Premium
Non‐linear co‐ordinate transformation of finite part integrals in two‐dimensional boundary element analysis
Author(s) -
Hildenbrand J.,
Kuhn G.
Publication year - 1993
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1620361706
Subject(s) - mathematics , finite element method , gaussian quadrature , quadrature (astronomy) , mathematical analysis , transformation (genetics) , boundary knot method , boundary element method , computation , boundary (topology) , numerical analysis , numerical integration , singular boundary method , boundary value problem , nyström method , algorithm , physics , biochemistry , chemistry , gene , optics , thermodynamics
This paper describes a method for the numerical computation of hypersingular integrals as they appear in the boundary element analysis. The proposed method is based on the finite part concept and allows for arbitrary curved boundary elements. Owing to the unknown transformation properties of finite part integrals undergoing a non‐linear co‐ordinate transformation, the definition formula of finite part integrals is applied prior to the transformation into the usual element co‐ordinate system. The resulting integrals are regular and may be evaluated by standard Gaussian quadrature rules. The method is described in detail for the boundary integrals of two‐dimensional linear elastostatics. Numerical examples are inclcded for this type of problem, but the method may easily be adapted to other two‐dimensional problems.