CONTINUITY AND COLLOCATION EFFECTS IN THE BOUNDARY ELEMENT METHOD

The presence of singularities in the integral operators of the boundary element methods requires that the density functions must satisfy certain continuity requirements if the displacements and stresses are to be bounded. Quite often the continuity conditions, particularly on the derivatives of the density functions, are relaxed at the element ends for the sake of simplicity in approximating the unknown density functions. In this paper, a numerical study on the e¤ects of satisfying or violating the continuity requirements and the e¤ect of the boundary condition collocating point on three di¤erent BEM formulations is presented. Two are indirect formulations using force singularities and displacement discontinuity singularities, and the third is RizzoÕs direct formulation. The two integral operators in the direct BEM appear individually in the two di¤erent formulations of the indirect BEM. This makes it possible to study the numerical error and other problems in each integral operator and the interaction of the two integral operators in the direct BEM. The impact of the study on numerical modelling for the three BEM formulations is presented in the paper