应用数学和力学

1994 Vol. 15, No. 10

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Iterative Construction of Fixed Points for Multivalued operators of the Monotone Type in Uniformly Smooth Banach Spaces

Deng Lei, Ding Xie-ping

1994, 15(10): 849-853.

Abstract(1893) PDF(561)

Abstract:
The fixed points of set-valued operators satisfying a condition of monotonicity type in s-uniformly smooth Banach spaces are approximated by recursive averaging process in the present paper.

The Random Variational Principle in Finite Deformation of Elasticity and Finite Element Method

Gao Hang-shan, Zhang Ru-qing

1994, 15(10): 855-862.

Abstract(2563) PDF(1634)

Abstract:
In the present paper,we have introduced the random materials.loads.geometrical shapes,force and displacement boundary condition directly.into the functional variational formula,by.use of a small parameter perturbation method,a unified random 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 in mechanics.

Two-Dimensional Deformation of an Anisotropic Elastic Body with a Parabolic Boundary

Hu Yuan-tai, Zhao Xing-hua

1994, 15(10): 863-871.

Abstract(1749) PDF(557)

Abstract:
In.the present paper,two-dimenstional deformation problems of an anisotropic boby.with a parabolic boundary.are sysiematically analysed by using Lekhnitskii's formalism and the mapping functions method.then a special.structure-the half-infinite crack problem is studied through the obtained results.the sinular fields and the sress iniensity 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): 873-877.

Abstract(1671) PDF(564)

Abstract:
This paper applies the multi-scale perturbation method suggested by Ref[3] to investigate 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): 879-883.

Abstract(2119) PDF(659)

Abstract:
In this paper.we make some comparisons between the solutions for Narier-Stokes equation and those.for heat conduction equation.In his study of Navier-Stokes equation.Professor J.Leray.a French mathematician and authority on partial differential equation,starting from heat conduction equation,obtained some results of properly posed of certain initial boundary 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 of comparing 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): 885-891.

Abstract(2154) PDF(627)

Abstract:
In this paper,in the space W₂¹ that possesses restoring nucleus,we obtain analytic solutions 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 Model of Catastrophe Theory

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

1994, 15(10): 893-900.

Abstract(1795) PDF(759)

Abstract:
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): 901-910.

Abstract(2032) PDF(888)

Abstract:
Taking the theory of mixture as a basic.framework,the paper merges the primesof rational mechanics irreivrsible thermodynamics and soil mechanics into an organic system and proposes an axiomatics of geomechanics.The theoretical system consists of 5 basis laws and 8 constitutive principles.and it erects a bridge across the gap between the pure theory of mechanics and engineering practice.

Bending Problems of Non-Homogeneous Cylindrical Orthotropic Circular Plate

Qin Sheng-li

1994, 15(10): 911-917.

Abstract(1623) PDF(637)

Abstract:
In this paper,the bending problem of the non-homogeneous cylindrical orthotropic circular plate is described.A general solution for the bending of circular plate under uniformly distributed transverse load is solved.and the exact solution of such circular plate with clamped edges is obtained.

The Maximum Dissipative Extension of Schrödinger Operator

Tian Li-xin

1994, 15(10): 919-926.

Abstract(1924) PDF(567)

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

Transfer Open or Closed Setvalued Mapping and Generalization of H-KKM Theorem with Applications

Li Bing-you, Su Jia-bao

1994, 15(10): 927-933.

Abstract(2127) PDF(620)

Abstract:
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 the corresponding results in[1,2,4,5,6,7].

An Elasticity Solution of a Nonhomogeneous Half-Plane Problem

Wo Guo-wei

1994, 15(10): 935-942.

Abstract(1743) PDF(641)

Abstract:
We employ fundamental equations of non-homogeneous elasticity and Fourier integral 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 non-homogeneous half-plane problems with the Young's modulus E(x)-E₀exp[βx].accurate solutions are obtained At last with the degeneracy it is obtained that thefamous Boussnesq solution and this method is successful.