Método dos elementos de contorno com interpolação direta regularizado aplicado a problemas de elasticidade linear com força de corpo

Abstract

Numerical methods have become indispensable for the progress and development of knowledge and technology in the areas of Science and Engineering. Among the various methods already developed, the Boundary Elements Method (BEM) has stood out for its uniqueness and applicability. To increase its field of action, new techniques, based on the BEM, have been proposed with the purpose of improving and expanding this method, as is the case of the DIBEM (Direct Interpolation Boundary Elements Method), which uses a process of interpolation using Radial Base Functions (RBF) to transform domain integrals into boundary integrals. In this context, the present work seeks to apply DIBEM in elastic problems with acting body forces, expanding the area of knowledge of this recent technique. For this, the governing equations of the Elasticity Theory, the BEM formulations for this type of problem, the mathematical development of the DIBEM interpolation and regularization procedure on the body force domain integral and also the discretization process are presented. of the contour that results in the system that is used for the numerical solution of the simulated elastic problems. Numerical tests with problems that have a known analytical solution are used to validate the method and to analyze the behavior of the responses generated when some parameters of the problem are modified. In addition to the analytical solutions, the DIBEM is also compared with the classical BEM technique that uses the Galerkin tensor to transform a body force integral into a boundary integral.