应用数学和力学

1995 Vol. 16, No. 6

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Asymptotic Solution of a Singularly Perurbed Nonlinear State Regulator Problem

Lin surong, Lin Zongchi

1995, 16(6): 479-483.

Abstract(2303) PDF(507)

Abstract:
This paper,will seek the optimal control and corresponding trajectories of the singularly perturbed nonlinear state regulator problem.Under appropriate hypotheses.it will be possible to complete an asymptotic solution which is uniformly valid when ε→0.

Effect of the Magnetic Field on the Pulsatile Flow Through a Rigid Tube

Feng Zhonggang, Wu Wangyi

1995, 16(6): 485-494.

Abstract(1969) PDF(470)

Abstract:
This study presents the effect of the magnetic field with constant intensity on the pulsatile flow through a rigid tube.Basing on the experimental results,the influence of the magnetic field on the blood viscosity is considered The analytic solution of the pulsatile flow through a rigid tube under constant magnetic field intensitier and the effect of the magnetic field on the velocity distribution,flow and impedance in a rigid tube are given.this investigation is valuable for understanding the influence of the magnetic field on the blood circulation.

Geodesic Precession in the(Ω,A_ab)-Field Theory

Hong Tam Judy

1995, 16(6): 495-499.

Abstract(2137) PDF(456)

Abstract:
This paper aims to determine the geodesic precession in Yu's(Ω,A_ab)-field theory^[1],and to compare the result with that of the Schwarzschild orbit.

Exact Solution of Sandwich Beams

Zheng Shiying, Jin Yao

1995, 16(6): 501-509.

Abstract(2126) PDF(547)

Abstract:
Seriously non-uniform warping cross-sections due to shear effects sharply expose the essential difference between solid and sandwich beams.Actually,the deflected configuration and stress distributions in sandwich beams are far beyond the scope that the elementary bending theory is applicable for their description.For analysis of sandwich beams,the most extensively employed classical theories are based on such assumption as the whole cross-section or each individual layer thereof remains plane for bent configuration.As a matter of fact,theories based on such assumptions appear particularly incapable of depicting the mechanical characteristic behavior of sandwich beams,with a weak core in particular.Not relying on any assumptions,the present work tends to have the sandwich beam considered as layered elastic continuum.Close solution thereupon obtained satisfies the governing equations,the boundary conditions,as well as the stress continuity and displacement compatibility requirements on interlayer interfaces.Experimental studies and numerical(finite element analysis) examinations favorably justify the validity of the present solution together with its superb capability of representing the displacement responses and stress distributions in sandwich beams.

Singular Perturbation for a Class of Coupled Chemical Reaction and Diffusion Systems

Chen Songlin

1995, 16(6): 511-517.

Abstract(1867) PDF(467)

Abstract:
In this paper,singular perturbation for a class of coupled chemical reaction diffusion system with initial and Neumann boundary conditions is considered.Under some suitable conditions and restrictions,we obtain a uniformly valid asymptotic solution of the stated system by using the iteration method and the method of upper and lower solutions.

Three-Dimensional Analysis of the Flow in the Cyclones

Xi Zhizhong

1995, 16(6): 519-525.

Abstract(1963) PDF(576)

Abstract:
This paper gives the detailed mathematical expression of the flow in the spherical coordinates system.Applying the law of conservation of mass,movement theorem of steady flow,and applying the mathematical method of stream function with consideration of the axis symmetry,the three components of velocity quantum of the flow are deduced in detail.Here the overall analysis of the flow is presented in the view of the concept of whole,and the paper gives the necessary corrections of some results of Ref.[1]

Analysis of Energy Release Rate for Cracked Laminates

Hu Hurang, Wu Chengping

1995, 16(6): 527-541.

Abstract(2751) PDF(497)

Abstract:
An interface crack analysis is presented for further understanding the characteristics of the crack-tip field.The conditions under which the energy release rate components would exist are emphasized and the relations between energy release rate components and the stress intensity factors are given.Combining with the results of chasical plate theory analysis.a closed-form solution for stress intensity factors in terms of external loading as well as some geometric and material parameters for fairly general composite laminates is derived Then.an analytical solution for energy release rate components is deduced.In order to get energy release rate components under general loading condition.a mode mix parameter,Ω,must be determined separately.A methodology for determining Ω is discussed.Finally.several different kinds of laminates are examined and the results obtained could be used in engineering applications.

Iterative Construction of Solution to Nonlinear Equations of Lipschitzian and Local Strongly Accretive Operators

Zeng Luchuan

1995, 16(6): 543-552.

Abstract(2186) PDF(506)

Abstract:
In this paper,we investigate the Ishikawa iteration process in a p-uniformly smooth Banach space X.Let T:X→X be a Lipschitzian and local strongly accretive operator and the set sol(T) of solutions the equation T_x=f be nonempty.We show that soil(T) is a singleton atul the Ishikawa sequence converges strongly to the unique solution of the equation T_x=f.In addition,whenever T is a Lipschitzian and local Psendcontractive mapping from a nonempty convex subset K of X into X and the set F(T) of fixed points of T is nonempty,we prove that F(T) is a singleton and the Ishikawa sequetwe converges strongly to the unique fixed point of T.Our results are the improvements and extension of the results of Deng and Ding^[4] and Tan and Xu^[5].

CC Series Solution for Bending of Rectangular Plates on Elastic Foundations

Zhu Jiaming

1995, 16(6): 553-561.

Abstract(2348) PDF(596)

Abstract:
The analytical solution for the bending problem of the rectangular plates on an elastic foundation is investigated by using the Stockes' transformation of a double variables function.The numerical results for the rectangular plates with free edges on the elastic foundations under a concentrated force are given in the example.

Numerical Simulation of Complicated Pipe Flow with K-ε Model

Yu Bin, Chen Junkai

1995, 16(6): 563-567.

Abstract(2031) PDF(489)

Abstract:
In this paper,turbulence in a complicated pipe is simulated by using the k-ε model.The ladder-like mesh approximation is used to solve the problem of complicated boundary with the result of numerical simulation favorable.Two computational examples are given to validate the strong adaptability and stability of k-ε model.

A Simplified Over-Stress Analytical Model of the Dynamic Buckling of a Perfectly Plastic Column under Axial Impact

Jie Min

1995, 16(6): 569-572.

Abstract(1929) PDF(446)

Abstract:
This paper introduces the strain-rate effects in the analysis of dynamic buckling of a perfectly plastic cohoumn.The corresponding differential equation of dynamics is deduced.The expressions of half-wave length of buckling mode.critical load and time of buckling are obtained.Discussion on the strain-rate effect on the plastic dynamic buckling of a column is presented.The results of this paper are compared with those of the theory and experiment in[4].