应用数学和力学

1998 Vol. 19, No. 11

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The Fundamental Solutions for the Plane Problem in Piezoelectric Media with an Elliptic Hole or a Crack

Gao Cunfa, Fan Weixun

1998, 19(11): 865-973.

Abstract(2499) PDF(562)

Abstract:
Based on the complex potential method, the Green's functions of the plane problem in transversely isotropic piezoelectric media with an elliptic hole are obtained in terms of exact electric boundary conditions at therim of the hole. When the elliptic hole degenerates into a crack, the fundamental solutions for the field intensity factors are given. The general solutions for concentrated and distributed loads applied on the surface of the hole or crack are produced through the superposition of the fundamental solustions. With the aid of these soltuions, some erroneous results provided previously in other works are pointed out. More important is that these solutions can be used as the fundamental solutions of boundary method to solve more practical problems in piezoelectric media.

A,φ-Ω Method for 3-D Eddy Current Field Analysis

Shi Zhanwei, Zhao Xinghua

1998, 19(11): 941-946.

Abstract(2136) PDF(885)

Abstract:
After the field equations and the continuous conditions beteen the interfaces for 3-D eddy current problems under various gauges were discussed, it was pointed out in this paper that using the vector magnetic potential A, electric scalar potential φ and Coulomb gauge A=0 in eddy current regions and using magnetic scalar potential Ω in the nonconducting regions are more suitable. All field equations, the boundary conditions, the continuous conditions between the interfaces and the corresponding variational principle corresponding with this method are also given.

Mass Transport in Solid Tumors(Ⅰ)—luid Dynamics

Lei Xiaoxiao, Wu Wangyi, Wen Gongbi, Chen Jianguo

1998, 19(11): 947-953.

Abstract(2102) PDF(482)

Abstract:
A three-porous-medium model for transvascular exchange and extravascular transport of fluid and macromolecules in a spherical solid tumor is developed. The microvasculature, lymphatics, and tissue space are each treated as a porous medium with the flow of blood, lymph, and interstitial fluid obeying Darcy's law and Starling's assumption. In this part, the role of int erstitial pressure and fluid convection are st udied. The analytical solutions are obtained for the isolated tumor and the normal-tissue-surrounded tumor respectively. The calculated interstitial pressure profile are consistent with the experimental observation that the elevated interstitial pressure is a major barrier in the penetration of macromolecular drug into tumors. The factors which may reduce the interstitial pressure are analyzed in details.

The Influence of the Different Distributed Phase-Randomized on the Experimental Data Obtained in Dynamic Analysis

Ma Junhai, Chen Yushu, Liu Zengrong

1998, 19(11): 954-864.

Abstract(2095) PDF(582)

Abstract:
In this paper the influence of the differently distributed phase-randomozed to the data obtained in dynamic analysis for critical value is studied. The calculation results validate that the sifficient phase-randomized of the different distributed random numbers are less influential on the critical value. This offers the theoretical foundation of the feasibility and practicality of the phase-randomized method.

Wavelet Basis Analysis in Perturbed Periodic KdV Equation

Lu Dianchen, Tian Lixin, Liu Zengrong

1998, 19(11): 974-979.

Abstract(2301) PDF(685)

Abstract:
In the paper by using the spline wavelet basis to construct the approximate inertial manifold, we study the longtime behavior of pert urbed perodic KdV equation.

Numerical Study of a Nonlinear Integro-Differential Equation

Zhu Yong

1998, 19(11): 980-985.

Abstract(1930) PDF(463)

Abstract:
In this paper, by using the pseudo-spectral method of Fornberg and Whitham, a nonlinear integro-differential equations is investigated numerically. It is found that for small, the result is close to that of the KdV equation, but the effects of lager and the initial condition are significant.

Research on Solid-Liquid Coupling Dynamics of Pipe Conveying Fluid

Wang Shizhong, Liu Yulan, Huang Wenhu

1998, 19(11): 986-993.

Abstract(2112) PDF(863)

Abstract:
On the basis of Hamilton princlple, the equation of solid-liquid coupling vibration of pipe conveying fluid is deduced. An asymmetrical solid-liquid coupling damp matrix and a symmetrical solid-liquid coupling stiffness matrix are obtained. Using QR method, pipe's nature frequencies are calaculated. The curves of the first four orders of natural frequency-flow velocity of pipe waw given. The influence of flowing velocity, pressure, solid-liquid coupling damp and solid-liquid coupling stiffness on natural frequency are discussed respectively. The dynamic respondence of the pipes for step-load with different flow velocity are calculated by Newmark method. It is found that, with the flow velocity increased, the nature frequency of the pipes reduced, increased, reduced again and so on.

Dynamic Response Analysis of Platform-Cylinder Group Foundation due to Impact by Water Wave Flow

Fang Yingguang, Du Hongbiao

1998, 19(11): 995-1003.

Abstract(2216) PDF(709)

Abstract:
This paper deals with the problem of dynamic response of platform-cylinder group foundation. Dynamic interaction of cylinder group foundation-water-soil is taken into account and the analysis of dynamic response to excitation of water wave force is given by analytic method. The numerical examples are presented and the influence of system's parameters on the dynamic behaviour is discussed.

Fuzzy Approaching Set and Fuzzy Approaching Functional Mapping

Cao Chun

1998, 19(11): 1004-1013.

Abstract(1957) PDF(777)

Abstract:
By establishing the concepts of fuzzy approaching set and fuzzy approaching functional mapping and making research on them, a new method for time series prediction is introduced.

A Numerical Study of Bingham Turbulent Flow in Sudden-Expansion Straight Circular Pipe

Hu Chunbo, Wei Jinjia, Jiang Peizheng, Miao Yongmiao

1998, 19(11): 1014-1020.

Abstract(2352) PDF(665)

Abstract:
The control equations for the turbulent flow of Bingham flulid are established according to Bingham fluid constitution equation. Pressure field and velocity field are correlated by pressure-correction equation. The numerical computations are performed on Bingham fluid turbulent flow in sudden-expansion straight circular pipe, and the flow mechanisms are discussed.

Existence of Solutions to Differential Inclusions in Banach Spaces

Song Fumin

1998, 19(11): 1021-1029.

Abstract(1953) PDF(806)

Abstract:
In this paper, the existence of solutions to differential inclusions is discussed in infinite dimensional Banach spaces. First, some comparability theorems for common differential inclusions are posed, relations between approximate solutions and solutions are studied. In the end, the existence theorem of solutions to differential inclusions is obtained.

A Comment on the Proof of Fermat’s Last Theorem

Zhang Baoshan

1998, 19(11): 1030-1034.

Abstract(1917) PDF(807)

Abstract:
In this paper, some comments on the proof of Fermat's last theorem are proposed. The main result is that the proof proposed by Wong Chiahe is only part of proof for Fermat's last theorem. That is to say, the proof is not all-full proof to Fermat's last theorem.