应用数学和力学

1987 Vol. 8, No. 3

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On the Linking up between Bingham Fluid and Plugged Flow

Tsai Shu-tang, Jiang Yi-an

1987, 8(3): 193-198.

Abstract(1782) PDF(695)

Abstract:
When Bingham fluid is in motion, plugged flow often occurs at places far from the boundary walls. As there is not a decisive formula of constitutive relation for plugged flow, in some problems the solutions obtained may be indefinite. In this paper, annular flow and pipe flow are discussed, and unique solution is obtained in each case by utilizing the analytic property of shear stress. The solutions are identical in form with the commonly used formula for the pressure drop of mud flow in petroleum engineering.

The Boundary Layer Scheme for a Singularly Perturbed Problem for the Second Order Elliptic Equation in the Rectangle

Su Yu-cheng

1987, 8(3): 199-206.

Abstract(1730) PDF(555)

Abstract:
Using singularly perturbation theory is constructed the boundary layer scheme for a Dirichlet problem for the second order singularly perturbed equation of elliptic type in the rectangle. The error estimate is given.

Fixed Point Index of Ultimately Compact Set-Valued Mappinps in Hausdorff Locally Convex Spaces and Its Applications

Ding Xie-ping

1987, 8(3): 207-214.

Abstract(1990) PDF(437)

Abstract:
The author defines a concept of fixed point index of ultimately compact set-valued mappings in Hausdorff locally convex spaces. Using this concept, the author establishes several nonzero fixed point theorems of set-valued Φ-condensing mappings. These theorems extend some known results in [1,2,7,8,9].

The Numerical Solution of the Unsteady Natural Convection Flow in a Square Cavity at High Rayleigh Number Using SADI Method

Wang Pu, R. Kahawita

1987, 8(3): 215-224.

Abstract(1591) PDF(437)

Abstract:
The unsteady natural convection flow in a square cavity at high Rayleigh number Ra=10⁷ and 2×10⁷ has been computed using cubic spline integration. The required solutions to thetwo dimensional Navier-Stokes and energy equations have been obtained using two alternate numerical formulations on non-uniform grids. The main features of the transient flow have been briefly discussed. The results obtained by using the present method are in good agreement-with the theoretical predictions^[1,2]. The steady state results have been compared with accurate solutions presented recently for Ra=10⁷.

Some Extensions of the Initial Value Problem for Second Order Evolution Equations

Nie Yi-yi, Zhou Hong-ding

1987, 8(3): 225-236.

Abstract(1627) PDF(496)

Abstract:
The initial problem for second order linear evolution equation systems is discussed by using the contraction semigroup theory. A kind of initial value problem for second order is also discussed with variable coefficients for evolution equations by using the analytical semigroup theory, and is unified with the solutions of the initial value problem for this class of equations and those of first order temporally inhomogeneous evolution equations. This is an important class of equations in mathematical mechanics.

Non-Linear Vibration of Circular Corrugated Piates

Wang Xin-zhi, Wang Lin-xiang, Hu Xiao-fang

1987, 8(3): 237-245.

Abstract(1712) PDF(631)

Abstract:
In this paper, first by using Hamilton principle, we derive the variational equation of circular corrugated plates. Taking the central maximum amplitude of circular corrugated plates as the perturbation parameter and adopting the perturbation variational method, in the first-order approximation, we obtain the natural frequency of linear vibration of circular corrugated plates and then the nonlinear natural frequency of the corrugated plates. By comparing with the linear results, the attempt of this paper is proved feasible.

Nonlinear Problems of Circular Plates with Variable Thickness under Central Concentrated Load

Wang Jin-ying

1987, 8(3): 247-252.

Abstract(1676) PDF(479)

Abstract:
Nonlinearly bending problems of circular thin plates with linearly varying thickness under central concentrated load are discussed.

The Relationship between the Stability and the Optimality of Linear Systems (Ⅱ)

Chen Xiao-lin, Huang Ling

1987, 8(3): 253-257.

Abstract(1955) PDF(828)

Abstract:
Different from the inverse problem put forward by R.E.Kalman, another kind of inverse problem of linear optimal control is proposed and discussed in [1] as follows:Given an asymptotically stable linear constant system and a nonnegative quadratic performance index, when can a state-feedback be separated from the stable system so that this state-feedback control law is optimal for the given index? In this paper this problem is extended. Similar conclusions are obtained for linear discrete systems and linear time-variable systems. According to these conclusions we can say that the correspondence between the asymptotically stable system and the optimal feedback system is the inherent character of all kinds of linear systems.

Stationary Points Iteration Method for Periodic Solution to Nonlinear System

Liu Tie-niu, Wang Wei

1987, 8(3): 259-265.

Abstract(1814) PDF(548)

Abstract:
The value method which is used to obtain the periodic solution to nonlinear system is mentioned in this article. Different point reflection is defined in the nonlinear autonomous and nonautonomous system firstly and then that linear reflection obtained from the inserting value of nonlinear reflection is asymptotic to original nonlinear reflection. The stationary points obtained by linear reflection are regarded as the asymptotic solution of the stationary points of original system. If this asymptotic solution of the stationary points is not satisfactorily accurate it can be used as the initial point of the next reflection. In addition,a corresponding method of researching the stability of periodic solution is put forward in this article.

Problem on Circular-Arc Cracks between Bonded Dissimilar Materials under Concentrated Force and Moment

Liu You-wen, Jiang Chi-ping

1987, 8(3): 267-276.

Abstract(2002) PDF(558)

Abstract:
The method is very efficient by applying extended Schwarz principle integrated with the analysis of the singularity of complex stress functions to solve some plane-elastic problems under concentrated loads, in Ref.[1], this method is used to deal with the elastic problems of homogeneous plane. In this paper, it is extended to the case of dissimilar materials with co-circular cracks under concentrated force and moment. For several typical cases the solutions of complex stress function in closed form are built up and the stress intensity factors are given. From these solutions, we provide a series of particular results, in which two of them coincide with those in Refs. [1] and [6].

A Perturbation Solution of Free Vibration of Cylindrical Shells with Ring-Stiffeners

Li Long-yuan

1987, 8(3): 277-286.

Abstract(2050) PDF(595)

Abstract:
In this paper, the free vibration of cylindrical sheel with ring-stiffeners is studied in detail by using the PLK method in singular perturbation and the general Hale's law, and the formulas calculating natural frequencies of cylindrical sheel with ring-stiffeners are expressed. Finally, the FEM solution is also given to prove the perturbation solution to be seemly, and this comparison shows that the method yields very good results.

Fixed Pansystems Theorems and Pansystems Logic Conservation of Chaos

Qin Guo-guang

1987, 8(3): 287-290.

Abstract(1701) PDF(459)

Abstract:
The study of nonlinear problems was developed in works^[1,2] by means of the pansystems methodology (PM) which does not need the condition related to differential manifolds and linear space. In work [2], within the framework of PM, we proved that study of panchaos, panattractor and strange panattractor can be transformed conditionally into some forms of fixed subsets. As a continuation of work [2], we now research the pansystems logic conservation of panchaos, panattractor, strange panattractor and some other fixed subsets.