Aplicação do esquema recursivo do método dos elementos de contorno em problemas de elasticidade

Abstract

This work presents the use of recursive integral equation of the Boundary Element Method (BEM) in problems of linear elasticity in order to improve the accuracy of their numerical results. Generally, the values at internal points of the domain with BEM are determined by applying the recursive integral equation after all the nodal values on the boundary are calculated. In scalar potential problems, demonstrates that the same idea can be used to improve the accuracy of the results on the boundary. Instead of the locating new source points within the domain, they are positioned on the boundary with different coordinates of nodal points. Thus, the values of the basic variable and its spatial derivatives at the boundary can be recalculated based on the previously calculated values of the contour. The result of this numerical procedure is based on the mathematical equivalence between the recursive use of boundary integral equation and the new application of the sentence of weighted residuals associated with the equation of government. In this paper, the procedure is applied to solve problems expressed by the Navier equation. Comparing the numerical results of the percentage errors made in calculating the potential and its derivative with examples of elasticity inwich the analytical solution is known and also the seamless integration with BEM, we evaluate the performance of the proposed procedure.