应用数学和力学

1992 Vol. 13, No. 7

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Some Generalizations of Generalized Bi-Quasi-Variational Inequalities

Zhang Shi-sheng, Rao Ling

1992, 13(7): 573-581.

Abstract(1826) PDF(524)

Abstract:
The purpose of this paper is to introduce and study the existence problems of solutions for a class of new bi-quasi-variational inequalities. The results presented in this paper unify, sharpen and extend many recent results.

A Finite Element Parallel Algorithm of the Parametric Variational Principle for Elastic Contact Problems

Hu Ning, Zhang Ru-qing

1992, 13(7): 583-591.

Abstract(2282) PDF(636)

Abstract:
Basetl on the finite element solution of the parametric varialional principle of elastic contact problem, a corresponding parallel algorithm has been created by utilizing the specialities of parallel computer and the architecture of concurrent processing in this paper. In this algorithm. the parallelisms have heen realized in the processes of creation and assembly of stiffness matrix, of the static condensation, of the solution of stresses and in many other aspects. The programme of this algorithm has been realized on ELXSI-6400 parallel computer of Xi'an Jiaotong University. The results of computation show that the computational time can be saved efficiently and it is an effective parallel algorithm for the analyses of contact problems.

Rolling Bearing Fault Detection Using Correlation Technique

Xu Yin-ge, Yan Yu-ling

1992, 13(7): 593-598.

Abstract(2179) PDF(577)

Abstract:
It's known that auto-correlation technique is effective in extracting periodical signals from random noises. In the case of fault monitoring of rolling element bearing, we can't acquire the fault information directly from the original signal because of the difference of signal phases. And the signal is shown as the wide band random signal in auto-correlation function. In this paper, the signal is pre-processed and the results are proved effective. Moreover, by taking the auto-correlation function we can obtain the determined and comparable samples. This is very important for establishing the data base of running condition and for detecting the faults.

The Buckled States of Annular Sandwich Plates

He Lu-wu, Cheng Chang-jun

1992, 13(7): 599-604.

Abstract(2289) PDF(444)

Abstract:
In this paper, the axisymmetric buckled states of an annular sandwich plate (Reissner-type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled slates in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.

Numerical Simulation of 1-D Unsteady Two-Phase Flows with Shocks

Wu Qing-song, Wang Bo-yi

1992, 13(7): 605-611.

Abstract(2210) PDF(582)

Abstract:
In the present paper, random-choice method (RCM) and second-order GRP difference method, which are high resolution methods used for pure gas flows with shocks, are extended and employed to study the problem of one-dimensional unsteady two-phase flows. The two-phase shock wave and the flow field behind it in a dusty gas shock tube are calculated and the time-dependent change of the flow parameters for the gas and particle phase are obtained. The numerical results indicate that both the two methods can give the relaxation structure of the two-phase shocks with a sharp discontinuous front and that the GRP method has the advantages of less time-consuming and higher accuracy over the RCM method.

Existence of Positive Fixed Points for Semidifferentiable Semicompact 1-Set-Contractions

Song Jian-wei

1992, 13(7): 613-617.

Abstract(1770) PDF(519)

Abstract:
This paper obtains some fixed point theorems of semidifferentiable semicompact 1-set-contraction maps, which extend some known results in [1, 2, 4, 5, 7].

Application of an Improved Boundary Element Method on the Problem of Elastic Torsion

Du Sheng-guang

1992, 13(7): 619-624.

Abstract(1889) PDF(515)

Abstract:
An improved boundary clement method has been used in analyzing and calculating the problems of the torsion of a prismatic bar with elliptical cross-section. In this paper the calculated results correspond with the values of boundary element method. However, the quantity of data required by the improved boundary element method is much less than that required by boundary element method, and the calculating time will be greatly reduced. Therefore, the procedure of this paper is an economical and efficient numerical computational way for solving Poisson equation problem.

The Asymptotic Solution of the Unsteady Planar Parallel Gas Flow for the Case that the Adiabatic Index Number Y is Big

Yuan Yi-wu

1992, 13(7): 625-631.

Abstract(1691) PDF(452)

Abstract:
In ref [1], under the condition that the components of velocity are only the functions of time and polar angle θ, Drornikov solved eqss. (1.1) (1.3) of the ideal gas unsteady planar parallel potential flow. It was pointed out in ref. [1] that in general cases, the evident solutions could not he obtained. Only for two especial cases, the evident solutions were obtained.In this paper, the author studies the same prohlein as that in ref. [1]. In the first section we obtain the evident solution of equations (1.1)-(1.3) under the condition that the sonic velocity is restricted by some complemental conditions. In the second section, we obtain the first-order approximate solutions of the fundamental equation for the case that γ>>1

Boundary Integral Equations for the Bending Problem of Plates on Two-Parameter Foundation

Li Zheng-liang, Deng An-fu

1992, 13(7): 633-643.

Abstract(1876) PDF(663)

Abstract:
By means of Fourier integral transformation of generalized function, the fundamental solution for the bending problem of plates on two-parameter foundation is derived in this paper, and the fundamental solution is expanded into a uniformly convergent series. On the basis of the above work, two boundary integral equations which are suitable to arbitrary shapes and arbitrary boundary conditions are established by means of the Rayleigh-Green identity. The content of the paper provides the powerful theories for the application of BEM in this problem.

Optimization of the Take-Off Movement of Ski Jumping with the Method of Mathematical Programming

Guan Ru-hua, Li Run, Yu Li-ran

1992, 13(7): 645-650.

Abstract(2700) PDF(568)

Abstract:
This paper is based on the finite and dispersed data which were obtained from the experiments of the wind tunnel and of the force measurement and from the high-speed photography. It analyses and optimizes the take-off movement of ski jumping with the theory of dynamics of systems of rigid bodies and with the method of mathematical programming. The paper describes the optimal take-off movement of ski jumping. Furthermore, it presents an example and compares the result with those of other papers published at home and abroad. The comparison shows that our computation and optimization are reasonable and well-grounded.

Nonlinear Strain Components of General Shells with Initial Geometric Imperfections

Li Li-juan, Mei Zhan-xin, Wan Hong, Liu Feng

1992, 13(7): 651-657.

Abstract(2039) PDF(598)

Abstract:
On the basis of nonlinear strain component formulations of three-dimensional continuum, this paper has derived the nonlinear strain component formulations of shells with initial geometric imperfections. The derivation is not confined to a special shell, therefore they possess general properties. These formulations provide the theoretical basis of the strain analysis for geometric nonlinear problems of shells with initial geometric imperfections.