Algoritmos não-singulares do método dos elementos de contorno para problemas bidimensionais de elasticidade

Abstract

Three non-singular boundary element algorithms for bidimensional elastostatics have been implemented in this work. The first algorithm is based on the standard boundary integral equation (BIE) with external collocation points. The other two algorithms are based on the self-regular form of the displacement and traction BIE. The displacement field is required to achieve C1, Hölder continuity in the self-regular tractionformulation. This requirement is not met by the use of standard boundary elements. Thus, a relaxed continuity hypothesis is adopted, allowing the displacement field to be C1, piecewise continuous. This formulation makes use of the displacement tangential derivatives, which are not part of the original BIE and are obtained from the derivatives of the element interpolation functions. Therefore, two additonal possible sources of error are introduced in the implementation of the self-regular tractionformulation with continuous elements. In order to establish the dominant error source, discontinuous elements are adopted. These elements satisfy the continuity requirement at each collocation point, so the sources of error can be split. In a post-processing stage, the displacements and stresses at internal points are obtained, either through the classical boundary element formulations, or through the self-regular formulations. In general, the standard formulation with external collocation points have provided accurate results. Nevertheless, the self-regular displacement formulation seems to be the best approach on the evaluation of elastostatic problems. The self-regular tractionformulation with continuous elements have not presented results accurate enough, for all problems, and in some cases it was not possible to guarantee the results convergence. However, the use of discontinuous elements represented a significant gain in resultsaccuracy, which led us to believe that the relaxed continuity approach is probably the most important error source in this algorithm. The self-regular formulations for displacements and stresses at internal points are shown to be very reliabe. The results obtained by means of these formulations are very accurate and stable, and do not depend on the internal point location regarding the boundary.