Analytical integral algorithm applied to boundary layer effect and thin body effect in BEM for anisotropic potential problems

Authors:
Huanlin Zhou;Zhongrong Niu;Changzheng Cheng;Zhongwei Guan
Affiliations:
Department of Engineering Mechanics, Hefei University of Technology, Hefei 230009, PR China and Department of Engineering, the University of Liverpool, Liverpool L69 3GQ, UK;Department of Engineering Mechanics, Hefei University of Technology, Hefei 230009, PR China;Department of Engineering Mechanics, Hefei University of Technology, Hefei 230009, PR China;Department of Engineering, the University of Liverpool, Liverpool L69 3GQ, UK
Venue:
Computers and Structures
Year:
2008

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Abstract

A new completely analytical integral algorithm is proposed and applied to the evaluation of nearly singular integrals in boundary element method (BEM) for two-dimensional anisotropic potential problems. The boundary layer effect and thin body effect are dealt with. The completely analytical integral formulas are suitable for the linear and non-isoparametric quadratic elements. The present algorithm applies the analytical formulas to treat nearly singular integrals. The potentials and fluxes at the interior points very close to boundary are evaluated. The unknown potentials and fluxes at boundary nodes for thin body problems with the thickness-to-length ratios from 1E-1 to 1E-8 are accurately calculated by the present algorithm. Numerical examples on heat conduction demonstrate that the present algorithm can effectively handle nearly singular integrals occurring in boundary layer effect and thin body effect in BEM. Furthermore, the present linear BEM is especially accurate and efficient for the numerical analysis of thin body problems.