REGULARIZATION OF NEARLY SINGULAR INTEGRALS IN THE BOUNDARY ELEMENT METHOD OF POTENTIAL PROBLEMS

IntroductionAsanimportantnumericalmethod ,BoundaryElementMethod (BEM)hasbeenappliedinmanyareas[1].However,theBEMhasthedifficultiesofcalculatingsingularintegralsatnodesonboundaryoratinteriorpointsveryclosetotheboundary .TheaccuracyoftheBEMdependsontheprecisionofthecalculatedvaluesofthesingularintegrals,toagreatdegree.Manyresearchersdevotethemselvestothetreatmentofthesingularintegrals[2～3],whicharereviewedindetailbyRef.[4] .Ageneralregularizationalgorithmofevaluatingthephysicalquantitiesa…     

Electro-mechanical coupling analysis of MEMS structures by boundary element method

In this paper, we present the applications of Boundary Element Method (BEM) to simulate the electro-mechanical coupling responses of Micro-Electro-Mechanical systems (MEMS). The algorithm is programmed in our research group based on BEM modeling for electrostatics and elastostatics. Good agreement is shown while the simulation results of the pull-in voltages are compared with the theoretical/experimental ones for some examples. The project supported by the 973 Program (G199033108) and the national Natural Science Foundation of China (10125211)     

A promising boundary element formulation for three‐dimensional viscous flow

In this paper, a new set of boundary‐domain integral equations is derived from the continuity and momentum equations for three‐dimensional viscous flows. The primary variables involved in these integral equations are velocity, traction, and pressure. The final system of equations entering the iteration procedure only involves velocities and tractions as unknowns. In the use of the continuity equation, a complex‐variable technique is used to compute the divergence of velocity for internal points, while the traction‐recovery method is adopted for boundary points. Although the derived equations are valid for steady, unsteady, compressible, and incompressible problems, the numerical implementation is only focused on steady incompressible flows. Two commonly cited numerical examples and one practical pipe flow problem are presented to validate the derived equations. Copyright © 2004 John Wiley & Sons, Ltd.     

Calculation of the J-integral for limited permeable cracks in piezoelectrics

Summary This paper deals with the calculation of the J-integral for electrically limited permeable cracks in piezoelectrics. The electromechanical J-integral is extended to account for electrical crack surface charge densities representing electric fields inside the crack. To avoid the costly implementation of the line integral along the crack faces, an alternative is proposed replacing the line integral by a simple jump term across the crack faces. Previous work by other authors related to the same subject is critically illuminated. The derivation was inspired by the Dugdale- Barenblatt cohesive zone model and yields an expression containing solely the local jump of displacements and electric potentials across the crack faces. This approach is shown to be exact for the Griffth crack.Numerical examples give evidence that the simplified approach works well for arbitrary crack configurations too.     

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations （BIE） and solved with the newly developed boundary point method （BPM）. The model is closely derived from the concept of the equivalent inclusion Of Eshelby tensors. Eigenstrains are iteratively determined for each short-fiber embedded in the matrix with various properties via the Eshelby tensors, which can be readily obtained beforehand either through analytical or numerical means. As unknown variables appear only on the boundary of the solution domain, the solution scale of the inhomogeneity problem with the model is greatly reduced. This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM. The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element （RVE）, showing the validity and the effectiveness of the proposed computational modal and the solution procedure.     

Computational model for short-fiber composites with eigenstrain formulation of boundary integral equations

A computational model is proposed for short-fiber reinforced materials with the eigenstrain formulation of the boundary integral equations(BIE)and solved with the newly developed boundary point method(BPM).The model is closely derived from the concept of the equivalent inclusion of Eshelby tensors.Eigenstrains are iteratively determined for each short.fiber embedded in the matrix with various properties via the Eshelby tensors,which can be readily obtained beforehand either through analytical or numerical means.As unknown variables appear only on the boundary of the solution domain,the solution scale of the inhomogeneity problem with the model is greatly reduced.This feature is considered significant because such a traditionally time-consuming problem with inhomogeneity can be solved most cost-effectively compared with existing numerical models of the FEM or the BEM.The numerical examples are presented to compute the overall elastic properties for various short-fiber reinforced composites over a representative volume element(RVE),showing the validity and the effectiveness of the proposed computational modal and the solution procedure.     

Boundary element analysis for elastic and elastoplastic problems of 2D orthotropic media with stress concentration

Both the orthotropy and the stress concentration are common issues in modern structural engineering. This paper introduces the boundary element method (BEM) into the elastic and elastoplastic analyses for 2D orthotropic media with stress concentration. The discretized boundary element formulations are established, and the stress formulae as well as the fundamental solutions are derived in matrix notations. The numerical procedures are proposed to analyze both elastic and elastoplastic problems of 2D orthotropic media with stress concentration. To obtain more precise stress values with fewer elements, the quadratic isoparametric element formulation is adopted in the boundary discretization and numerical procedures. Numerical examples show that there are significant stress concentrations and different elastoplastic behaviors in some orthotropic media, and some of the computational results are compared with other solutions. Good agreements are also observed, which demonstrates the efficiency and reliability of the present BEM in the stress concentration analysis for orthotropic media. The project supported by the Basic Research Foundation of Tsinghua University, the National Foundation for Excellent Doctoral Thesis (200025) and the National Natural Science Foundation of China (19902007). The English text was polished by Keren Wang.