应用数学和力学

1998 Vol. 19, No. 4

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On the Initial Value Problems of First Order Impulsive Differential Systems

Zhang Shisheng, Wang Fan

1998, 19(4): 279-284.

Abstract(2029) PDF(676)

Abstract:
The purpose of this poper is to study the existence and iterative approximation of minimax quasi-solutions for a class of initial value problems of first order impulsive differential systems by using monotone iterative methods.

The Solution for the Generalized Riccati Algebraic Equations of Linear Equality Constraint System

Deng Zichen, Zhong Wanxie

1998, 19(4): 285-289.

Abstract(2245) PDF(862)

Abstract:
Based on the dynamic equation,the performance functional and the system constraint equation of time-invariant discrete LQ control problem,the generalized Riccati equations of linear equality constraint system are obtained according to the minimum principle,then a deep discussion about the above equations is given,and finally numerical example is shown in this paper.

Horizontal Well Pressure Analysis in Box-Bounded Reservoirs

Wang Xiaodong, Liu Ciqun

1998, 19(4): 291-296.

Abstract(2045) PDF(703)

Abstract:
In this paper,solutions to the 3D transient flow mathematical model for horizontal wells in box-rounded reservoirs are presented.The solutions are derived in Laplace transform domain by employing integral transform and point-source superposition.Both efficient computation of pressure responses and practical technology of oil field application mentioned here may be used to interpret the data from unsteady-state horizontal well testing.

The Theory of Fractal Interpolated Surface and Its Applications

Xie Heping, Sun Hongquan

1998, 19(4): 297-306.

Abstract(2283) PDF(1153)

Abstract:
In this paper the principle of construction of a fractal surface is introduced,interpolation functions for a fractal interpolated surface are discussed,the theorem of the uniqueness of an iterated function system of fractal interpolated surface is proved,the theorem of fractal dimension of fractalinterpolated surface is derived,and the case that practical data are used to interpolate fractal surface is studied.

A Note on a Theorem of Tas, Telci and Fisher

A. Banerjee, B. Singh Thakur

1998, 19(4): 307-309.

Abstract(2537) PDF(606)

Abstract:
In this paper,it has been shown that the condition of continuity in the fixed point theorem of Tas,Telci and Fishe^[2] is not necessary.Also the completeness of (X,d)can be replaced by the completeness of T(X).

Complex Fundamental Solutions for Semi-Infinite Plane and Infinite Plane with Hole under Various Boundary Conditions

Tang Shougao, Cao Zhiyuan

1998, 19(4): 311-319.

Abstract(2087) PDF(645)

Abstract:
A general method of finding the complex fundamental solutions for semi-infinite plane and infinite plane with hole under various boundary conditions has be established by using Riemann-Schwarz symmetric principle and superposition principle fo the solutions of elasticity.More than ten solutions have been derived respectively.

A Group Representation of Canonical Transformation

Hou Bihui, Yang Hongbo

1998, 19(4): 321-326.

Abstract(2378) PDF(772)

Abstract:
The mutual relationships between four generating functions F₁(q,Q),F₂(q,P),F₃(p,P),F₄(p,Q) and four kinds of canonical variables q,p,Q,P concerned in Hamiltion's canonical transformations,can be got with linear transformations from seven basic formulae.All of them are Legendre's transformation which are implemented by 32 matrices of 8×8 which are homomorphic to D₄ point group of 8 elements with correspondence of 4:1.Transformations and relationships of four state functions G(P,T),H(P,S),U(V,S),F(V,T) and four variables P,V,T,S in thermodynamics,are just the same Lagendre's transformations with the relationships of canonical transformations.The state functions of thermodynamics are summarily founded on experimental results of macroscrope measurements,and Hamilton's canonical transformations are theoretical generalization of classical mechanics,Both group represents are the same,and it is to say,their mathematical frames are the same.This generality indicates the thermodynamical transformation is an example of one-dimensional Hamilton's canonical transformation.

Boundary Integral Equations for Bending Problem of Reissner’s Plates on Two-Parameter Foundation

Li Zhengliang, Zhou Yongming, Deng Anfu

1998, 19(4): 327-334.

Abstract(2340) PDF(615)

Abstract:
Two fundamental solutions for bending problem of Reissner's plates on twoparameter foundation are derived by means of Fouier integral transformation of generalized function in this paper.On the basis of virtual work principles,three boundary integral equations which fit for arbitrary shapes,loads and boundary conditions of thick plates are presented according to Hu Haichang's theory about Reissner's plates.It provides the fundamental theories for the application of BEM.A numerical example is given for clamped,simply supported and free boundary conditions.The results obtained are satisfactory as compared with the analytical methods.

Elasto-Plastic Coupled Analysis of Buried Structure and Soil Medium by Perturbational Semi-Analytic Method

Lü Anjun, Cao Zhiyuan

1998, 19(4): 335-339.

Abstract(2122) PDF(503)

Abstract:
In this paper,an effective numerical method for physically nonlinear interation analysis is studied,in which the elasto-plastic problem of coupled analysis between the structure and medium may be transformed into several linear problems by means of the perturbation technique,then the finite strip method and finite layer method are used to analyse the underground structure and rock respectively,for their corresponding linear problems,so the purpose of simplifing the calculation can be achieved.This kind of method has made use of the twice semi-analytical technique.the perturbation and semi-analytic solution function to simplify 3-D nonlinear coupled problem into 1-D linear numerical one.In addition,this method is a new advance of semi-analytical method in the application to nonlinear problems by means of combinating with the analytical perturbation method,and it is also a branch of the perturbational numerical,nethod developed in last years.

Dynamic Analysis to Infinite Beam under a Moving Line Load with Uniform Velocity

Sun Lu, Deng Xuejun

1998, 19(4): 341-347.

Abstract(2436) PDF(754)

Abstract:
Based on the principle of linear superposition,this paper proves generalized Duhamel's integral which reverses moving dynamical load problem to fixed dynamical load problem.Laplace transform and Fourier transform are used to solve patial differential equation of infinite beam.The generalized Duhamel's integral and deflection impulse response function of the beam make it easy for us to obtain final solution of moving line load problem.Deep analyses indicate that the extreme value of dynamic response always lies in the center of the line load and travels with moving load at the same speed.Additionally,the authors also present definition of moving dynamic coefficient which reflects moving effect.

Minimax Theorem and Saddle Point Theorem without Linear Structure

Zheng Xiyin, Wen Zhonglin

1998, 19(4): 349-354.

Abstract(2509) PDF(740)

Abstract:
In the paper,a new kind of concavity of a function defined on a set without linear structure is introduced and a generalzation of Fan Ky ineqality is given.Minimax theorem in a general topological space is obtained.Moreover,a saddle point theorem on a topological space without any linear structure is established.

The Analytical Solution with Respect to Characteristics of Elements’ Cross Section as Variables of the Plane Frame

Sui Yunkang, Wang Wenjun

1998, 19(4): 355-364.

Abstract(2123) PDF(598)

Abstract:
Taking the sectional area and the bending moment of inertia as variables for each beam element,the plane frame will possess a stiffness matrix containing parameters.In terms of the symbolic computation software,the inverse matrix is solved to obtain the new analytical solution with respectic characteristics of elements cross-section.The general program is coded in the microcomputer and corresponding exmpales are computed.

Ultimate Strength of Postbuckling for Simply Supported Rectangular Composite Thin Plates under Compression

Zhou Zhulin

1998, 19(4): 365-371.

Abstract(2323) PDF(1371)

Abstract:
It is proved that the ultimate strength of postbuckling for simply supported rectangular composite thin plates under compression is far higher than their buckling stress through the tests of 283 rectangular composite thin laminates in this paper.The ultimate strength of the composite thin plates is studied using large-deflection theory and small-deflection theory of thin plates.According to the failure criterion of the composites ultimate strength is found finally.It is in accordance with the experimental values,for the plates having 45 degrees off-axial,and for longitudinal and latitudinal plates.when β<0.11,the theoretical values are higher.The coefficient C given in this paper may be referred to in product designing.