应用数学和力学

Covering Properties of H Spaces and Applications

Ding Xie-ping, Tan Kok-keong

1993, 14(12): 1025-1033.

Abstract(2117) PDF(481)

Abstract:
Several theorems on closed(resp. open) covering properties of H-spaces are obtained which improve and generalize the corresponding results of Sperner, Klee, Alexandroff-Pasynkoff, Berge, Ghouila-Houri, Danzer-Grunbaum-Klee, Ky Fan, Shih-Tan, Horvath and Lassonde. As application an almost fixed point theorem for lower semi-continuous map in l.c.-spaces and a generalization of Tychonoffs fixed point theorem are proved in l.c.-spaces which improve those results of Ky Fan and Horvath.

Existence of Solutions for a Singularly Perturbed Boundary Value Problem for the Third Order Semi Linear Differential Equation with a Turning Point

Cai Jian-ping, Lin Zong-chi

1993, 14(12): 1035-1039.

Abstract(1683) PDF(594)

Abstract:
In this paper, by using the techniques of differential inequalities, we prove the existence of the solutions of a singularly perturbed boundary value problem for the third order semilinear differential equation with a turning point.

On Robust Stability of a Class of Polynomial Families

Wang Yong, Yu Nian-cai

1993, 14(12): 1041-1048.

Abstract(1638) PDF(479)

Abstract:
In this paper, we discuss the robust stability of a class of polynomial families more general than the interval polynomial family and diamond polynomial family. We prove that the Hurwitz stability of some special cases of this class of polynomial families can be determined by checking finite polynomials. We also give an example to illustrate that it is not always possible to determine the Hurwitz stability of all this class of polynomial families by checking finite polynomials.

Fundamental Equations of Large Spatial Deflection Problems of Rods and Its Application to Drilling Engineering

Cai Zong-xi

1993, 14(12): 1049-1056.

Abstract(1669) PDF(452)

Abstract:
The fundamental equations for analysis of a straight slender rod which deform at large deflections of order of several times of the dimension of the cross section of the rod are derived by using convecled coordinate system. In accordance with the practice of oil drilling, an effective method of three dimensional static analysis of bottom-hole assemblies is simply described. Errors in reference [8] are pointed out.

On Some Important Problems in Analytical Dynamics of Non-Holonomic Systems

Liang Li-fu, Shi Zhi-fei

1993, 14(12): 1057-1067.

Abstract(2021) PDF(643)

Abstract:
By using deductive method, Chetaev condition is derived in this paper. We point out that the processes of variation and differentiation are not permutable in non-holonomic dynamics is a misunderstanding. The paper gives two classical relations of non-holonomic systems and points out integral variational principles can be applied in non-holonomic systems.

Rated Generalized Sub-Region Variational Principles in Nonlinear Elastodynamics

Zhao Guo-qiao

1993, 14(12): 1069-1075.

Abstract(1623) PDF(456)

Abstract:
In this paper, the rated generalized sub-region mixed and hybrid variational principles in nonlinear elastodynamics are constructed on the basis of Co-Moving coordinate description and S-R decomposition theorem, which contain five independent arguments, or velocity gradient, momentum, velocity, stress and strain rate.

New Model of Gas Flow Problem in Multi-Layered Gas Reservoir and Application

Li Xiao-ping

1993, 14(12): 1077-1083.

Abstract(1845) PDF(443)

Abstract:
In this paper, the new model of the real gas filtration problem has been presented multi-layered gas reservoir, when a gas well output and wellbore storage may be variable, and have obtained the exact solutions of pressure distribution for each reservoir bed under three kinds of typical out-boundary conditions. As a special case, according to the new model have also obtained the qxact solutions of presssure distribution in homogeneous reservoir and is given important application in gas reservoir development.

On the Mathematical Problems of Composite Materials with a Doubly Periodic Set of Cracks

Li Xing

1993, 14(12): 1085-1092.

Abstract(1928) PDF(443)

Abstract:
In this paper, the mathematical problem of the second fundamental problem of composite materials with a doubly periodic set of arbitrary shape cracks are investigated, and the interface are arbitrary smooth closed contours. At first, we establish mathematical models by using Muskhelisvili complex variable methods, change the primitive problems into searching complex stress functions which satisfy four boundary value problems and construct forms of the solution, then, under some general restrictions it is reduced to normal type singular integral equation, the unique solvability is proved mathematically.

Instability Theory of Shock Wave in a Channel

Xu Fu, Chen Le-shan

1993, 14(12): 1093-1104.

Abstract(2416) PDF(523)

Abstract:
The instability theory of shock wave was extended from the case with an infinite to the case of a channel with a rectangular cross section. First, the mathematical formulation of the problem was given which included a system of disturbed equations and three kinds of boundary conditions. Then, the general solutions of the equations upstream and downstream were given and each contained five constants to be determined. Thirdly, under one boundary condition and one assumption, it was proved that all of the disturbances in front of the shock front and one of the two acoustic disturbances behind the shock front should be zero. The boundary condition was that all of the disturbed physical quantities should approach to zero at infinity. The assumption was that only the unstable shock wave was concerned here. So it was reasonable to assume, ω=iY. Ywas the instability growth rate and was a positive real number. Another kind of boundary conditions was that the normal disturbed velocities should be zero at the solid wall of the channel, and it led to the result that the wave number of disturbances could only be a set of discrete values. Finally, a total of five conservation equations across the disturbed shock front was the third kind of boundary conditions which was used to determine the remained four undetermined constants downstream and an undetermined constant representing the amplitude of disturbed shock front. Then a dispersion relation was derived. The results show that a positive real γ does exist, so the assumption made above is self-consistent, and there are two modes, instead of one, for unstable shock. One mode corresponds to γ=-W·k(W<0) It is a newly discovered mode and represents an absolute instability of shock. The instability criterion derived from another mode is nearly the same as the one obtained in [2, 3], in addition, its growth rate is newly derived in this paper, and on this basis, it is further pointed out that at j²(∂v/∂p)_H=1+2M the shock wave is most unstable, i.e. its nondimensional growth rate Γ=∞ If ω is assumed to be a complex number with Im(ω≥0) instead of being assumed a pure imaginary number at the beginning, it can be proved in Section V that there are still two modes for the instability criteria, besides, the roots ω of the dispersion equation are still imaginary.

The Variational Inequality Formulation for the Deformation Theory in Plasticity and Its Non-Iterative Solution

Guo Xiao-ming, She Ying-he

1993, 14(12): 1105-1113.

Abstract(1992) PDF(529)

Abstract:
In this paper, the deformation theory in plasticity is formulated in the variational inequality, which can relax the constraint conditions of the constitutive equations. The new form makes the calculation more convenient than general energy forms and have reliable mathematical basis. Thus the plasticity theory may be solved by means of the quadratic programming instead of the iterative methods. And the solutions can be made in one step without any diversion of the load.

A Modification of Taylor-Galerkin Finite Element Method and its Application

Zhu Gang, Gu Chuan-gan, Hu Qing-kang

1993, 14(12): 1115-1120.

Abstract(2061) PDF(737)

Abstract:
Two basic hypothesises of Taylor-Galerkin Finite Element Method are studied in this paper. One of them which is unreasonable is redefined. The only hypothesis becomes the standpoint of Generalized Finite Element. We use this idea to analysis stream function-vorticity equations with Modified Taylor-Galerkin Finite Element Method, and give the two-step solving method, which makes the solving process more reasonable than ever before. Several computational examples reveal that the results of this new method are satisfied.

1993 Vol. 14, No. 12