应用数学和力学

1988 Vol. 9, No. 8

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Nonlinear Analysis of a Corrugated Circular Plate under Combined Lateral Loading

Liu Ren-huai

1988, 9(8): 661-674.

Abstract(1740) PDF(479)

Abstract:
In this paper,nonlinear bending of a corrugated circular plate with a plane central region under the combined action of uniformly distributed load and a concentrated load at the center has been investigated by using large deflection theories of isotropic and anisotropic circular plates.The quite accurate analytical solutions for rigidly as well as loosely clamped edge conditions have been obtained following the modified iteration method.

Positive Solution of a Class of Equations Involving Noncompact Mappings

Lan Kun-quan, Ding Xie-ping

1988, 9(8): 675-684.

Abstract(1839) PDF(485)

Abstract:
In this paper,we define a generalized relative degree for A-proper mappings from a relative open subset of a Banach space into another Banach space and introduce the concepts of generalized P-compact and P₁-compact mappings.Next,we show several existence theorems of positive solutions for the equations involving these mappings.Our theorems improve and extend some recent results.

On Self-Excited Oscillation of Dynamic Systems with Gap

Li Li, Ren Bao-jing

1988, 9(8): 685-692.

Abstract(1539) PDF(485)

Abstract:
In this paper,the sufficient condition for self-excited oscillation of dynamic systems with gap is given by using qualitative method of differential equations.

On the Torsion of a Cylinder with Several Cracks

Wang Xiao-chun, Tang Ren-ji

1988, 9(8): 693-702.

Abstract(1682) PDF(450)

Abstract:
In this paper,based on paper [1],the analytic expression of the torsion Junction for a cylinder containing arbitrary oriented cracks is obtained.The problem is reduced to solve a system of singular integral equations for the unknown dislocation density functions.Using the numerical method of the singular integral equations^[2,7],the torsional rigidities and stress intensity factors are evaluated for several multicracked cylinders.Next,the crk-cutting method^[5] is firstly extended to lve the torsion problem for a rectangular prism.The numerical results show that the method presented here is successful.

The Finite Dynamic Annular Element for the Vibration Analysis of Variable Thickness Discs

Xu Yin-ge, Zhang Yi-song

1988, 9(8): 703-712.

Abstract(1696) PDF(477)

Abstract:
According to the gyro-periodicity of dynamic displacements,the two-dimensional problems of circular plates with variable thickness are simplified into one-dimensional ones in this paper.Taking the expanded form of frequency power series of the dynamic displacement functions as the dynamic shape functions of the finite annular element,the mass and stiffness matrices as well as their one-order revised matrices are given succinctly.The dynamic method is used to analyse the vibration characteristics of a bladed disc assembly and is compared with conventional finite element method and experiment,and is proved to be superior to other numerical methods.

The Blood Flow and the Motion of Vessel Wall

Cen Ren-jing

1988, 9(8): 713-724.

Abstract(1673) PDF(744)

Abstract:
The correlation problem between the blood flow and the motion of vessel wall in the mammalian circulatory system is discussed in this paper.Supposing the blood flow is under the stable oscillatory condition,a set of formulas for velocity distribution,pressure distribution,displacement of vessel wall and constraining stress are obtained.Kuchar's formulas are extended from steady flow to unsteady oscillatory flow by means of the formulas obtained in this paper.The problem of elasticity effect of vessel wall is also discussed.

The Approximate Solution of the Self-Similar Problem for Radial Flow of Non-Newtonian Fluids through Porous Media

Yuan Yi-wu

1988, 9(8): 725-733.

Abstract(1564) PDF(453)

Abstract:
In this paper,we study the approximate solution of the self-simikar problem for radial flow of non-Newtonian fluids through porous media.Assuming that the fluids obey the exponential function law,we obtain an exact solution for the exponent n=0 and compare it with the approximate solution in ref.[1].For n>1 and n<1,we obtain respectively approximate solutions.Some exampls are presented.

On Several Problems for Lateral Instability of Cantilever Plates

Cheng Xiang-sheng

1988, 9(8): 735-739.

Abstract(1594) PDF(874)

Abstract:
The present article researches several problems about the lateral instability,of cantilever plates by means of the energy method,in which we discuss the minimum critical load of cantilever rectangular plates under a concentrated force,a uniformly distributed load,a distributed load in triangular form and a concentrated couple,respectively,when the lateral buckling takes place.

Perturbation Analyses for the Postbuckling of Simply Supported Rectangular Plates under Uniaxial Compression

Shen Hui-shen, Zhang Jian-wu

1988, 9(8): 741-752.

Abstract(2035) PDF(923)

Abstract:
In this paper,applying perturbation method to von Karman nonlinear large deftection equations of plates by taking deflection as perturbation parameter,the postbuckling behavior of simply supported rectangular plates under uniaxiai compression is insestigated.Two types of in-plane bouridary conditions are now considered and the effecis of initial imperfections are also studied.It is found that the theoretical results are in good agreement with experiments.The method suggested in this paper which has not been found in previous papers is rather simple and easy for the postbuckling analysis of rectangular plates.

On the Global Asymptotic Stability of Periodic Solutions of a Class of Ecological System

Jin Jun

1988, 9(8): 753-758.

Abstract(1830) PDF(483)

Abstract:
In this paper,we have made researches on the mathematical models which have three populations of mutual action: and We have obtained the sufficient conditions respectively for the systems(*) and(**) for existence and uniqueness of single positive periodic solutions which are globally asymptotically stable.

Operation Analysis of Natural Resources and Their Pan Weighted Network Models

Zan Ting-quan, Zhu Li-xin

1988, 9(8): 759-769.

Abstract(1705) PDF(531)

Abstract:
In this paper,we propose a competition-share 3-category principle,on which we unite the problems of natural resources,energy,population and environment and so on into a mutual scheme,and provide a united model for the comprehensive research on these problems.This makes the idea of operation analysis of natural resources clearer and the relationships between each of their parts more obvious.On the basis of the above discussion,we propose mathematical models for the operation analysis of multi-networks and the solution of the above global comprehensive problems.We discuss,especially,Shengke(growth and restraint) relationships between two networks of natural resources and share-competitors and their analysis models,providing mathematical tools for solving the problems of the resource-population and the resource-economy,etc.