应用数学和力学

Hopf Bifurcation in a Three-Dimensional System

Li De-ming, Huang Ke-lei

1989, 10(11): 816-968.

Abstract(1647) PDF(422)

Abstract:
In this paper,Liapunor-Schmidl reduction and singularity theory are employed to discuss Hopf and degenerate Hopf bifureations in global parametric region in a three-dimensional system , The conditions on existence and stability are given.

Analytical Solutions for Equations of Unsteady Flow of Non-Newtonian Fluids in Tube

Liu Ci-qun, Huang Jun-qi

1989, 10(11): 939-946.

Abstract(1862) PDF(649)

Abstract:
This paper presents analytieal solutions to the partial differential equations for unsteady flow of the second-order fluid and Maxwell fluid in tube by using the integral transform method. It can be used to analyse the behaviour of axial velocity and shear stress for unsteady flow of nun-Newtonian visco-elastie fluids in tube, and to provide a theoretical base for the projection of pipe-line engineering.

A Rectangular Element of Thin Plates Based upon the Generalized Variational Principles

Chien Wei-zhang, Wang Gang

1989, 10(11): 947-953.

Abstract(1844) PDF(492)

Abstract:
Based on generalized variational principles, an element called MR-12 was constructed for the static and dynamic analysis of thin plates with orthogonal anisotropy. Numerical results showed that this incompatible element converges very rapidly and has good accuracy. It was demonstrated that generalized varialional principles arc useful and effective in founding incompatible clement.Moreover, element MR-12 is easy for implementation since it does not differ very much from the common rectangular element R-12 of thin plate.

Numerical Solution of Quasilinear Singularly Perturbed Ordinary Differential Equation without Turning Points

Lin Ping, Su Yu-cheng

1989, 10(11): 955-959.

Abstract(1696) PDF(656)

Abstract:
In this paper we consider a quasilinear second order ordinary diferential equation with a small parameter ε, Firstly an approximate problem is constructed. Then an iterative procedure is developed. Finally we give an algorithm whose accuracy is good for arbitrary ε>0.

Shakedown Analysis of Shell Structures of Kinematic Hardening Materials

Jin Yong-jie, Zhao Xiao-jin

1989, 10(11): 969-976.

Abstract(1873) PDF(555)

Abstract:
It is of great practical importance to analyze the shakedown of shell structures under cyclic loading, especially of those made of strain hardening materials.In this paper, same further understanding of the shakedown theorem for kinematic hardening materials has been made, and it is applied to analyze the shakedown of shell structures Though the residual stress of a real stale is related to plastic strain, the time-independent residual stress field as we will show in the theorem may be unrelated to the time-independent kinematically admissible plastic strain field For the engineering application, it will lie much more convenient to point this out clearly and definitely, otherwise it will be very difficult. Also, we have proposed a new method of proving this theorem.The above theorem is applied to the shakedown analysis of a cylindrical shell with hemispherical ends. According to the elastic solution, various possible residual sfcss and plastic strain Jlelds, the shakedown analysis of the structure can be reduced to a mathematical programming problem.The results of calculation show that the shakedown load of strain hardening materials is about 30-40% higher than that of ideal plastic materials. So it is very important to consider the hardening of materials in the shakedown analysis,for it can greatly increase the structure design capacity, and meanwhile provide ascicntific basis to improve the design of shell structures.

The Criterion Algorithm of Relation of Implication between Periodic Orbits(Ⅰ)

Zhang Jing-zhong, Yang Lu, Zhang Lei

1989, 10(11): 977-985.

Abstract(1754) PDF(542)

Abstract:
In recent years, there is a wide interest in Sarkovskii's theorem ami the related study. According to Sarkovskii's theoren if the continuous self-mapf of the closed interval has a 3-pcriodic orbit, then fmust has an n-pcriodic orbit for any positive integer n. But f can not has all n-periodic orbits for some n.For example, let Evidently,f has only one kind of 3-periodic orbit in the two kinds of 3-periodic orbits. This explains that it isn't far enough to uncover the relation between periodic orbits by information which Sarkovskii's theorem has offered. In this paper, we raise the concept of type of periodic orbits, and give a feasible algorithm which decides the relation of implication between two periodic orbits.

Stability of Stationary State Solution for a Reaction Density-Dependent Diffusion Equation

Zhang Guo-chu

1989, 10(11): 987-996.

Abstract(1815) PDF(569)

Abstract:
In this paper we are interested in the large time behavior of the nonlinear diffusion equation u₁=(φ(u))_xx+φ(u), (x∈R, f∈R+=(0,+∞)) We consider functions φ(u) and φ(u) which allow the equation to possess traveling wave solutions. We first present an existence and uniqueness as well as some comparison principle result of generalized solutions to the Cauchy problem. Then we give for some threshold results, from which we can see that u=a is stable, while u=0 or u=1 is unstable under some assumptions, etc.

Elastic Media with Randomly Distributed Defects

Wang Biao, Wang Dian-fu, Wang Duo

1989, 10(11): 997-1008.

Abstract(1528) PDF(414)

Abstract:
In this paper, the clastic field in a solid with randomly distributed defects is derived. These defects are composed of cavities and microcracks, whose locations, orientation and size are random variables. The Random Point field Model is proposed to describe the random defects, and the basic equations far elastic field in a random defect medium are dcveloped Two exaniples are studied in detail. One is a solid with random microcracks and the other is a solid with ellipsoidal cavities.

An Analytic Solution on Hypersonic Flow over an Arbitrary Slender Body with Near Power-Law Profile (Ⅰ)

Chen Yao-song, Chen Yong-ze

1989, 10(11): 1009-1024.

Abstract(1594) PDF(608)

Abstract:
On the basis of a self-similar solution as well as of the assumption of the "Transserse Motion",a general linear theory on hypersonic flow over a general slender body is set up in this paper By means of this theory, the problem concerned can he put into a universal system of O.D Eqs.which can be integrated manerically in advance.

Chaos and Bifurcation of Phase Locking Loops under Periodic Perturbation

Guo Rui-hai, Yuan Xiao-feng

1989, 10(11): 1026-1032.

Abstract(1575) PDF(452)

Abstract:
This paper discusses the chaos and bifurcation for equation . By use of the Melnikov method the conditions to have the chaotic behavior and to have subharmonic oscillations are given.

1989 Vol. 10, No. 11