应用数学和力学

1997 Vol. 18, No. 9

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On Uniqueness, Existence and Objectivity of S-R Decomposition Theorem

Chen Mian, Liang Jingwei, Chen Xi, Chen Zhida

1997, 18(9): 763-768.

Abstract(2028) PDF(690)

Abstract:
For a physically possible deformation field of a continuum, the deformationgradient function F can be decomposed into direct sum of a symmetric tensor S andan orthogonal tensor R. which is called S-R decomposition theorem. In this paper,the S-R decomposition unique existence theorem is proved. by employing matrix andtensor method. Also, a brief proof of its objectivity is given.

Nonlinear Stability Analysis of a Clamped Rod Carrying Electric Current

Cheng Changiun, Yang Xiao

1997, 18(9): 769-777.

Abstract(2179) PDF(526)

Abstract:
This paper is devoted to the analysis of the nonlinear Stability of a clamped rodcarrying electric current in the magnetic field which is produced by the current frowingin a pair of inifinitely long parallel rigid wires. The natural State of the rod is in theplane of the wires and is equidistant from them.Firstly under the assumption of apatial deformation, the governing equations of the problem are derived, and the linearizedproblem and critical currents are discussed. Secondly, it ls proved that the buckledstates of the rod are always in planes. Finally. the global responses of the bifurcationproblem of the rod are compuled numerically and the distributions of the deflections.axial forces and bending monents are obtained. The results show that the buckledslates of the rod may be either supercritical or Subcritical. depending on the distancebetween the rod and the wires. Furthermore, it is found that-there exists a limit pointon the branch solution of the supercritical buckled State. This is distinctively differentfrom the buckled slate of the elastic compressive rods.

On the Two Bifurcatinos of a White-Noise Excited Hopf Bifurcation System

Liu Xianbin, Chen Qiu, Chen Dapeng

1997, 18(9): 779-788.

Abstract(2151) PDF(561)

Abstract:
The present work is concerned with the behavior of the second bifurcation of aHopf bifurcation system excited by white-noise. It is found that the intervention ofnoises induces a drift of the bifurcation point along with the subtantial change inbifurcation type.

A Combinatorial Algorithm for the Discrete Optimization of Structures

Chai Shan, Sun Huanchun

1997, 18(9): 789-797.

Abstract(2146) PDF(722)

Abstract:
The definition of local optimum solution of the discrete optimization is first given.and then a comprehensive combinatorial algorithm is proposed in this paper. Two-leveloptimum method is used in the algorithm. In the first level optimization, anapproximate local optimum solution X is found by using the heuristic algorithm,relative difference quotient algorithm. with high computational efficiency and highperformance demonstrated by the performance test of random samples. In the secondlevel, a mathematical model of(-1, 0, 1) programming is established first, and then itis changed into(0, 1) programming model. The local optimum solution X^* will befrom the(0, 1) programming by using the delimitative and combinatorial algorithm orthe relative difference quotient algorithm. By this algorithm, the local optimumsolution can be obtained certainly, and a method is provnded to judge whether or notthe approximate optimum solution obtained by heuristic algorithm is an optimumsolution. The above comprehensive combinatorial algorithm has higher computationalefficiency.

A Note on Probabilistic Interpretation for Quasilinear Mixed Boundary Problems

Ding Deng

1997, 18(9): 799-805.

Abstract(1968) PDF(499)

Abstract:
Solutions of quasilinear mixed boundary problems for the some parabolic andelliptic partial differential equalions are interpreted as solutions of a kind of backwardstochastic differential equalions, which are associated with the classical Ito forwardstochastic differential equations with reflecting boundary conditions.

Kinematical Force-Free Fields of a Magnetic Arch

Feng Qingzeng

1997, 18(9): 806-812.

Abstract(1698) PDF(425)

Abstract:
Basic equations are derived for kinematical force-free of a magnetic arch ina perfect conducting fluid. and the stationary and unsteady similarity solutions arediscussed in this paper.

The Optimal Control of Delay Control Systems with Restricted State Right Endpoint

Jiang Wei, Zheng Zuxiu

1997, 18(9): 813-817.

Abstract(2215) PDF(613)

Abstract:
In this paper, for the delay control system:x(t)=f[x(t),x(t-1),u(t),t] t∈[t₀,t₁] x(t)=φ(t) t∈[t₀,t₁] with State right endpoint restricled by condition φ_k=[x(t₁)]=0(k=1,2,…,l) a maximum principle is given. And as a specificexample. this paper gives a maximumprinciple under the condition that partial states right endpoints be completely fixed.Finally, this paper gives an example to explain the application of the main result ofthis paper. All the results are suitable for the control systems with multidelay as well.

Construction Space Harmonic Functions in Polynomial Form and Spherical Functions by Complex-Functional

Wang Qishen

1997, 18(9): 819-823.

Abstract(2097) PDF(464)

Abstract:
In this paper, applying the theory of complex-functional, not only the spaceharmonic functions in polynomial form. but aIso the spherical functions are obtained.

Basic Equations of Turbulent Flow for Variable Density and Variable Viscosity Newtonian Fluid in Open Channel

Zheng Yonggang, Fang Duo, Li Guifen

1997, 18(9): 825-831.

Abstract(2267) PDF(470)

Abstract:
In this paper. using Navier-Stokes equations and Reynolds time-averaged rules,the turbulent motional differential equations of voriable density and variable viscosity Newtonian fluid have been presented. and the turbulent motional differential equationsof variable density and variable viscosity Newtonion fluid in open channel have beenfurther proposed. The concepts of the density turbulence Stress and the viscosityturbulence stress have been firstly presented in the paper for the first time.

Three-Dimensional Analysis on Plates

Xiao Wanshen, Zeng Qingyuan, Liu Qingtan

1997, 18(9): 833-844.

Abstract(2120) PDF(439)

Abstract:
The displacements of the plate are assumed appropriately to derive the solutionsof the 3-D Navier equations. And the conditions on the plate’s surface are investigaled.In the examples. the boundary-value problems of the plate are solved by applying theNavier-equation's solutions and their closed-form solutions are obtained. The resultsformulated in the present paper satisfy exactly the governing equations and can reflectprecisely the boundary effects of complicated distributions on the edge of plates.

A New Algorithm for Solving Differential/Algehraic Equations of Multibody System Dynamics

Wang Yibing, Zhao Weijia, Pan Zhenkuan

1997, 18(9): 845-852.

Abstract(2273) PDF(612)

Abstract:
The second order Euler-Lagrange equations are transformed to a set of first orderdifferentiallalgebraic equations. which are then transformed to state equations by usinglocul parameterization. The corresponding discretization method is presented. and theresults can be used to implementation of various numerical integration methods. Anumerical example is presented finally.

Compensated Compactness Applied to Perturbed Fourth and Sixth Order P.D.E.

Yin Zhaoyang

1997, 18(9): 853-858.

Abstract(2134) PDF(576)

Abstract:
In the paper, by using the methods of compensated compactness and energyestimate, the convergence of class of fourth and sixth orders singular perturbed. partialdifferential equations is obtained, and furthermore, the regularity of solutions is improved.