应用数学和力学

1993 Vol. 14, No. 4

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A New Derivation of the Vectorial Equation of Motion for a Test Particle in the Schwarzchild Field

Alfred Yu(Yu Xin), J. Hong, Y. Y. Lam, W. T. Lee

1993, 14(4): 287-288.

Abstract(2578) PDF(569)

Abstract:
A new derivation of the vectorial equation of motion for a test particle in the Schwarzchild field is given which greatly simplifies the procedure given by C. A. Murray^[1].

Stress Intensity Factors of the Eccentric and Edge Cracked Cylinders

Chen Wei-jiang, Wang Kai, Tang Ren-ji

1993, 14(4): 289-294.

Abstract(2224) PDF(552)

Abstract:
Using the single crack solution and the regular solution of harmonic funetion the torsion problem of a cracked cylinder is reduced to solving a set of mixed-type integral equations which can be solved by combining the numerical method of singular integral equation with the boundary element method. Several numerical examples are calculated and the stress intensity factors are obtained.

Creep Buckling of Cross-Ply Symmetric Laminated Cylindrical Panels

Wang Ying-jian, Wang Zhen-ming

1993, 14(4): 295-300.

Abstract(2484) PDF(794)

Abstract:
A creep buckling analysis of cross-ply symmetric laminated cylindrical panels is given in this paper. By means of theoretical analysis, a method to determine the critical load of creep buckling of the panels with simply supported boundary conditons is obtained.

Boundary Layer Development of Pulsatile Blood Flow in a Tapered Vessel

Cen Ren-jing, Qin Chan

1993, 14(4): 301-308.

Abstract(2552) PDF(613)

Abstract:
Assuming that the tapered angle is small, the problems of developing flow under unsteady oscillatory condition are studied in this paper. The formula of velocity distribution is obtained.The analyses for the results show that the blood flow in a converging tapered vessel remains a developing flow throughout the length, and the effects of tapered angle on the developing flow are increased with the increment of the tapered angle.

Formulation and Solution for Inverse Problem of Nonholonomic Dynamics

Liu Feng-li, Mei Feng-xiang

1993, 14(4): 309-314.

Abstract(2601) PDF(603)

Abstract:
This paper presents a formulation and solution for the inverse problem of nonholonomic dynamics:to find the form of nonholonomic constraints when some integrals are given and to find the generalized reactive forces of constraint acting on the system when the expression of the kinetic energy is given. An example is given to illustrate the application of the result.

Generalized Variational Inequalities and Generalized Quasi-Variational Inequalities

Zhang Cong-jun

1993, 14(4): 315-325.

Abstract(2444) PDF(534)

Abstract:
Under much weaker hypotheses and in a more general setting some existence theorems of solutions to generalized variational inequalities, generalized quasi-varia-tional inequalities and minimax inequalities are established. The results presented in this paper generalize the corresponding results of[3-13]to the noncompact case, thus improving these results.

The Precise and New Analysis for a Mode Ⅲ Growing Crack in an Elastic-Perfectly Plastic Solid

Yi Zhi-jian

1993, 14(4): 327-333.

Abstract(2645) PDF(589)

Abstract:
The near crack line field analysis method has been used to investigate into Mode III quasistatically propagating crack in an elastic-perfectly plastic material. The significance of this paper is that the usual small scale yielding theory has been broken through. By obtaining the general solutions of the stresses and the displacement rate of the near crack line plastic region, and by matching the general solutions with the precise elastic fields(not the usual elastic K-dominant fields)at the elastic-plastic boundary, the precise and new solutions of the stress and deformation fields, the size of the plastic region and the unit normal vector of the elastic-plastic boundary have been obtained near the crack line. The solutions of this paper are sufficiently precise near the crack line region because the roughly qualitative assumptions of the small scale yielding theory have not been used and no other roughly qualitative assumptions have been taken, either. The analysis of this paper shows that the assumingly "steady-state case" for stable crack growth, which has been discussed attentively in previous works, do not exist, and the plastic strains near the crack line do not have singularities, Two most important cases for stable crack growth have been discussed.

Investigation of the Turbulent Model for Pressure Fluctuations with Spectral Theory

Jin Sheng, Ni Han-gen

1993, 14(4): 335-342.

Abstract(2553) PDF(1022)

Abstract:
The pressure fluctuations in turbulent shear flows are investigated with the theory of spectral analysis. An expression for pressure spectra is analytically derived in terms of velocity spectra. This derivation is based on a formal solution of the Navier-Stokes equation and quasi-normal assumption to express the third and fourth order velocity correlations in terms of double velocity correlation. Then, a turbulent model for the computation of pressure fluctuation intensity with Renolds stress and mean flow velocity gradients is established. The turbulent constants in the model are calculated from the assumptions about the general behaviour of velocity spectra in high Renolds number flows. Comparison with direct simulation of turbulent boundary layer is made. It is found that the turbulent-turbulent, cross correlation, and turbulent-shear source terms for mean square value of pressure fluctuation are about the same magnitude.

Principle of Equal Effects of General Relativity and Invariance of Classical Mechanics Equations

Liang Tian-lin, Zhou Ling-yun

1993, 14(4): 343-347.

Abstract(2855) PDF(706)

Abstract:
This paper gives the proof that the "inertial forces" in a noninertial system are not fabricated forces, but potential forces which actually act on the objects in motion in the acceleration field, according to the equivalent principle between gravitation and inertial forces in the theory general relativity. Further, the invariance of kinetical equation is illuminated.

Pansystems Logic Conservation of Bifurcation, Catastrophe, Chaos and Stability

Wu Chen

1993, 14(4): 349-352.

Abstract(2164) PDF(544)

Abstract:
It is in references [4, 5] that the combination of the relative researches of pansystems methodology and the researches of bifurcation, catastrophe, chaos and stability in nonlinear mechanics was put forward and the concepts were redefined from the point of view of pansystems methodology. The present paper studies the logic conservation law of these nonlinear mechanics phenomena under the framework of pansystems methodology.

Improved Preconditoned Conjugate Gradient Method and Its Application in F. E. A. for Engineering

Zheng Hong, Ge Xiu-run

1993, 14(4): 353-361.

Abstract(2188) PDF(659)

Abstract:
In this paper two theorems with theoretical and practical significance are given in respect to the preconditioned conjugate gradient method(PCCG). The theorems discuss respectively the qualitative property of the iterative solution and the construction principle of the iterative matrix. The authors put forward a new incompletely LU factorizing technique for non-M-matrix and the method of constructing the iterative matrix. This improved PCCG is used to calculate the ill-conditioned problems and large-scale three-dimensional finite element problems, and simultaneously contrasted with other methods. The abnormal phenomenon is analyzed when PCCG is used to solve the system of ill-conditioned equations, It is shown that the method proposed in this paper is quite effective in solving the system of large-scale finite element equations and the system of ill-conditioned equations.

Asymptotic Solution of Brusselator Limit Cycle in Biochemistry

Yang Hong-chun, Xu Zhen-yuan

1993, 14(4): 363-366.

Abstract(2717) PDF(569)

Abstract:
In this paper, two kinds of asymptotic analytic expression of the Brussdator limit cycle are given by means of two simple methods. To some extent, they are better than the analytic expression in [2].

A General Mathematical Framework of Complex Systems(Ⅰ)

Zan Ting-quan

1993, 14(4): 367-375.

Abstract(2385) PDF(813)

Abstract:
The fundamental and simplest structure of a complex system is a network. According to this idea, we plan to develop a general methematical framework of complex systems. In this paper, we discuss in detail the concept of systems, a general description of systems:System=(Hardware, Software, Environment), and whole-part relations, including relations between elements and systems, subsystems and systems, and between systems. The rules of operations of systems are given, and the induced transformations between hardware and software of systems are briefly discussed.