Boundary Element Methods with Overlapping Domain Decomposition for Parabolic Problem

Boundary element method is a numerical method for solving partial differential equations. There are several formulations of boundary element method (BEM) applied to solve a parabolic differential equation.The approach,which employs time- dependent fundamental solution,allows longer time steps in time integration than other approaches,and this can cut down on time for computer implementation with high precision.Domain decomposition method,which decompose the domain that a given problem is to be solved into subdomains,has the advantages of reducing the large problem into smaller ones and reducing the complex problem into simpler ones,and allows parallel computing.An overlapping domain decomposition method is applied combining a boundary element formulation with time-dependent fundamental solution to solve a diffusion equation. Firstly, by domain decomposition, the problem divided into two problems on subdomains, and then the initial-Boundary problems are solved by boundry element method on each subdomain.Some numerical examples are presented to illustrate feasibility and efficiency of the method. The numerical experiments show that the convergence rate of the method is dependent with the overlapping degree of the subdomains.     

Boundary Element Method for Time-dependent Chloride Diffusion and the Chloride Distribution in Concrete

The process of chloride diffusion in concrete is time-dependent.The boundary element method (BEM) with a time-dependent diffusion coefficient is presented for chloride diffusion in concrete based on the suitable transformation of variables.The fundamental solution of the partial differential equation for time-dependent chloride diffusion in concrete is developed,and the compensation length of the diffusion field is defined as well as the compensation coefficient.The scheme of BEM with a time-dependent diffusion coefficient is developed.Two examples are given to demonstrate the accuracy and efficiency of the presented method and the rationality and the importance of the compensation length for the method.     

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.     

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).     

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.     

Exact Integration of Constant Element of Elastomer in Boundary Element Method

The boundary integral in Boundary Element Method affects the precision and the speed of the method. If the boundary integral with constant element, the nonsingular integrals are popularly calculated by the Gauss numerical integral, and the singular integrals are popularly calculated by the analytical integral. This paper presents an alternative way with Gauss formula to transform the double integral in elastic problem on 3-d into the linear integrals on the boundary of each subdomains, so that all the singular integrals and nonsingular integrals are calculated by analytical method. The example indicates that this method makes the precision and the speed of BEM improve.     

Exact Integration of Biharmonic Equation In Boundary Element Method

The boundary integral in Boundary Element Method effects the precision and the speed of the method. The boundary integrals are composed of the normal integrals and singular integrals. The normal integrals are popularly calculated by exact integral, and the singular integrals by the Gauss numerical integral. The singular integrals are low in precision when the source points approach the element. This paper presents an alternative way to transform the double integral in Biharmonic Equation on 3-d into the linear integrals on the boundary of each subdomain, so that all the singular integrals and nonsingular integrals are calculated by analytical method. It makes the precision and the speed of BEM improve.     

Comparison of Constant and Linear BEM Analysis for Small Viscous Fluid Sloshing

Linear boundary element method is used for the analysis of viscous fluid. The velocity components and the fluid mean pressure are taken as unknown functions. The comparison of linear BEM with constant BEM shows that the former presents much better precision and better convergence.     

A Method Coupling FEM and Singular Solution of Infinite Plane with a Hole for Underground Engineering

In this paper, a simpler and direct coupling method, i.e. finite element method coupled with singular solution of infinite plane with a hole, is proposed for the analysis of underground engineering. The numerical example shows that the elastic effectiveness of the infinite plane outside the artificial boundary upon the inside region is exactly expressed.     

THE METHOD AND ITS APPLICATION FOR COUPLED ANALYSING PLASTIC DEFORMATION OF ROLLING WORKPIECE AND ELASTIC DEFORMATION OF ROLLS

A method for coupled analysing plastic deformation of rolling workpiece and elastic de'formaticn of rolls is developed. The interaction of plastic defo rmation of rolling workpice and elastic deformation of rolls is considered. The couple is formulated by setting up force equilibrium equation at the interface of the rolling workpiece and tne rolls. The plastic deformation of rolling workpiece is treated by the rigid plastic finite element method and the elastic deformation of rolls is treated by the boundary element method. The rolling presure, perunit. forward slip, neutral from angle obtained from coupled analysis are lower than those obta-ined rigid rolls. The results obtained from analysis show that the analytical accuracy can be heightened using the coupled ana-ytical methcd dveeloped for treatng rolling3proccss.     

Four-node Membrane Element of Vector Form Intrinsic Finite Element for Large Deformation Analysis of Membrane Structures

Based on fundamental principles of the vector form intrinsic finite element (VFIFE), the basic formulas of 4-node quadrilateral membrane element were first derived in this paper. The procedure for the determination of pure nodal deformation through reverse movement was elaborated, and the method for the calculation of internal nodal forces through deformation coordinate system was presented. Feasible approaches were also proposed for several issues for 4-node membrane element, including the location statuses and the numerical integration for internal forces. A computer program of 4-node membrane element was developed. By the analysis of the numerical example, the correctness and validity of the membrane element theory and the computer program were verified. Then the approach was applied for more analysis of large deformation and large rotation problems of membrane structures, including cushion inflating and cloth draping.     

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.     

Numerical Analysis of Thermo-Elastic Deformation for Cyindrical Gears

In this paper,both non-coupled numerical method of thermo-elastic deformation and coupled procedure for meshing gear are presented. The illustrative examples of gears applied in machine-tools and rolling mills show that this procedure is ralid and efficient.     

AN ENTHALPY METHOD OF SOLVING PHASE CHANGE PROBLEMS BY COUPLING THE ENTHALPY AND THE MOVING BOUNDARY

A numerical enthalpy method is proposed for solving the multi-dimensional phase change problem by coupling the enthalpy and the moving boundary. Its basic feature is to sepasate appearent and latent heat terms by transforming the standard enthalpy relation and to couple them into the latent heat term by introducing the idea of phase change rate between the axes and simultaneously to correct the heat flux of the inflowing/outflowing phase change control volume element , so that the accuracy of numerical solution is improved and the moving boundary can be accurately followed.     

A Treatment to the Isoline for Finite Element Solution to Ferrite-Martensite Microstructure

The numerical solution of sample point stress field in finite element network of ferrite-martensite microstructure under finite deformation has a high-gradient distributive characteristic whose stress gradient between ferrite and martensite crystalline element is very high. If the interpolation method is used in the whole region,the isogram will be seriously smooth so that the original high-gradient sample point stress field will become untrue. This paper presents a new method for drawing isogram of ferrite-martensite microstructiire stress field by interpolating sample points in an element one by one. This method can make the post-treatment of high-gradient discrete stress field in crystalline network approach to a truer condition and solve the problem of arbitrary curve boundary of the deformed two phase steel.     

Service Life Prediction of Concrete Structures under Chloride Environment

The problems rendered from the conventional time marching, referring to stepwise time marching scheme (STMS) adopted in boundary element method (BEM) for chloride diffusion in concrete structures, were investigated, and a new time marching, referring to initial time marching scheme (ITMS) in BEM, was developed for evaluation of service life of the concrete structures under chloride environment. Results of the numerical examples show that the ITMS-BEM proposed can eliminate domain integral and simplify the computational model, so that the stability in iteration process can be improved, resulting in better efficiency and accuracy, compared with the STMS-BEM. It can also be concluded that the dimensions of the diffusion of chloride can affect the service life of the concrete structure significantly, which should be taken into account in structural design.     

3D BE Analysis on Stress Intensity Factor of a Fatigue Crack in a Welded T-joint

In this paper, based on multi region boundary element method (BEM), a general procedure to calculate stress intensity factors(SIF) of a 3D mixed mode fatigue surface crack is detailed. A BEM model for a welded T joint is constructed referring to the test specimen. The crack corner points are indirectly estimated to circumvent the treatment of the different crack tip singularity at the corner regions. Numerical results from the welded T joint show that this procedure is reliable.     

THE RIGID-VISCOPLASTIC FINIT ELJMENT ANALYSIS OF NON-STATIONARY FLOW OF METALS IN THE EDGE ROLLING

The rigid-viscoplastic finite element formulations for the analysis of non-stationary deformation in the edge rolling is established on the basis of the simplified 3-D. element. A new method for obtaining inital velocity field is developed in this paper. It has been used successfully to analyse the non-stationary deformation in the edge rolling of lead plates. The calculated results are found to be in good agreement with those obtained from expriements.     

Complex Variable Function Solution of Stress and Displacement of Surrounding Rock Buried Deep Horseshoe-Shaped Tunnel Excavation

An analytical solution was presented for the stresses and displacements around horseshoe-shaped tunnel using Cauchy integral method and Optimization theory in an elastic half-plane. Since the depth of a tunnel was larger than the size of the tunnel, gravity loads were simplified as uniform normal loads along far-field boundary. Finite element model was used to verify the accuracy of analytical solutions. Comparison between the results of numerical analysis by finite element method and those from the closed solutions indicates that the closed solution is reliable and applicable for the stress and displacement field around horseshoe-shaped tunnel tunnels at great depth.     

STUDY OF SOLUTION METHODS FOR SEPARATOR EQUATIONS OF HIGH GRADIENT MAGNETIC SEPARATION

In this paper, an analytical solution,approximate solution of initial retention, steady-state solution and numerical solution of separator equations of high gradient magnetic separation are discussed. A backward-vave method used to improve the steady-state solution and Treanor-four order Taylor numerical method are suggested for magnetic separator equations and are compared with experimental results.