On the three-dimensional alternative to the Blasius boundary-layer solution

Theoretical investigations have shown that there is a three-dimensional alternative to the Blasius solution for laminar boundary layer flow past a semi-infinite flat plate at zero incident. In this Note we show numerically that there exists a class of three-dimensional solutions confined to almost zero incident conditions. To cite this article: A. Ridha, C. R. Mecanique 333 (2005).     

General solution of A 2-D weak singular integral equation with constraint and its applications

Hertz'ssolutionTheProjectsupportedbytheNaturalScienceFoundationofGuangdongProvinceofChina[.IntroductionTheintegralequationsubjecttoconstraintp(s,te)=o,for(s,W)-(r,o)6Q={(r,O)lF(r,o)>c.}'(l.2)hasbeenstudiedin[l].Themultipleintegrationsimilartothelefthandsi…     

A generalized auxiliary equation method and its applications

In this paper, a generalized auxiliary equation method with the aid of the computer symbolic computation system Maple is proposed to construct more exact solutions of nonlinear evolution equations, namely, the higher-order nonlinear Schrödinger equation, the Whitham–Broer–Kaup system, and the generalized Zakharov equations. As a result, some new types of exact travelling wave solutions are obtained, including soliton-like solutions, trigonometric function solutions, exponential solutions, and rational solutions. The method is straightforward and concise, and its applications are promising.     

Retrospective time integral scheme and its applications to the advection equation

To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme. The project supported by the National Key Program for Developing Basic Sciences (G1999043408 and G1998040901-1) and the National Natural Sciences Foundation of China (40175024 and 40035010)     

失效准则在广义Mohr空间的表示及应用

在广义的Mohr空间研究材料的破坏和屈服(失效),找到了主应力空间和广义Mohr空 间中失效曲面的变换,以及适用于所有失效准则的应力和失效面法向的普适相容关系. 对于 双剪强度理论,根据它在广义Mohr空间的表示,将之归于最大偏应力理论一类.     

The differential solution to the flyinc locus equation of the shot and its application

This paper establishes a locus equation of the shot according to kinematical principes. By using differential and integral calculus and trigonometric function, we have found the extreme valve of the angles of delivery and the best flying distances, with the falling points of t’ short considered. Thus a simple expression showing the relationships among the bes’ angle o delivery, the best flying distance, the height of delivery point and its initial velocity can be attained and a diagram can be made by calculating, showing the best angle of delivery and the best flying distance.     

A direct representation of the rotation tensor in polar decomposition of deformation gradient and its applications

Through a variational approach, an explicit connection between the additive and the polar decompositions of deformation gradient has been established. An exact formula for determining the rotation tensor in polar decomposition is obtained. The formula is fundamental in continuum mechanics and can be used to separate the rotation and the pure strain in deformation, by which various approximate expressions can be easily obtained.     

The general solution of spherically isotropic magnetoelectroelastic media and its applications

A general solution of the three-dimensional equilibrium problem of spherically isotropic magnetoelectroelastic media is presented. Base on the obtained general solution, exact and compact form solutions are obtained for (1) a spherically isotropic magnetoelectroelastic cone subjected to concentrated force, concentrated couple, a point charge and a point electric current at its apex; (2) a spherically isotropic magnetoelectroelastic space with a concentrated force at the origin; (3) a spherical shell under spherically symmetric deformation; and (4) stress concentration around a spherical cavity subjected to remote uniform tensile force, electric charge and electric current.     

Boltzmann equation in the α, u representation

It is proposed, as in [1, 2], to regard the distribution function as a set of all possible Maxwellian distributions with arbitrary temperatures and mean velocities, with each Maxwelian distribution taken with its own weight (, u). An equation equivalent to the Boltzmann equation is constructed for this weight function. The cases of one-dimensional, twodimensional, operator in the arbitrary case in the , u representation it suffices to know the corresponding kernel for the one-dimensional problem.Leningrad. Traslated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 117–123, July–August, 1972.     

Exact solution of the Boltzmann equation

We build up immediate connection between the nonlinear Boltzmann transport equation and the linear AKNS equation, and classify the Boltzmann equation as the Dirac equation by a new method for solving the Boltzmann equation out of keeping with the Chapman, Enskog and Grad’s way in this paper. Without the effect of other external fields, the exact solution of the Boltzmann equation can be obtained by the inverse scattering method.     

Numerical solution of the entrainment equation

An equation describing the change in body shape as a result of intense mass entrainment from the surface under the effect of convective aerodynamic heating under the simplest assumptions (dependence of the pressure on only the local slope of the surface, the method of local similarity to compute the heat fluxes) is considered. Mathematical questions originating during its numerical solution are investigated. The instability of explicit schemes is proved in the neighborhood of the stagnation point. A stable explicit-implicit scheme, suitable for a through computation of unsmooth solutions, is proposed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 147–154, March–April, 1978.The author is grateful to V. V. Lunev for constant attention to the research and for useful discussions.     

A periodic solution of the diffusion equation

Under some circumstances, autooscillations can arise in an electrochemical system with decreasing characteristics [1–3]. A method for finding the polarization curve P=P() (here is the electrode potential, P=i I c (0, t), where i is the current density, and c(0, t) is the mass concentration at the electrode surface), if the distribut ion in time of the current density is given, is proposed in [1]. In the numerical solution of this problem, which is considered below, considerable computational difficulties were encountered.     

求一般结构系统部分复模态的Ritz向量法及应用

构造了一种获取一般结构系统（刚度，阻尼矩阵可以是非对称的）Ｒｉｔｚ向量基的迭代方法，从而可以高维阻尼系统部分复模态解降价成为一个低维二次特征问题，将此降阶后的二次特征问题化成标准特征值后即可用ＱＲ方法求得系统的部分低阶持征解，作为应用，对一个实际转子－轴承系统的动力特性进行了计算分析。     

Superfluous order and the proper solution of the Maxwell equation

In this paper it is proved that Maxwell equation is equivalent to a fourth order equation. Under a certain condition, its general solution is given by     

GENERAL SOLUTION OF THE OVERALL BENDING OF FLEXIBLE CIRCULAR RING SHELLS WITH MODERATELY SLENDER RATIO AND APPLICATIONS TO THE BELLOWS (Ⅰ)-GOVERNING EQUATION AND GENERAL SOLUTION

The overall bending of circular ring shells subjected to bending moments and lateral forces is discussed. The derivation of the equations was based upon the theory of flexible shells generalized by E.L. Axelrad and the assumption of the moderately slender ratio less than 1/3 (i.e., ratio between curvature radius of the meridian and distance from the meridional curvature center to the axis of revolution). The present general solution is an analytical one convergent in the whole domain of the shell and with the necessary integral constants for the boundary value problems. It can be used to calculate the stresses and displacements of the related bellows. The whole work is arranged into four parts: (Ⅰ) Governing equation and general solution; (Ⅱ) Calculation for Omega-shaped bellows; (Ⅲ) Calculation for C-shaped bellows; (Ⅳ) Calculation for U-shaped bellows. This paper is the first part.     

A particular solution for the chaplygin equation

In the theoretical studies of several gasdynamic problems a major role is played by the hodograph plane, where the equations in terms of velocity component variables are linear. In these studies a primary role is played by the Chaplygin equation for the stream function . Chaplygin [1] obtained a general solution for the equation of motion in the hodograph plane. Particular exact solutions of the hodograph are also known [2]: radial flow, spiral flow, etc. Below we consider a particular solution of the Chaplygin equation.     

Displacement type unified equation for bending, buckling and vibration of conical shells and its applications

By using Donnell's simplication and starting from the displacement type equations of conical shells, and introducing a displacement functionU(s,,) (In the limit case, it will be reduced to cylindrical shell displacement function introduced by V. S. Vlasov) and a generalized loadq,(s,,),the equations of conical shells are changed into an eighth—order solvable partial differential equation about the displacement functionU(s,,). As a special case, the general bending problem of conical shells on Winkler foundation has been studied. Detailed numerical results and boundary coefficients for edge unit loads are obtained.The project supported by the National Natural Science Foundation of China.