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Principal Value Seperation Radial Integration BEM and Its Application in Nonlinear Problems

2015年04月08日 18:32  点击:[]

The National Natural Science of China, No.11172055, 2012-2015

Xiaowei GAO

Boundary element method (BEM) has distinct advantages in solving fracture,moving boundary,infinite media and super thin structural problems.However,conventional BEM can exhibit the advantages only in solving linear problems.Solving nonlinear problems still is a challenge topic in BEM.This project is aimed to research a BEM algorithm being able to solve general nonlinear,varying coefficients,and anisotropic problems.The basic research strategy is as follows: firstly, the Weighted Residual Method is applied to establish boundary-domain integral equations for general nonlinear problems;then an integral  principal value isolation technique is developed to derive explicit displacement integral equations.The Radial Integration Method is employed to transform domain integrals involved in the integral equations into boundary integrals,forming a pure boundary element algorithm to solve general nonlinear problems with boundary discretization only.The features of the proposed algorithm are that the explicit expression of displacement derived from the principal value isolation tachnique makes it feasible to derive high accurate stress integral equations ; the nonlinear effect is involved in integration coefficients;the nonlinear integral equations only explicitly include displacements and tractions so that it is very easy to establish multi-domain BEM algorithm for problems consisting of different materials.The research of the project can provide theoretical and numerical foundations of BEM for solving complicated engineering problems.

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