Applied Mathematics and Mechanics (English Edition)

ITERATIVE CONSTRUCTION OF FIXED POINTS FOR MULTIVALUEDOPERATORS OF THE MONOTONE TYPE IN UNIFORMLY SMOOTH BANACH SPACES

Deng Lei;Ding Xie-ping

1994, 15(10): 897-902.

Abstract ( 587 )

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The fixed points of set-valued operators satisfying a condition of monotonicitytype in s-uniformly smooth Banach spaces are approximated by recursive averagingprocess in the present paper.

THE RANDOM VARIATIONAL PRINCIPLE IN FINITEDEFORMATION OF ELASTICITY ANDFINITE ELEMENT METHOD

Gao Hang-shan;Zhang Ru-qing

1994, 15(10): 903-911.

Abstract ( 692 )

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In the present paper, we hare mtroduced the random materials. loads. geometricalshapes, force and displacement boundary condition directly. into the functionalvariational formula, by. use of a small parameter perturbation method, a unifiedrandom variational principle in finite defomation of elastieity and nonlinear randomfinite element method are esiablished, and used.for reliability, analysis of structures.Numerical examples showed that the methods have the advontages of simple andconvenient program implementation and are effective for the probabilistic problems inmechanics.

TWO-DIMENSIONAL DEFORMATION OF AN ANISOTROPICELASTIC BODY WITH A PARABOLIC BOUNDARY

Hu Yuan-tai;Zhao Xing-hua

1994, 15(10): 913-922.

Abstract ( 659 )

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In.the present paper, two-dimenstional deformation problems of an anisotropicboby. with a parabolic boundary. are sysiematically analysed by using Lekhnitskii’sformalism and the mapping functions method.then a special.structure─the half-infinitecrack problem is studied through the obtained results. the sinular fields and the sressiniensity..factors near the crack tip are also obiained.

THE APPLICATION OF MULTI-SCALE PERTURBATION METHOD TO THE STABILITY ANALYSIS OF PLANE COUETTE FLOW

Zhou Zhe-wei

1994, 15(10): 923-928.

Abstract ( 715 )

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This paper applies the multi-scale perturbation method suggested by Ref [3] toinvestigate the linear stability behavior of distorted plane Couette.flow. Using thismethod, the unstable Tollmien-Schlichting wave in plane Couette flow can be found,but not the most unstable mode. By comparing the results of this paper with those ofRef. [3], the effectiveness of this method is investigated.

STABILITY OF NAVIER-STOKES EQUATION(II)

Shi Wei-hui;Fang Xiao-zuo

1994, 15(10): 929-933.

Abstract ( 580 )

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In this paper. we make some comparisons between the solutions for Narier-Stokesequation and those.for heat conduction equation.In his study of Navier-Stokes equation.Professor J.Leray. a Frenehmathematician and authority on partial differential equation, starting from heatconduction equation, obtained some results of properly posed of certain initialboundary value problems of Navier-Stokes equation. Professor R. Temam of University de Paris XI and other experts in this field also brought up the possibility ofcomparing these two classes of equations. This paper attempts to describe and provethe.fundamental difference between these two.

THE SOLUTIONS OF STEADY-STATE CONVECTION EQUATIONS IN THE SPACES THAT POSSESS RESTORING NUCLEUS

Zhang Chi-ping;Cui Ming-gen

1994, 15(10): 935-942.

Abstract ( 529 )

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In this paper ,in the space W₂¹ that possesses restoring nucleus, we obtain analyticsolutions in the series form for the steady-state convection diffusion equation The solutions have the following characteristics: (1) they ave given in the accurate form:(2)they can be calculated in the explicit way, without solving the eguations;(3) the error of the approximate solution will be monotonically decreased under the meaning of the norm of the spaces when a cardinal term is added in the procedure of numerical solution.Finally, we calculated the example in [2] the result shows that our solution is more accurate than that in [2].

THE STUDY OF CHAMBER ROCKBURST BY THE CUSP MODELOF CATASTROPHE THEORY

Pan Yi-shan;Zhang Meng-tao;Li Guo-zheng

1994, 15(10): 943-951.

Abstract ( 663 )

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By means of CUSP model of catastrophe theory. this paper has studied thephysics process of rockburst occured on circular chamber. The present paper has nolonly described the instability process of rockburst more deeply. but also got the crilicaldepth of plastic softening area of chamber that is valuable in the controlling engineering of rockburst. the chamber displacement jump and energy liberation have been derived. the influence of rock parameters on the rockburst has been discussed.

AN AXIOMATICS OF GEOMECHANICS

Chen Zheng-han

1994, 15(10): 953-964.

Abstract ( 552 )

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In the present paper we study the maximum dissipative extension of Schrodingeroperator.introduce the generalized indefinite metvic space and get the representation ofmaximum dissipative extension of Schrodinger operator in natural boundary space.make preparation for the further study longtime chaotic behaxior of infinite dimensiondynamics system in nonlinear Schrodinger equation.

TRANSFER OPEN OR CLOSED SETVALUED MAPPING AND GENERALIZ-ATION OF H-KKM THEOREM WITH APPLICATIONS

Li Bing-you;Su Jia-bao

1994, 15(10): 981-987.

Abstract ( 620 )

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In this paper ,we introduce a class of generalized mapping called transfer open orclosed valued mapping to generalize the KKM theorem on H-space.Then asapplications,using our H-KKM theorem,we prove some coincidence theorems.matching theorems and vector valued minimax inequalities which generalize slightly thecorresponding results in[1,2,4,5,6,7].

AN ELASTICITY SOLUTION OF A NONHOMOGENEOUSHALF-PLANE PROBLEM

Wo Guo-wei

1994, 15(10): 989-996.

Abstract ( 599 )

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We employ fundamental equations of non-homogeneous elasticity and Fourierintegral transformations to obtain the general solutions of the stress function.On thebasis of these points of view and when the forces on the boundary are arbityary for nonhomogeneous half-plane problems with the Young’s modulus E(x)-E₀θxp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.

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