops into larger scale inhomogeneity of granular material, which is considered to be one of the fundamental processes leading to macroscopic long range catastrophic phenomena like network formation and landslides.

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This paper describes a glow discharge technique for visualizing shock waves around models in short duration hypersonic flows. A glow discharge is generated by applying a short high voltage pulse between a gap in the flows. To demonstrate the capability of the technique, visualization of oblique shock waves around a flat plate at angles of attack in the range from 10 to 30deg is performed. Besides, to search the minimum amount of electric energy discharged into the flow required for photographic purposes, gap voltage and current measurements are carried out. These experiments are performed in a hypersonic gun tunnel at Mach number 10 and the stagnation enthalpy 0.71MJ/kg, which corresponds to a lower limit for the tunnel operation without air condensation. The experimental angles of the shock waves agree well with the oblique shock wave theory, namely, the glow discharge does not distort the shape of the shock wave. It is shown that the optimum ratio of the amount of the energy discharged to that of the total enthalpy of the flow is at most 0.1.

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The numerical investigation of the self-induced flow oscillation caused by the interaction of a supersonic impinging jet is carried out in this paper. The self-induced flow oscillation occurs at the specific conditions and causes the noise problem. The characteristic of the oscillated flow and the mechanism of the oscillation, therefore, have to be cleared to control the oscillation. This paper aims to clear the characteristic of a pressure fluctuation during the under-expanded supersonic jet impinges on the perpendicular plate. The TVD numerical method is used in the numerical analysis. From the results of numerical analysis, it is concluded that the pressure fluctuation on the plate surface depends on the pressure ratio and the position of a plate.

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EOF analyses were performed for midsummer pressure anomaly patterns near the tropopause around Japan, and a Rossby wave train propagating from Europe to North America through Japan was identified on the subtropical jet. Firstly, a vorticity anomaly generated over western Europe is slowly transferred to the jet. When it enters the wave guide on the jet, barotropic kinetic energy conversion occurs from the climatological field to the anomaly field, associated with an abrupt change in the absolute vorticity gradient in the basic field. It then propagates rapidly eastward. The energy conversion depends on the phase of the anomalous wave train.

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An attempt was made to construct a self-contained, feedback control system for separation. The fundamental elements of the control system are sensors, actuators, and their controllers. To establish the basis of a smart control system for wing separation, a cantilever sensor (CS) and a control system using it were tested successfully. A fiber Bragg grating sensor (FBG) was tested using a suction-blowing type actuator. In this study, we confirmed that 1) the CS was an effective flow direction discriminator, 2) the closed-loop control system for wall separation with a CS worked well, 3) the present FBG sensor system could measure the flow drags precisely, and 4) the suction-blowing type actuator actually reduced the turbulent skin friction drags.

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In this work, we propose a model for explanation for friction induced vibration in a brake pad and disk system. In this model, a brake pad is regarded as a set of many blocks two-dimensionally arranged and connected to each other with springs. We assume that shear forces act on each block besides elongation and compression forces. The blocks are placed on a floor which moves with constant velocity, and irregular normal forces are applied to each block. The velocity-dependent sliding friction force of exponential type is assumed. The results of numerical simulation show that characteristic oscillation are generated in all cases examined, and the features and frequencies determined by these modes depend on the block size and constraint to blocks. The frequencies of these modes almost coincide with those observed by experiments.

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Magnetic dampers used in turbo-molecular pump and the like in order to reduce vibration sometimes generate unstable vibrations. In this report, the authors present a new modeling and a new method using an infinitesimal conductor loop for calculating magnetic damping force, which acts on a conductor disk moving and rotating in a static magnetic field. The advantages of this method are that it doesn't need a complicated calculation of scalar potential's distribution in the conductor and that the magnetic damping force is derived with ease from the static magnetic field analysis through FEM or some fairly simple measurements. In addition, the magnetic damping force computed by the present method is very useful for obtaining the solution to an unstable vibration of a rotating machine caused by a magnetic damper. In conclusion, the analytical results agreed well quantitatively with the experimental ones.

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A formulation is proposed to investigate the effect of horizontal constraints in regard to the lateral displacements of a long elevator rope on the undamped flexural vibration modes. The formulation is based on a model of the rope as a serial assembly of virtual rotary springs and rigid links. The horizontal constraints are modeled by virtual rectilinear springs and expressed as equality constraint conditions imposed on the lateral displacements. The undamped vibration eigenvalue problem is derived from the Lagrange's equation of motion in terms of the potential energy and kinetic energy of the springs and links. The numerical examples are concerned with a rope system consisting of the main rope, cab and compensation rope that stand for an elevator system while the relative lateral displacements of the cab and bottom end of the rope to the top end are constrained.

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The dynamic electroelastic response of a penny-shaped crack in a piezoelectric ceramic cylinder under normal impact is investigated in this study. A plane step pulse strikes the crack and stress wave diffraction takes place. Laplace and Hankel transforms are employed to reduce the transient problem to the solution of a pair of dual integral equations in the Laplace transform plane. The solution of the dual integral equations is then expressed in terms of a Fredholm integral equation of the second kind. A numerical Laplace inversion technique is used to compute the values of the dynamic stress intensity factor, energy release rate and energy density factor for some piezoelectric ceramics, and the results are graphed to display the electroelastic interactions.

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This paper investigated the physical properties of the racket and the ball, and predicted the impact force, the contact time, the deformation of ball and rubber, the coefficient of restitution and the racket rebound power associated with the frontal impact when the impact velocity and the impact location on the racket face are given. This study is based on the experimental identification of the dynamic characteristics of the ball-racket- arm system and an approximate nonlinear impact analysis, where the contact time is determined by the natural period of the whole system composed of the mass of the ball, the nonlinear stiffness of the ball and rubber, and the reduced mass of the handled racket at the impact location on the rubber face. Also considered is the energy loss during the impact. It was found that the racket rebound power peaks when the hitting point is 16 cm from the grip end of the racket and then decreases because of the mass distribution of the racket. The racket rebound power decreases remarkably with increasing impact velocity. Although the player's arm gives a remarkable effect on the reduced mass of racket, it does not give an effect on the rebound ball velocity because the mass of ball is too small compared to the mass of racket. This study enables us to predict quantitatively the various factors associated with frontal impact between a racket and a ball in table tennis.

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The cracking damages frequently occur near both of bridge supports in the reinforced concrete (RC) slabs of highway bridges. This phenomenal fact may result from the load fluctuations when the heavy vehicles travel over the level differences of expansion joints. The present study used three types of RC beams in which the vibration loads having the load fluctuations with a sine wave pattern were move within the full beam span. The results have demonstrated that the vibrations with a load amplitude of ±20% or more in case of the Type A beam was given, having exceeded the impact coefficient defined in the existing Specifications. To correct this problem, an equation for evaluating the “dynamic effect coefficient” using the load amplitude as one of variables was newly proposed.

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In this paper, we consider a design method for feed-forward controllers using preview control. Feed-forward controllers are important when dynamic character disturbances with known dynamics are attenuated and when an input-output characteristic is specified. Yamada and Kinoshita proposed a design method for feed-forward controllers for multivariable systems with non-zero relative degree. The feed-forward controllers by Yamada and Kinoshita can follow a step reference input without steady state error. However, Yamada and Kinoshita did not consider design methods of feed-forward controllers for general reference inputs, such as a sine wave. In this paper, we propose a design method for feed-forward controllers for general reference inputs such that the output follows the reference input without steady state error. To obtain the feed-forward controllers for general reference inputs, we use a fusion of the method of Yamada and Kinoshita with preview control.

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We propose a new approach in numerical computations of integral equations of the first kind. Some important integral equations of the first kind arise in the analysis of inverse problems, but they are often typically ill-posed so that numerical construction of their solutions is hard. To overcome the difficulty, two devices play essential roles in our proposal: the use of multiple-precision arithmetic and that of high-accurate numerical integration formula. The latter is a generalization of the spectral collocation method, and we mainly discuss it in this paper. We also show some numerical examples.

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Three-dimensional flow above the sand dunes have been studied numerically by using Large-Eddy Simulation (LES) method. In the flow direction and span direction cyclic boundary conditions are imposed for velocity and pressure. The movement of the sand which is known as the two kinds of the elemental types of desert have been investigated. The numerical method employed in this study can be divided into three parts: (i) calculation of the air flow above the sand dunes using standard MAC method with a generalized coordinate system; (ii) estimation of the sand transfer caused by the flow through the friction; (iii) determination of the shape of the ground. Since the computational area has been changed due to step (iii), steps (i)-(iii) are repeated until prescribed times. One kind of the simulated dunes, which is formed by unidirectional wind, develops wings from the each end of them, connects with each other and becomes essentially parallel straight ridges which is known as transverse dune. The other one, which is formed by two directional winds, extends at the converging direction which is known as linear dunes.

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The energy-momentum method is one of the formulations of the nonlinear dynamics of flexible structures. It provides modified equations of motion that conserves the linear and angular momentum of the system as well as the total energy, so that it guarantees unconditional stability of the numerical time integration. In this paper, the author proposes modified equations of three-dimensional motion of flexible multibody system with joint constraints based on the energy-momentum method, i.e. it exactly conserves total mechanical energy and momentum. The conservation condition for arbitrary holonomic constraint system is described. Numerical examples show that the energy and the momentum are exactly conserved under the holonomic constraint, which means that the proposed method is applicable to the finite element dynamic analysis of flexible multibody system.

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The classical limit of the Yang and Yang's integral equation for the Sutherland lattice (the sinh^-2x potential) is investigated. Two kinds of perturbation expansion of the integral equation are proposed. One is from the δ-potential lattice and the other from the Toda lattice. The merits of these methods are discussed.

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An eight-parameter family of two-dimensional piecewise linear mappings is discussed. Since the dynamical system is obtained from the QRT system through the ultradiscretization, the dynamical system is called the ultradiscrete QRT system. The ultradiscrete QRT system is considered to be integrable because it has an eight-parameter family of invariant curves which fills the plane. It is shown that, for particular parameters, the dynamical system can be regarded as a dynamical system on a fan associated with the conserved quantity. It is also shown that such a dynamical system has periodic solutions for any initial value. Therefore we call such a dynamical system the ultradiscrete periodic QRT system. From the ultradiscrete periodic QRT system, the periodic QRT system is obtained in terms of the inverse ultradiscretization.

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The linear stability of small-amplitude internal solitary waves with respect to transverse (two-dimensional) perturbations is studied in the framework of the modified Kadomtsev-Petviashvili (MKP) equation. This equation is an analogue of the ordinary KP equation that describes nonlinear motion of small-amplitude waves in fluids. The difference appears in nonlinear terms that has a third-order nonlinear terms in addition to the usual second-order term of the KP equation. Then it is newly discovered that for some types of density profiles, the small-amplitude internal solitary waves could be unstable to long-wavelength transverse perturbations. A numerical example of instability is also presented.

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An iterative domain decomposition method is applied to numerical analysis of 3-dimensional (3-D) nonlinear magnetostatic problems taking the magnetic vector potential as an unknown function. The nonlinear simultaneous equations are solved with the Picard iteration or the Newton iteration. In Picard iteration, we compute the reluctivity using H-B curves, and in Newton iteration we compute the reluctivity using n-B curves or n-B2 curves. The simultaneous linear equations at each step of the nonlinear iteration are solved by the iterative domain decomposition method. The iterative domain decomposition method is combined with the Conjugate Gradient (CG) procedure, and the Hierarchical Domain Decomposition Method (HDDM) which is adopted for the parallel computing. Numerical results show that the iterative procedure converges, and that the computed magnetic flux density is suitable.

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In this paper, an approximation scheme to a classical one-phase Stefan problem is presented. This scheme is constructed by using the properties of the singular limit solutions of a reaction-diffusion equation, and its convergence is stated. Numerical simulations are included to demonstrate the effectiveness of the scheme.

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A minimizing method for calculating the American call option is developed. The American option pricing is a heat type obstacle problem but it contains some di.culties on the initial condition. In spite of these di.culties, the discrete Morse semi.ow which is a minimizing scheme via the time semidiscretized variational functional, works well. The derivative of the solution is also useful for determining the precise position of the free boundary.

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