应用数学和力学

1992 Vol. 13, No. 4

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Difference Scheme for an Initial-Boundary Value Problem for Linear Coefficient-Varied Parabolic Differential Equation with a Nonsmooth Boundary Layer Function

Su Yu-cheng, Zhang You-yu

1992, 13(4): 279-286.

Abstract(1986) PDF(609)

Abstract:
In this paper, using nonuniform mesh and exponentially fitted difference method, a uniformly convergent difference scheme for an initial-boundary value problem of linear parabolic differential equation with the nonsmooth boundary layer function with respect to small parameter εis given, and error estimate and numerical result are also given.

An iterative Parallel Algorithm of Finite Element Method

Hu Ning, Zhang Ru-qing

1992, 13(4): 287-295.

Abstract(2169) PDF(751)

Abstract:
In this paper, a parallel algorithm with iterative form for solving finite element equation is presented. Based on the iterative solution of linear algebra equations, the parallel computational steps are introduced in this method. Also by using the weighted residual method and choosing the appropriate weighting functions, the finite element basic form of parallel algorithm is deduced. The program of this algorithm has been realized on the ELXSI-6400 parallel computer of Xi'an Jiaotong University. The computational results show the operational speed will be raised and the CPU time will be cut down effectively. So this method is one kind of effective parallel algorithm for solving the finite element equations of large-scale structures.

The Expression of Stress and Strain at the Tip of Notch in Reissner Plate

Qian Jun, Long Yu-qiu

1992, 13(4): 297-306.

Abstract(2207) PDF(660)

Abstract:
In this paper, the eigenequation of notch in Reissner plate is derived by the eigenfunction method. Eigenvalues of different notches with different angles are calculated by Muller iteration method. The expression of stress and strain at the tip of notch in Reissner plate is obtained.

A Method of Determining Buckled States of Thin Plates at a Double Eigenvalue

He Lu-wu, Cheng Chang-jun

1992, 13(4): 307-311.

Abstract(2356) PDF(545)

Abstract:
A method of determining bifurcation directions at a double eigenvalue is presented by combining the finite element method with the perturbation method. By using the present method, the buckled states of rectangular plates at a double eigenvalue are numerically analyzed. The results show that this method is effective.

Nonlinear Vibrations of Orthotropic Shallow Shells of Revolution

Li Dong

1992, 13(4): 313-325.

Abstract(2183) PDF(652)

Abstract:
A set of nonlinearly coupled algebraic and differential eigenvalue equations of nonlinear axisymmetric free vibration of orthotropic shallow thin spherical and conical shells are formulated following an assumed time-mode approach suggested in this paper. Analytic solutions are presented and an asymptotic relation for the amplitude-frequency response of the shells is derived. The effects of geometrical and material parameters on vibrations of the shells are investigated.

A Class of Kolmogorov’s Ecological System with Prey Having Constant Adding Rate

Wang Cheng-wen

1992, 13(4): 327-334.

Abstract(2152) PDF(462)

Abstract:
In this paper, by using the qualitative method, we study a class of Kolmogorov's ecological system with prey having constant adding rate, discuss the relative position and the character of the equilibriums, the global stability of the practical equilibriums and give a group of conditions for the boundedness of the solutions, the nonexistence, the existence and the uniqueness of the limit cycle of the system. Most results obtained in papers [1] and [2] are included or generalized.

A Special Solution of Wave Dissipation by Finite Porous Plates

Wang Jin-jun

1992, 13(4): 335-339.

Abstract(1989) PDF(565)

Abstract:
The reflection and transmission of water waves caused by a small amplitude incident wave through finite fine porous plates with equal spacing and permeability in an infinitely long open channel of constant water depth and zero slope are studied. A special solution is obtained when the distance between the two neighbouring plates is an integral multiple of the half-wavelength of the incident wave. It is found that when the dimensionless porous-effect parameter G₀ is equal to half the total plate number, the wave dissipation reaches a maximum, and only 50% of the incident wave energy remains in the reflected and transmitted waves. Meanwhile, the reflected and transmitted waves have the same amplitude.

Influences of Gas Nucleus Scale on Cavitation

Huang Jing-chuan, Han Cheng-cai

1992, 13(4): 341-348.

Abstract(1846) PDF(648)

Abstract:
The influences of gas nucleus scale on cavitation are analysied in this paper. The results show that there are different inception conditions, growth and collapse processes of bubble for the gas nucleus with different scale. The influences shouldbe considered in calculating and simulating cavitation.

A Hierarchy of Liouville Integrable Finite-Dimensional Hamiltonian Systems

Ma Wen-xiu

1992, 13(4): 349-357.

Abstract(2080) PDF(608)

Abstract:
A hierarchy of Liouville integrable finite-dimensional Hamiltonian systems whose Hamiltonian phase flows commute with each other is generated and an infinite number of involutive explicit common integrals of motion and a set of its involutive explicit generators are given.

Oscillation Theorems for a Second Order Nonlinear Differential Equation

Yu Yuan-hong, Jin Ming-zhong

1992, 13(4): 358-365.

Abstract(2119) PDF(492)

Abstract:
In this paper, some new oscillation criteria for a second order nonlinear differential equation with dampings are established. These criteria improve and generalize the related results given in [1-4].

The Numbers of Jump Layers of Boundary Value Problems in Quasilinear Differential Equations

Cheng Jian-hua, Zhu Qing

1992, 13(4): 367-371.

Abstract(1955) PDF(605)

Abstract:
This paper discusses the numbers of jump layers of boundary value problems in quasilinear differential equations. In addition, the paper gives several examples to explain why the original equation must be rediscussed when the determinate function in reference [1] is always equal to zero.