INTEGRATION OF SINGULAR GALERKIN-TYPE BOUNDARY-ELEMENT INTEGRALS FOR 3D ELASTICITY PROBLEMS

A Galerkin approximation of both strongly and hypersingular boundary i ntegral equation (BIE) is considered for the solution of a mixed bound ary value problem in 3D elasticity leading to a symmetric system of li near equations. The evaluation of Cauchy principal values (v. p.) and finite parts (p. f.) of double integrals is one of the most difficult parts within the implementation of such boundary element methods (BEMs ). A new integration method, which is strictly derived for the cases o f coincident elements as well as edge-adjacent and vertex-adjacent ele ments, leads to explicitly given regular integrand functions which can be integrated by the standard Gauss-Legendre and Gauss-Jacobi quadrat ure rules. Problems of a wide range of integral kernels on curved surf aces can be treated by this integration method. We give estimates of t he quadrature errors of the singular four-dimensional integrals.