An effective method for finding values on and near boundaries in the elastic BEM.

*(English)*Zbl 0941.74075From the summary: We study in detail the elimination of various kinds of singular integrals in displacement boundary integral equations and their derivative forms. First, a modified treatment which uses rigid body displacement solutions is introduced to calculate displacements near the boundary. Then derivative formulations of the displacement boundary integral equations are deduced, which form the basis of an investigation of the related hypersingular and nearly singular integrals. Similarly, a modified treatment, which uses the unit displacement derivative solutions together with some general numerical techniques, is proposed for the calculation of displacement derivatives on and near the boundary considered. Finally, strains and stresses are obtained from the calculated displacement derivatives by the use of the compatibility and constitutive equations. Numerical examples show that the proposed method is accurate in treating most singular or nearly singular integrals in the elastic BEM.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

74B05 | Classical linear elasticity |