The finite voluem method is used to discretize the Navier-Stokes equation together with a standard k-ε double equation turbulence model for closing the set of equations.

The charachteristics of the proposed approach are that the formulation of the set of equations for special configuration analysis is simple and that all the special configuratinos can be found for a planar linkage.

This paper starts from the equations of motion in generalized curvilinear coordinates and the model of Head's two-dimensional entrainment theory, and derives a set of equations along surface curve on normal profile of a yawed wing for a compressible three-dimensional turbulent boundary layer.

A complete set of equations for determining the energy levels and the wavefunc-tions with different symmetry of electronic states of the ideal divacancy in cubic semiconductors is obtained using the Koster-Slater Green's function method.

This set of equations is general in the sense that it can be used to the optimizations of either the number of ADM's or the number of wavelengths or both of them simultaneously;

The Climatology and peristance (CLIPER) models for predicting typhoon motion were proposed from regression analysis of the future zonal and meridional displacements based on climatology, persistance and some combined predictors for the South China Sea (113-123°E, 10-25°N) , and a set of equations to predict the zonal and meridional displacements of typhoon track were derived based on entire samples at24 h to 120 h intervals.

The Climatology and persistance (CLIPER) models for predicting typhoon motion were proposed from regression analysis of the future zonal and meridional displacements based on climatology, persistance and some combined predictors for the South China Sea (113-123°E, 10-25°N), and a set of equations to predict the zonal and meridional displacements of typhoon track were deriyed based on entire samples at24 h to 120 h intervals.

From the exact solution of stress along the direction θ=0° and θ=90° at crack-tip of mode Ⅰ、Ⅱ and Ⅲ, a set of equations is produced for determination of stress intensity factor by photoelasticity and holo-photoelasticity.

The issues of approximate solution of an infinite set of equations for the moments are discussed.

A closed set of equations where higher-order correlation moments of statistical fields serve as transferable entities is derived.

The basic principles of the model, set of equations, and the initial and boundary conditions are described.

This formula enables one to directly calculate the solubility of steam in compressed gas without using the previously suggested solution of the set of equations.

It is shown that the associated-mass effect has a pronounced impact on the acoustic characteristics of the set of equations.

Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear...

Due to the gradual energy decay the free turbulent shear flow far downstream resembles the final stage motion of homogeneous isotropic turbulence. As in the latter case we adopt the concept of vortex motion structure of turbulence to solve the present problem. The dynamical basis of vortex motion solution is the set of equations of turbulent velocity fluctuation. In the flow field of the final stage motion of free turbulence the Reynolds number of turbulence is comparatively small, hence the non-linear terms in the dynamical equations can be neglected. Furthermore the size of vortices which form the turblent flow is regarded small, so within the range of each vortex the mean turbulent velocity and its gradient can be considered to be independent of the changes of the space coordinates. We now seek the following approximate solution of the linearized equations of turbulent velocity fluctuation; one part of the turbulent velocity fluctuation represents the final stage motion of homogeneous isotropic turbulence, while the other is proportional to the gradient of mean velocity, the latter part being smaller than the former. From this approximate solution the shearing component of the Reynolds stress is found to be directly proportional to the gradient of mean velocity. As a special example of the general solution we consider the case of the two-dimensional wake. Within the wake we put, furthermore, a plane grid normal to the plane of symmetry of the wake. This grid then creates in its downward stream a homogeneous isotropic turbulence field superimposed upon that of the wake. Our solution is applicable to places far downstream both from the body which creates the wake and from the grid. Since the flow here is nearer to the grid, so the turbulence level of the homogeneous isotropic turbulence would be higher than that of the wake. Consequently the conditions of the general solution can be satisfied. The present paper presents the solutions of the mean velocity and the mean squares of turbulent velocity fluctuation of the wake. These theoretical results can all be tested by experiment. On account of that we only discuss the final stage motion of free turbulence, the question how to lay down the upstream boundary condition of the flow field when solving the differential equations of the mean flow needs further consideration by other methods.

In this paper a generalized theory of coupled local normal modes is developed, which is based on the mathematical method-"method of slowly varying coefficients", introduced by the author in a previous paper. By this method, the set of ordinary coupled wave equations is transformed into a new set of equations for the local normal modes with much reduced couplings. To illustrate the applicability of the method, the all-important problem of bend with slowly varying curvature is solved by considering two and...

In this paper a generalized theory of coupled local normal modes is developed, which is based on the mathematical method-"method of slowly varying coefficients", introduced by the author in a previous paper. By this method, the set of ordinary coupled wave equations is transformed into a new set of equations for the local normal modes with much reduced couplings. To illustrate the applicability of the method, the all-important problem of bend with slowly varying curvature is solved by considering two and three coupled modes succesively. For the two coupled-modes case, our results agree with those by Louisell and Unger. Solution for the three coupled-modes problem has not been appeared in literatures heretofore. A numerical evaluation of the spurious modes in an S-shaped bend is given. Further applications are discussed.

The first part of this paper deals with a brief survey and discussion of the limit analysis in solid mechanics. Since the complete establishment of the well-known theorems of the upper and lower bounds, considerable advances have been made in the limit analysis as a branch of applied plasticity. Now, exact calculation of the plastic limit load is feasible with no apperciable difficulty for rigid framed structures, consisting of systems of members subjected mainly to bending action. In the field of two and three...

The first part of this paper deals with a brief survey and discussion of the limit analysis in solid mechanics. Since the complete establishment of the well-known theorems of the upper and lower bounds, considerable advances have been made in the limit analysis as a branch of applied plasticity. Now, exact calculation of the plastic limit load is feasible with no apperciable difficulty for rigid framed structures, consisting of systems of members subjected mainly to bending action. In the field of two and three dimensional structures, especially in the plate and shell problems, although many results have also been found for a wide variety of practical problems, but further progress seems to be very difficult in encountering with more complicate problems. Progress is restricted by the fact that, the limit theorems cannot in these cases give results sufficiently approached to the upper and lower bounds. Moreover, the application of lower bound theorem is especially difficult.The second part of this paper suggests a generalized variational principle, in which both stress distribution σij and velocity field vi are introduced and vary independently. This variational principle is equivalent mathematically to the whole set of equations, which must be satisfied by the limit analysis: equalibrium, mechanism, yield condition and flow law. It is proved that with independently assumed kinematically admissible velocity field and statically admissible stress distribution, the generalized variational principle gives the approximate plastic limit load, lying between the upper and lower bounds obtained from bound theorems. Moreover, numerical examples for circular plates are carried out to show that, the generalized variational principle gives rather stable answers for different combinations of assumed stress distribution and velocity field. It is remarked, furthermore, that the generalized variational principle can be applied to the limit analysis dealing with non-homogeneous as well as anisotropic perfectly plastic materials.