SINGULARITIES IN BOUNDARY ELEMENT METHODS

This paper presents an all round review of recent deve-lopments in treating the singularities in boundary element methods bothfor numerical computing and for mathematical analysing.Approachesfor numerical treatment of singular and hyper-singular integrations arelisted.Singular behaviour of solution on non-smooth boundary are discus-sed and the mathematical tools for describing it,such as the Sobolevspaces defined on a part of boundary,the pseudo-differential operatorsare presented.In order to incorporate the singular behaviour into theboundary element approximation,the technique of introducing singularboundary element is suggested.     

BOUNDARY ELEMENT METHODS FOR PLATES ON TwO-PARAMETER ELASTIC FOUNDATION

In this paper,the boundary element methods are applied to analyse the plates ontwo-parameter elastic foundation according to two boundary integral equations.The bending mo-ment,torsion and shear force at any point of plates are discussed by means of the theory of elasticitymechanics.An example and a plate in practital engineering are analysed.The resulta show that thereare high efficiency,good accuracy and little storage with this method.     

THE REANALYSIS THEORY OF COUHLED METHOD OF FINITE ELEMENT AND BOUNDARY ELEMENT METHOD WITH VARIATION OF BOUNDARY

The coupled element of finite element and boundary element theory has been used to carry out the reanalysis of structures with geomeotric variation based on the varitional principle. It will not only reduce the amount of analyser' work,save the memory of computer,but also enhance the accuracy of reanalysis. So it will effectively make the reanalysis of large structures easy.     

AN EXTENDED TRANSFER MATRIX AND BOUNDARY ELEMENT METHOD

A combination of extended transfer matrix and boundary element method is proposed for solving two dimentional statics problems of complicated nonhomogeneous structure. It is explained with the theory and the example. The method can get greater numerical accuray and shorten computation time in small amount of computer storage without getting involved with large matrices.     

BOUNDARY ELEMENT METHODS AND ERROR ANALYSIS FOR THE SOLUTION OF ELLIPTIC NEUMANN PROBLEM IN R~2

This paper presents boundary element methods for the solution of elliptic partial differential equation with Neumann boundary problem in R~2. Total details of error analysis are given for general condition, and optimal estimates are obtained. For simplicity Laplace's equation is discussed in illustration.     

THE SPLINE BOUNDARY ELEMENT METHOD FOR CALCULATION OF ELECTROMAGNETIC FIELD PROBLEMS

The spline boundary element method is presented for electromagnetic field problems. Based on B-spline function interpolation, the formulation of calculation of two dimensional statical electromagnetic field problems is obtained. Boundary corner and singular integration problems are efficiently handled. Furthermore,the Method is used for solving two calculation examples.     

BOUNDARY ELEMENT METHOD FOR MULTI-BODY CONTACT PROBLEM AND ITS APPLICATION IN HUGE EXCAVATOR

A boundary integrate equation and its discrete technique for multi-body contact problem is carried out on basic equations of boundary element method and its fortran program is compiled. Using the method ,the press distribution on the roller plate of the huge excavator with capacity 16 m3 was calculated and a distroy stress analysis of caterpillar of the excavator was carried out.     

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.     

THE VISCOELASTOPLASTIC BOUNDARY ELEMENT ANALYSIS FOR THE UNDERGROUND ROCK CAVERNS

In this paper,the theological model is presented,and the ba-sic principle of the viscoelastoplastic problem is worked out by the boundaryelement direct method,and the relevent formulations are derived.Several exam-ples show that the theological model and the corresponding boundary elementmethod presented in this paper are effective and reasonable.     

A BOUNDARY ELEMENT METHOD FOR THE NEUMANN PROBLEM OF HELMHOLTZ EQUATION BY USE OF A DOUBLE LAYER POTENTIAL IN R~3

This paper presents a new numerical solution for Neumann problem of Helmholtz equation in R~3. The expression of the solution for this problem is obtained by use of a double layer potential and it leads to a Fredholm boundary integral equation of the first kind. Then, the existence and unicity of the integral equation which is equivalent to the boundary value problem are obtained in a suitable Sobolev space. Finally, a variational form which is equivalent to the integral equation is applied to the construction of a finite element method and the error estimate is given.     

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.     

Similar Boundary Element Method in Elastodynamics

For the boundary element method of elastodynamics, some properties of matrices are discussed in case of similar boundary elements and the similar boundary element method is presented. In a series of similar boundary elements, when the corresponding matrices of a boundary element are obtained, the ones of other boundary elements in the series can be obtained by proportion. Then the coefficient matrix of the last system of linear algebraic equations can be obtained by the method of superposition. Compared with the general boundary element method, the computing speed can be raised by the similar boundary element method given in this paper.     

THE APPLICATION OF FINITE - ELEMENT METHODS FOR THE ANALYSIS OF GALLBLADDER BILE FLOW IN VIVO

The transient flow fields of gallgladder bile in vivo are calculated by finite element methods. Computer tomograph, ultrasound B and contrast radiography are applied to determine the moving boundary conditions, The penalty formulation and moving triangle elements have been successfully adopted and be flow fields for axisymmetric Newtonian bile flow have been obtained. The results show that there exists obvions reverse flow at the cross section (Perpendicular to Center axis) and thus forms axisymmetric vartexes inside a contracting gallbladder in vivo,Which well agree with the previous prediction.     

Preprocessor of Reinforced Concrete FEM Analysis

Reinforcing element and concrete element have effects on the order of the stiff-matrix of the reinforce-concrete FEM. The program divided the elements is programmed by FORTRAN language in current analysis, and the data of the elements are stored by the array. The stiff-matrix of the reinforce-concrete FEM is extended by the large residual between the serial numbers of the nodes of cohering element. This paper establishes the graph class, path class and point class via objectoriented programming. The storage of the points and the paths by the chain structure realization of copying graph, moving graph, adding graph, continuously numbering the cohering elements are built. This paper presents the example of the dividing domain with the crack.     

Discussions on Discontinuous Boundary Element Analysis

In this paper,several questions associated with discontinuous boundary elements are discussed.1.The optimum position of collocation point is reevaluated and it is found that accuracy of integrals,especially the nearly singular integrals, is the key factor that influences the accuracy of discontinuous boundary element analysis.2.Discontinuous boundary element is employed for combination of FEM BEM coupling procedure.The patch test, devised by Lu et al,is reconsidered. It is demonstrated that coupling procedure by discontinuous boundary element can achieve results of high accurary.     

A BOUNDARY ELEMENT METHOD WITH LOWER-ORDER SINGULARITY

In this paper, a lower-order singular BEM based on original BEM is presented by introduccing a new variable of angle. In the new method, kernel of force is the same as kernel of displacement which is only singularity of InR ( R is the distance between a source and a field point ) . Hence, it results in a new BEM formulation, whose singularity is lower than that of the original BEM formulation. What's more, in calculating stress, it eliminates the boundary-layer effect in the main. A software which is based on lower-order singular formulation is used to analysis the bar of 300T coiningmachine, its result is coincident with that obtained by the original BEM and photo-elastic experiment.     

Effects of Thorax Muscle Fiber on Body Surface Potentials

A numerical method calculating the forward problem of electrocardiogram (ECG) has been presented. By using this method, the torso part including anisotropic muscle layers has been discretized by means of the finite element method (FEM). The rest of torso have been divided into the surface elements by the boundary element method (BEM). The effects of the skelltel muscle layers over thorax wall, have been discussed in terms of a three-dimensional torso models.     

VBEM Analysis for Signorini Problem

the virtual boundary element method is applied for the numerical solution of a Signorini problem, which is conduced by an electro-paint process. The present method base on a switching algorithm, which can be applied to the problem defined in a non-regular domain, and it can reach good accuracy with less elements.     

A Three Dimensional Torso Model for the Numerical Simulation of ECG--Forward Problem of ECG(1)

In this paper,a numerical model of a three dimensional human torso has been presented.In this model,the torso part including anisotropic muscle layers has been discretized by means of the finite element method(FEM).The rest of torso have been divided into the surface elements by the boundary element method(BEM).This discretized model can be used in the field such as the forward problem and the inverse problem of the electrocardiogram(ECG).     

The Taylor series multipole boundary element method (TSM BEM)and its applications in rolling engineering

Rainfall is the main input for probabilistic analysis and prediction of rainfall-triggered landslide. The joint probabilistic structure of daily rainfall (DR) and cumulative rainfall (CR), which are dominant parameters of rainfall related on landslide in Chongqing region, was analyzed. Following the traditional technology, daily rainfall was translated into discrete variable by rainfall grade and cumulative rainfall became continuous variable if records with very small cumulative rainfall were ignored. Then joint probabilistic model of discrete variable and continuous one was derived, and transiting solution of conditional density function was put forward, together with its approximation via a family of Dirac δ sequences. Naturally, the proposed method was used to analyze conditional density function of cumulative rainfall in Chongqing region, and the numerical results were verified by comparison. However, most of the conditional density functions were irregular and not modeled by simple probability density function, thus the finite mixture distribution was introduced, which is of uncomplicated format and relatively high precision. At last, the joint probabilistic model of daily rainfall and cumulative rainfall was built up by combining frequency function of grade of daily rainfall with conditional density model of cumulative rainfall.