应用数学和力学

1994 Vol. 15, No. 1

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3-D Numerical Study on the Bending of Symmetric Composite Laminates

Qian Wei-zhang, Huang Qian, Feng Wei

1994, 15(1): 1-6.

Abstract(1859) PDF(531)

Abstract:
In this paper,the composite laminates subjected to pure bendinq are modelled by using 3-D anisotropic finite elements and the distributions of stress and strain alongthe thickness are presented.The numerical results show that there is a stress concentration near the bonding interface in the central region(far from traction boundaries and free edges)of symmetric angle-ply laminates,which should be called "interlaminar effect". The abrupt change of the mechanical behavior of material onthe interfaces causes interlaminar stresses.The laminates are in 3-D stress state nearthe interfaces. The strain distribution of the 3-D numerical model is different from thestrain hypothesis of the classical laminate theory based on the Kirchhoff-Love hypotheses of straight inextensional normals.

Asymptotic Analysis if a Class of Nonlinear Oscillation Equation in Electrical Engineering

Cheng You-liang, Dai Shi-qiang

1994, 15(1): 7-12.

Abstract(2333) PDF(450)

Abstract:
In the present paper,we investigate a class of nonlinear oscillation equations inelectrical engineering by using the modified Krylov-Bogolyubov method presentedin[1]. We obtain quantitatively ihe parameier range for the existence of a limit cycleand the amplitude of the limit cycle,and find that the limit cycle is unstable. All the results agree entirely with the known results given by qualitative analysis,and hence confirm the effectiveness of the above-mentioned asymptotic method

A New Equilibrium Existence Theorem of Generalized Game

Ding Xie-ping

1994, 15(1): 13-17.

Abstract(1955) PDF(447)

Abstract:
In the present paper,we prove a new equilibrium existence theorem for generalized games with uncountable number of agents,noncompact choice sets and general preference correspondences which do neither have open graph nor have open lower sections. This theorem improves a recent result of kim.

A Formula Solution to the Integral of Rational Functions

Gni Zu-hua

1994, 15(1): 19-27.

Abstract(3118) PDF(1252)

Abstract:
A usual method is the method of waiting coefficient to solve integral of a rational function. We shall propose a non-waiting coefficient formula of solution about this kind of integral in this article and perfectly solve this kind of integral problem. Inpractical application this new method is simple,direct and effective. Its advantage isnot only to give a simple solution for several problems which are very difficult or aren't solved by usual method,but also to solve more complex problems by computer.

Motion Equations of Multilayered Elastic Electroconductive Plates in a Magnetic Field

Gou Xing-hua, Zhang Fa-xiang

1994, 15(1): 29-36.

Abstract(1893) PDF(543)

Abstract:
The motion equations of multilayered elaslic electroconductive: plates in amagnetic field are obtained The well known Ambartsumian's equations of plates are the special ones of this paper. The equations of transverse vibration of multilayered plate are also discussed here.

The Variational Principles of Coupled Systems in Photoelasticity

Fu Bao-lian

1994, 15(1): 37-47.

Abstract(2135) PDF(685)

Abstract:
This paper presents an energy principle,zero different principle of coupled systems in photoelasticity,from which potential energy,complementary energy,generalized potential energy and generalized complementary energy variational principles of the coupled systems in photoelasticity are derived. What is called the coupled systems means that two deformational bodies,forwhich figures,sizes,loads and boundary conditions are the same and they are all inactual states but they are made of different materials.Prototype body and model body in photoelasticity are essentially the coupled systems,therefore the above principles become the theoretical basis of defining the influnce of Poissons ratio v on accuracy of the frozen-stress method.

The Existence of Periodic Solutions for a Class of Functional Differential Equations and Their Application

Zhao Jie-min, Huang Ke-lei, Lu Qishao

1994, 15(1): 49-58.

Abstract(2045) PDF(621)

Abstract:
In this paper,the retarded functional differential equation are considered, We obtain four existence theorems of periodc solutions of it, The application of these theorems are convenient and efficient and the theorem of this paper is better than the well-known Yoshizawa's periodic solution theorem.A feedback system is discussed in detail and a sufficient condition of guaranteeing the existence of an ω-Periodic motion of the system is got by applying these theorems in this paper.

A Study of J-lntegral of the Orthotropic Composite Material

Wang Ai-qin, Feng Bao-lian, Yang Wei-yang

1994, 15(1): 59-67.

Abstract(1739) PDF(586)

Abstract:
The relation between J-integral near model I crack tip in the orthotropic plate and displacement derivative is derived in this paper. Meanwhile,the relation between stress intensity factor K₁ and displacement is also given in this paper.With sticking film moire interferometry method,the three-point bending beam is tested,thus the values of J-integral and K₁ can be obtained.from the displacement field,and then the truth of relation formula between J-integral and K₁ in the orthotrtopic composite materials is experimentally verified.

Mikusiński’s Operators Solution of Three-Order Linear Difference Equation with Variable Coefficients

zhou Zhi-hu

1994, 15(1): 69-76.

Abstract(1758) PDF(558)

Abstract:
This paper proceeds the papers [3] [4],we make use of the idea of the variable ,number operators and some concepts and conclusions of the shifting operators series with variable coefficients in the operational field of Mikusinski,it is devoted to the solution of the general three-order linear difference equation with variable,coefficients,and it is also devoted to the better solution .formula for the some special three-order linear difference equations with variable coefficients,in addition,we try to provide the idea and method for realizing solution of the more than three-order linear difference equation with variable coefficients.

A Complete Expression of the Axymptotic Solution of Differential Equation with a N-th Order Turnlng Point

Zhang Ju-ling

1994, 15(1): 77-86.

Abstract(2156) PDF(498)

Abstract:
A second order linear ordinary differential equation has been studied,and the complete expression.of the formal uniformly valid asymptotic solutions to the equation near turning point is obtained by using extended airy function.

The lntegral as a Function of the Upper Limit and Depending on a Parameter to Solve Drawing Through ldling Rolls

Zhao De-wen, Li Long-Xu, Fang You-kang

1994, 15(1): 87-94.

Abstract(2114) PDF(564)

Abstract:
The relocity and sirain-rate .field which are different from Avilzur's have been established in Caitesian coordinates. Using the integral as a function of the upper limitand integration depending on a parameler,an analylical upper-bound solution todrawing stress through idling rolls has been obtained in this paper.