NONLINEAR ELASTIC-DAMAGE CONSTITUTIVE EQUATION OF BRITTLE ROCK AND EXPERIMENAAL VERIFICATION

on the basis of the experimental studies of mechanical properties in brittle rock,the generalized elastic modulus,generalized elastic Poisson ratio,irreversible deformation Poisson ratio and damage deformation characteristic arediscussed.And then,a new damage variable is defined.A new nonlinear elastic-damage constitutive equation is built and the damage evolution equation is proposed.The nonlinear elastic-damage constitutive equation is verified in the uniaxialcompression test of quartz sandstone in Chongqing.The results show that reasonableagreement exists between the theoretical analysis and the experimental data.     

A SINGULARITY PROPAGATION FOR SEMILINEAR WAVE EQUATIONS

This paper discusses the propagation of singularity forsemilinear wave equations.By use of the theory of para-differentialoperators and the method of microlocal analysis,some results for generalsemilinear wave equations are obtained.     

A NONLINEAR PROGRAMMING MODEL AND ITS ALGORITHM FOR TRANSMISSION NETWORK PLANNING

The problem of transmission network planning is studied thoroughly by applying the mathmatical optimal tecqhniue in this paper. A novel approach is put forward for computer aided transmission network planning, which is quite different from what is based on D.C. load flow equations. A nonlinear transmission planning model is set up by regarding A.C. load flow equations as the system model. A practical model which can be solved more easily, and an united algorithm are obtained by applying the SUMT to the nonlinear model. The results of some practical examples indicate that this method can not only make the planning results more accurate, but also provide the voltage qualities and produce planning plans autometically and seek the plans optimally and fast.     

ON THE EXISTENCE OF LIMIT CYCLES OF A CLASS NONLINEAR EQUATION

This paper uses the Poincare-Bendixson's annular region theorem with existenceof limit cycles of a cfass of nonlinear differential equation.     

A BOUNDARY ELEMENT METHOD FOR SOLVING DIRICHLET PROBLEM OF THE HELMHOLTZ EQUATION IN R~2

This paper presents a boundary element method for solving Dirichlet bou-ndary value problem of the Helmholtz equation in R~2.First,the existence andthe uniqueness of an extended solution for the problem are obtained.Then,thesolution is expressed in terms of simple layer potentials,and this expression,which is suitable to the interior as well as the exterior problem,leads to aboundary integral equation of the first kind.Finally,a finite element approachis applied to solve a variational form which is equivalent to the boundaryintegral equation.     

A NEW BOUNDARY INTEGRAL EQUATION METHOD FOR SOLVING EXTERIOR BOUNDARY VALUE PROBLEMS OF THREE-DIMENSIONAL HELMHOLTZ EQUATION

This paper pressnts a new boundary integral equation method for solving exteri-or boundary value problems of three-dimensional Heimheltz equation by using the multiple reciproc-ity method.Firstly,integral representations of the solution in an exterior domain as well as on itsboundary,which have the peculiarity that integral kernels are infin ite seriesea developed from thenormal fundamental solution of Laplace equation and independent of the wavenumber,are given andproved under the Dirichlet condition.Then,based on the representation of the solution on the bound-ary,boundary integral equations for solving the Dirichlet and the Neumann boundary value prob-lems are obtained,and remarks for some problems concerned with solving these integral equationsnumerically are made.Finally, the advantages of the proposed method,as compared with the conven-tional boundary element methods,are summarized.     

EXISTENCE OF A BASIC OPTIMAL SOLUTION FOR LINEAR VECTOR EXTREME VALUE PROBBEM

In this paper, the concept of basic for linear vector extreme value problem is introduced in the partially ordered vector space. Some properties and results of the linear programming are generalized. And the existaence therom of basic optimal solution is proved.     

BOUNDEDNESS AND GLOBAL STABILITY FOR A CLASS OF VOLTERRA PREY-PREDATOR SYSTEMS

The boundedness for a class of Volterra prey-predator systems is proved and the conditions of the global stability for this class are given.which are formally different from the previous conditions obtained by the same author.