应用数学和力学

1986 Vol. 7, No. 3

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Interior Layer Phenomena of Semilinear Systems

Lin Zong-chi, Lin Su-rong

1986, 7(3): 197-204.

Abstract(1519) PDF(548)

Abstract:
In this paper, we study the interior layer phenomena of singular perturbation boun-dary value problems for semilinear systems:
εy″=f(t,y,ε) (ay(a,ε)=A(ε), y(b,ε)=B(ε)
where ε>0 is a small parameter, y, f, A and B arc n-dimensional vector functions, This vector boundary value problem does not appear to have been studied, although the scalar boundary problem has been treated extensively, Under appropriate assumptions we obtain existence of solution as in the scalar problem and the estimate of this solution in terms of appropriate inequalities as well.

Subharmonic Solution of a Piecewise Linear Oscillator with Two Degrees of Freedom

Chen Yu-shu, Jin Zhi-sheng

1986, 7(3): 205-213.

Abstract(2043) PDF(582)

Abstract:
In the present paper subharmonic resonance solution of a piecewise linear loscillator with two degrees of freedom is studied, It is shown that in this system there eaist a series of subharmonic resonance solutions, among them there are 1/2, 1/3, 1/4,1/5,1/6, …subharmonic resonance solutions, The calculated results by the analogy computer and the field experiments in the factory partly verify this theory, Under certain circumstances, the generation of chaotic states of the oscillation is observed in analogy computer solutions.

The Method of Mixed Boundary Condition for a Kind of Linear and Nonlinear Composite Structure

Chen Shan-lin, Zhang Li-ying

1986, 7(3): 215-224.

Abstract(1851) PDF(455)

Abstract:
This paper deals with the aaisymmetrical deformation of shallow shells in large deflection, which are in conjunction with linear elastic structures at the boundary. A method of mired boundary condition for this problem is introduced, then the problem of a composite structure is transformed into a problem of a sinlgle structure and the integral equatiaus are given, The perturbation method is used to obtain the solutions and an eaemple of composite structure consisting of a shallow spherical and a cylindrical shell is presented.

Plastic Analysis of Thin Plates with Anisotropic Hardening

Jing Yong-jie

1986, 7(3): 225-234.

Abstract(1687) PDF(536)

Abstract:
In this paper we discuss the adoption of the anisotropic hardening model due to the existence of Bauschinger effect when thin plate is applied by repeated loading, The loading condition of thin plates for linear kine matic hardening has been deduced in terms of generalized forces and generalized plastic deformation, And it can be extended to non-linear results kinematic hardening and mixed hardening, hinally as an example the numerical are obtained for a circular place.

Nonlinear Oscillation of a Two-Dimensional Lift Body

Wang Mao-hua

1986, 7(3): 235-238.

Abstract(1412) PDF(389)

Abstract:
It is very difficult to obtain an enact analytical solution to a nonlinear ordinary differential equation,so till now analytical solutions are rare in this area, The author has obtained the exact analytical solutions of this type of nonlinear oscillations, In this paper as an example,the exact analytical solution of nonlinear oscillation of a two-dimensional lift body,which has attracted the attention of research workers for a long time, is given.

Contact Problem of Rubber Rings with Large Deformation

Lü He-xiang

1986, 7(3): 239-248.

Abstract(1553) PDF(754)

Abstract:
A combined problem with and linear elastic thin plate of the influence of frictional frictional contact between a rubber ring with large deformation is solved by means of the substructuring technique, A study coefficient and the influence of plate thickness is presented.

Uniformly Convergent Difference Method for the Convection-Diffusion Singular Perturbation Problem in a Curved Boundary Region

Sheng Qin

1986, 7(3): 249-258.

Abstract(1609) PDF(448)

Abstract:
In this paper we construct a difference scheme for the convection-diffusion.singular perturbation problem in a convex curved boundary region, and discuss the uniform convergence of its solution. We have proved that the, order of uniform convergence of its solution is O(h^β+τ^β/2)(0<β<1/2),where h,τ are the mesh steps in the space and time directions respectively.

On Problems of Optimal Design of Shallow Shell with Double Curvature on Elastic Foundation

Cheng Xiang-sheng

1986, 7(3): 259-263.

Abstract(1757) PDF(458)

Abstract:
The present paper discusses a method of optimal design of the shallow shell, with double curvature on the elastic foundation, Substantially we take the initial flexural function as the control function or design variable which will be found and the potential energy of the eternal loads as the criterion of quality of the optimal design of the shallow shell with double curvature, therefore the functional of the potential energy will be aim function, The optimal conditions and the isoperimetric conditions belong to the constrained conditions, thus we obtain the necessary conditions of the optimal design for the given problems, at the same time the conjugate function is introduced, then the problems are reduced to the solutions of two boundary value problems for the differential equation of conjugate function and tba initial fleeural function.

Random Region Function and Its Applications

He Chong

1986, 7(3): 265-271.

Abstract(1709) PDF(448)

Abstract:
This paper establishes some basic concepts of the random region and random region function, From these concepts and with the existence of a random stable point of a random region function of the random region, the necessary and sufficient conditions of the existence of a random stable centre of any random region are defined.

The Transformation Function Φ and the Condition Needed for KUR Space Having the Fixed Point

Gu An-hai

1986, 7(3): 273-277.

Abstract(1881) PDF(454)

Abstract:
In the last several years some progress has been made in the study of the properties of the extent of Banaeh space: In 1979, for example, when SuiIIivan discussed a related characterization of real L^P(x) space,he used uniform behavior of all two-dimensional subspace and defined this concept of a KUR space; In 1980 Huff used the concept of an NUC space when he discussed the property of generalizing uniform convexity which was defined in terms of sequence; And in 1984 Yu Xin-tai(俞鑫泰)stated certainly and proved that the RKU space is equal to the NUC space^[1]. However, the following quite interesting questions raised by Suillivan and Huff merit attention; Does every super-reflexive space have the fixed point propertyyand what conditions are needed for an L^P(x) space to be NUC space^[3]? respectively. The purpose of this paper is to study the characterization of transformation functionary and relationships between transformation function ^[4] and the two questions above.

Determination of Expression of Continuous Damage Parameter for Non-Ageing Materials Under Constant Tensije Load

Cheng Yuan-sheng

1986, 7(3): 279-284.

Abstract(1715) PDF(448)

Abstract:
Under constant uniazial tensile load continuous damage parameter for non-ageing brittle materials may be ezpressed as
w(P/A₀)=g(P/A₀)+f₁(P/A₀)f₂(t)
The determination of the expression for g(P/A₀)had been pointed out by[4].Hut how to determine the expressions for f₁(P/A₀)and f₂(t), the solution to this problem is not yet in sight.Now the solution to this problem is given by the present paper, This paper points out f₁(P/A₀) f₂(t)=φ(P/A₀)t and the method of the determination of the expression for φ(P/A₀).