INTEGRATION OF SINGULAR-INTEGRALS FOR THE GALERKIN-TYPE BOUNDARY-ELEMENT METHOD IN 3D ELASTICITY

The mixed boundary value problem in three-dimensional linear elasticit y is solved via a system of boundary integral equations. The Galerkin approximation of the singular and hypersingular integral equations lea ds to (hyper)singular and regular double integrals. The numerical cuba ture of the singular integrals is discussed in the case of domains whi ch have piecewise smooth surfaces with a Riemann metric structure. We give a method for reducing finite part integrals to at most Cauchy sin gular integrals. The presented integration method applied to Cauchy si ngular integrals leads to explicitly given regular integrand functions which can be integrated by standard Gaussian product quadrature rules . The number of necessary Gaussian knots depends on the shape of the b oundary elements and on the curvature of the surface. We give estimate s of the quadrature error including constants, which mark the properti es of the boundary elements. The error estimates can be taken to imple ment adaptive cubature methods. The numerical example is a mixed bound ary value problem with corner and edge singularities. (C) 1998 Elsevie r Science S.A.