应用数学和力学

1993 Vol. 14, No. 9

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Numerical Solutions for Singularly Perturbed Semi-linear Parabolic Equation

Wu Qi-guang, Li Ji-chun

1993, 14(9): 753-761.

Abstract(2121) PDF(473)

Abstract:
In this paper, we discuss singularly perturbed semi-linear parabolic equations for one dimension and two dimension, we find numerical solutions by using both the line-method and the exact difference scheme on a special non-uniform discretization mesh. The uniform convergence in ε of the first order accuracy is obtained.

Section Theorems, Coincidence Theorems and Intersection Theorems on H-Spaces with Applications

Zhang Shi-sheng, Zhang Yin

1993, 14(9): 763-774.

Abstract(1993) PDF(554)

Abstract:
The purpose of this paper is to study the section theorems, coincidence theorems and intersection theorems on H-spaces. As a way of application, we use these results to study the existence problems of solutions for minimax inequalities and variational inequalities. The results presented in this paper improve and extend the corresponding results in [1, 3, 5, 6, 8, 9, 12, 14,15, 17].

The Analyses of the Three-Dimensional Stress Structurenear the Crack Tip of Mode I CT Specimens in Elastic-Plastic State Part 2:The Analyses of the Stress Structure

Yue Z. F., Zheng C. Q.

1993, 14(9): 775-785.

Abstract(2070) PDF(540)

Abstract:
Based on [1], the stress structures of the smooth region and shear lip of the specimens have been investigated in the paper.The characteristics of the stress structure in the smooth region have been found that the variable z can be separated out;the stresses in the midsection can be obtained by the plane strain FEM results or HRR structure modified by the stress triaxiality. The effects of load level and thickness on the stress structure can be reflected by the distribution of CTOD along the thickness direction. The obtained expressions of the stresses are very simple and visualized. The analyses of the stress structure in the shear lip show that the stresses can be obtained by different methods of interpolation to a certain precise degree.A new degree parameter of the plane strain state has been put forward and studied. The parameter can reflect relatively well the variation of the kind and thickness of the specimen as well as the load level. The fracture parameter has also been investigated to be sure that it can be obtained by modified CTOD with the stress triaxiality.

The Numerical Method for Analysing the Transient Temperature Field and Transient Phase Transformation of Metal Materials in Heat Treating

Yuan Fa-rong, Yang Shu-shen

1993, 14(9): 787-792.

Abstract(1850) PDF(735)

Abstract:
In this paper, the Kirchhoff's transformation is popularized to the nonlinear heat conduction problem which the heat conductivity can be expressd as a multinomial of temperature firstly, the boundary condition of heat conduction problem is determined by analytics.Secondly, the incubation peroid superposition and the linear combination law is employed to simulate the transient phasses transformation in the process of heat treatment of materials. That the begin time of phase transformation, the type of phase transformation and the amount of phase constitution is determined simply.Finally, the three-dimension Dual Reciprocity Boundary Element Method is used to analysis the total process of various heat treatment of component, the results of numerical calculation of examples show that the method provided in this paper is effectivce.

A Study on Flow Resistance in the Entrance Region of Isosceles Triangular Ducts

Zhu Shi-xing, Wang Zhi-qing

1993, 14(9): 793-807.

Abstract(2064) PDF(666)

Abstract:
In the present paper the variational solution of velocity profile for an incompressible laminar and fully developed flow in isosceles triangular ducts is derived by applying the Kantovorich method. The theoretical and experimental results of pressure loss are also given. The velocity distribution model, additional pressure loss coefficient and calculating method of inlet length in the entrance region of isosceles triangular ducts are also derived, which are suitable for various kinds of vertex angles. The calculations and experiments are also performed for two models:the isosceles triangular channels with vertex angles 2a=45.1°and 2a=60°. Comparisons are made between the theoretical analysis in this paper and those of the other authors. It can be seen that the present analytical result is of high, accuracy and wide practicability, and agrees well with the authors' experiment.

An Analysis of Hemodynamics of the Anterior Descending Branch of the Arteria Coronaria Sinistra

Huang Jing-quan, Li Jing-mei

1993, 14(9): 809-813.

Abstract(2479) PDF(630)

Abstract:
This paper analyses the anterior descending branch of the arteria coronaria sinistra from the view of hemodynamics.The results show that the branching of the anterior descending branch with an angle of 90° at the opening and the formation of the mural arteria coronaria are the hemodynamic characteristics.The shearing stress of the turbulent flow, the additional pressure, the formation of the blood vertex, and the impulsive pressure, caused by these characteristics, are hemodynamic reasons that leads to the occurence of atherosclerosis in anterior descending branch.

Summation of Fourier Series with Parameter by Laplace Transforms

Bu Xiao-ming

1993, 14(9): 815-822.

Abstract(2117) PDF(430)

Abstract:
In this paper, the theorems concerning the summation of Fourier series with parameter are given by using the Laplace transforms. By means of the known result of Laplace transforms, many new, important problems of summation of Fourier series with parameter in mechanics can be solved.

The Application of the Asymptotic Method to a Class of Strongly Nonlinear Systems

Xie Liu-hui

1993, 14(9): 823-828.

Abstract(2263) PDF(480)

Abstract:
In this paper, according to the form of the asymptotic solution of papers [1,2], the asymptotic method is extended to the following a class of more general strong nonlinear vibration systems where g and f are the nonlinear analytical-functions of x and , and ε>0 is a small parameter. We assume that the derivative system corresponding to ε=0 has periodic solution. The recurrence equations of the asymptotic solution for the system(0.1) are deduced in this paper, and they are applied to practical examples.

Generalized Dynamic Model for Multibodies Manipulator

Zhao Yu-shan, Gu Liang-xian

1993, 14(9): 829-833.

Abstract(2184) PDF(565)

Abstract:
In this paper the general dynamical equations were given for multibodies manipulator. The system is a topologic tree structure consisting of arbitrary number of rigid bodies. The hinges allow the rotational and/or tranlalional motion. In consideration of influence of friction the dynamic equations are established by means of Newton-Euler's method. Further, the equations are separated by way of constructing the distribution matrices and a group of force and motion equations are obtained.

Bifurcations of Periodic Solutions for Plane Mappings

Cao Jin-de, Li Qiong

1993, 14(9): 835-840.

Abstract(1853) PDF(553)

Abstract:
In this paper, using some techniques, we prove that there exists the regular homodinic point for Taylor mapping with 4<A≤1.5π and motion of bouncing ball with 4<r≤1.5π. This result implies that the corresponding systems have infinitely many distinct periodic points.

The Limiting Stokes Wave with Finite Water Depth

Ma Yu, Chen Yao-song

1993, 14(9): 841-844.

Abstract(1717) PDF(430)

Abstract:
In this paper we extend the method developed in[1] for limiting Stokes wave of infinite water depth to cover the case of finite depth. The method has high efficiency and the result is accurate.