应用数学和力学

1990 Vol. 11, No. 5

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Torsional Rigidity of Shells of Revolution

Chien Wei-zang

1990, 11(5): 373-381.

Abstract(1767) PDF(786)

Abstract:
In this paper, the general equations of equilibrium for axisymmelrical deformation including the torsional deformation of revolutional shells are derived. It is shown that the shearing stress distribution due to torsion is independent of other stress components including those of membrane stress and bending stress.In this paper, the torsional deformation is considered to he represented by membrane action only, and also by the combined action of bending membrane deformation. It is shown that the main contribution of torsional rigidity is that related to membrane action.

An Exact Element Method for Plane Problem

Yeh Kai-yuan, Ji Zhen-yi

1990, 11(5): 383-389.

Abstract(1949) PDF(694)

Abstract:
In this paper, based on the step reduction method^[1] and exact analytic method^[2] anew method-exact element method for constructing finite element, is presented. Since the new method doesn't need the variational principle, it can be applied to solve non-positive and positive definite partial differential equations with arbitrary variable coefficient. By this method, a quadrilateral noncompatible element with 8 degrees of freedom is derived for the solution of plane problem. Since Jacobi's transformation is not applied, the present element may degenerate into a triangle element. It is convenient to use the element in engineering. In this paper, the convergence is proved. Numerical examples are given at the endof this paper, which indicate satisfactory results of stress and displacements can be obtained and have higher numerical precision in nodes.

Why We Have Not Yet Found a Retrograde Planet in the Solar System

Wong Chia-ho

1990, 11(5): 391-398.

Abstract(2165) PDF(612)

Abstract:
In this paper we use the Jacobian integral of the circular restricted three-body problem to establish a testing function of a moving testing particle when it moves like a planet. This function determines whether or not the particle will stay in a definite region(which may be called "stable region", SR). By means of checking with an electronic computer, we can find that the SR of quasicircular orbit of retrograde planet motion is much less than the SR of direct planet motion. It is the reason why the existence of a retrograde planet is very rare.

The Solution of Rectangular Plates with Large Deflection by Spline Functions

Pan Li-zhou, Chen Wei-zhong

1990, 11(5): 399-408.

Abstract(1711) PDF(662)

Abstract:
In this paper, Von Kármán's set of nonlinear equations for rectangular plates with large deflection is divided into several sets of linear equations by perturbation method, the dimensionless center deflection being taken as a perturbation parameter. These sets of linear equations are solved by the spline finite-point(SFP) method and by the spline finite element(SFE) method. The solutions for rectangular plates having any length-to-width ratios under a uniformly distributed load and with various boundary conditions are presented, and the analytical formulas for displacements and deflections are given in the paper. The computer programs are worked out by ourselves. Comparison of the results with those in other papers indicates that the results of this paper are satisfactorily better.

Degree Theory for Multivalued(S) Type Mappings and Fixed Point Theorems

Zhang Shi-sheng, Chen Yu-qing

1990, 11(5): 409-421.

Abstract(1984) PDF(655)

Abstract:
The main purpose of this paper is devoted to generalizing the results of Browder[1,2]This paper consists of four parts. In the first part, we introduce the concepts of multivalued(S) and(S)₊, type mappings and the concepts of the limits of multivalued(S) and(S)₊ type mappings. These kinds of mappings contain many monotone type mappings, such as maximal monotone mapping, bounded pseudo-monotone mapping and bounded generalized pseudo-monotone mapping, as its special cases. In the second part we define the pseudo-degree for(S) type mapping and the degree for(S)₊ type mapping. These two kinds of degrees are all the generalizations of the degree defined by Browder^[1,2] As applications, we utilize the degree theory presented in part 2 to study the existence of solutions for the multivalued operator equations(see part 3) and to obtain some new fixed point theorems in part 4.

The Embedded Theorem for Family of Quasi Metric Spaces in Menger Space and Its Application

Liu Zuo-shu, Zheng Quan

1990, 11(5): 423-430.

Abstract(1991) PDF(540)

Abstract:
In this paper the notion of embedding for family of quasi metric spaces in Menger spaces is introduced and its properties are investigated. A common fixed point theorem for sequence of continuous mappings in Menger spaces is proved. These mappings are assumed to satisfy some generalizations of the contraction condition. The proving technique herein seems to be new even for mappings in Menger spaces.

Second-Order Accurate Difference Method for the Singularly Perturbed Problem of Fourth-Order Ordinary Differential Equations

Wang Guo-ying, Chen Ming-lun

1990, 11(5): 431-437.

Abstract(1795) PDF(560)

Abstract:
In this paper, we construct a uniform second-order difference scheme for a class of boundary value problems of fourth-order ordinary differential equations. Finally, a numerical example is given.

The Free Bending Vibration of Cylindrical Tank Partially Filled with Liquid and Submerged in Water

Zhou Ding

1990, 11(5): 439-446.

Abstract(1767) PDF(688)

Abstract:
This paper studies the free bending vibration of cylindrical tank partially filled with liquid and submerged in water. The depths of liquid and water may be completely arbitrary. The exact calculating formulae of mode shape functions and inherent frequencies are deduced. The results can be gained by means of computer. The analysis shows that the effect of liquid and water on vibration of cylindrical tank is respectively equivalent to a generalized distributive mass attached to the tank.

On the Stokes Entry Flow into a Semi-Infinite Circular Cylindrical Tube

Wang Lu-nan, Wang Min-zhong

1990, 11(5): 447-455.

Abstract(1807) PDF(663)

Abstract:
The problem of Stokes entry flow into a semi-infinite circular cylindrical tube was studied in this paper. A new kind of series solutions was derived. Their evident difference from the solutions in References [1,2] is that the present solutions don't involve infinite integral. So they are favourable for calculation. We calculated an example by allocated method and obtained satisfied results.

An Application of Topologicai Analysis to Studying the Three-Dimensional Flow in Cascades;Part Ⅰ——Topologicai Rules for Skin-Friction Lines and Section Streamlines

Kang Shun

1990, 11(5): 457-462.

Abstract(2033) PDF(701)

Abstract:
Based on the working of Lighthill and Hunt et al., in the present paper the author has established the topological rules adapting to analysing the skin-friction lines and the section streamlines in cascades. These rules are(1) for a rotor cascade without shroud band, the total number of nodal points equals that the saddle points on the skin-friction line vector fields in eachpitch range;(2) for an annular or straight cascade with no-clearances at blade ends, the total number of saddle points is two more than that of nodal points on the skin-friction line fields in a pitch;(3) the total number of saddles in the secondary flow fields on cross-sections in cascade is one less than that of nodes;(4) in the section streamline vector fields on a meridian surface penetrating a flow passage, and on leading and trailing edge sections, the total number of nodes is equal to that of saddles;(5) on the streamline vector fields of a blade-to-blade surface, the total number of nodes is one less than that of saddles.

Extended Mac-Millan’s Equation

Qiu Rong

1990, 11(5): 463-466.

Abstract(1815) PDF(532)

Abstract:
The principle of classical dynamics and Appell-Chetayev's assumption are extended to non-inertial frame, from which extended Mac-Millan's equation is derived for non-holonomic system in non-inertial system.