NONLINEAR COORDINATE TRANSFORMATION OF FINITE-PART INTEGRALS IN 2-DIMENSIONAL BOUNDARY-ELEMENT ANALYSIS

This paper describes a method for the numerical computation of hypersi ngular integrals as they appear in the boundary element analysis. The proposed method is based on the finite part concept and allows for arb itrary curved boundary elements. Owing to the unknown transformation p roperties of finite part integrals undergoing a non-linear co-ordinate transformation, the definition formula of finite part integrals is ap plied prior to the transformation into the usual element co-ordinate s ystem. The resulting integrals are regular and may be evaluated by sta ndard Gaussian quadrature rules. The method is described in detail for the boundary integrals of two-dimensional linear elastostatics. Numer ical examples are included for this type of problem, but the method ma y easily be adapted to other two-dimensional problems.