Study On Boundary Layer Effect In Indirect Regular Boundary Element Analysis

The BEM is a usual numerical method in computational mechanic, this paper provides an overview of computational mechanics and numerical methods, and then gives the detailed information about the development and basic principles of BEM.In boundary element analyses, when a considered field point is very close to an integral element, the nearly singular integrals lead to the "boundary layer effect", so the numerical results become less satisfactory or even out of true. For the higher order geometry elements, which can be describe the true geometrical domains in engineering more accurately, the exact evaluation of nearly singular integrals is a difficult problem because of the complex forms of Jacobian and integrands. The problem limit the application of BEM to a certain extent, therefore, the accurate evaluation of nearly singular integrals, especially the nearly singular integrals with high order geometry elements, is necessary and very important. In this paper, a new exact integration method for the nearly singular integrals with high order geometry elements was presented. The suggested method can improve the accuracy of numerical results of nearly singular integrals greatly, and avoid the "boundary layer effect" efficiently.The given method was applied to the potential problems, based on the equivalent regularized BIEs with indirect unknowns, the nearly singular integrals with quadratic geometry element was expressed by some exact formulations, and the "boundary layer effect" was avoid efficiently. Therefore, the high accurate numerical results of the potentials and potential gradients at interior points close to the boundary were achieved.The suggested method was applied to the 2D elasticity problems, Based on a kind of newnonsingular BIEs for elastic plane problems, Exact formulations were obtained in order to calculate the nearly singular integrals with isoparametric quadratic element. The accurate numerical results ofσ_r andσ_θwere achieved, even the interior points are very close to the boundary. Therefore, the "boundary layer effect" was avoid efficiently.The given method was adopted to calculate the shear stress on the end. Based on the equivalent nonsingular boundary integral equations of two-dimensional isotropic uniform bar torsion, the accurate results of the shear stress on the end were obtained, even the calculate points close to the boundary 10^-9.Finally, it summarized the research results and made the outlook for the given method' applications in practical problem.