About the Application of BEM Based on the Self-Regular Traction BIE in Elasticity

Abstract

Self-regular BEM algorithm avoids Cauchy principal value or Hadamard finite part evaluations as regularization is applied prior to discretization. Smoothness requirement for traction BIE is more stringent (C1, alfa for displacement). Boundary discretization into standard continuous elements leads to a loss of the smoothness required. Relaxation of the smoothness requirement has been proposed using C0 continuous elements with collocation points at the intersection between elements. Some researchers claim that this procedure cannot be theoretically justified. Interpolation of displacement tangential derivative an ‘relaxed continuity ’ hy pothesis are pointed out as possible sources of error introduced on the discretization of self-regular traction-BIE. Discontinuous elements are implemented in order to verify the possible sources of error. Such elements allow the split of these sources of error. Numerical results show that the ‘relaxed continuity ’ hypothesis seems to be the dominant source of error. Apparently the smoothness requirement for the self-regular traction-BIE must be preserved to guarantee converge.