Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática
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2013-07-31
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Universidade Federal de Goiás
Resumo
The Boundary Element Method (BEM) has been successfully employed in the analysis of various engineering problems. The BEM consists in a mathematical modeling, for a numerical solution of a system of integral equations, and in their cores may appear singularities. This paper presents the Classical and Hypersingular formulation of the Boundary Element Method for dimensional elastostatic problems with smooth boundary geometry. The improper integrals arising from the singularities of the core in the hypersingular formulation are treated by Hadamard finite parts. In the discretization process two types of interpolation are used, one traditional and the other special. Traditional interpolation is used in all bondary elements that have no point , special interpolation ensures the continuity of the tangential derivative of displacements on the element that contains the point . To accomplish this, a theoretical mathematics study of related topics was performed. The hypersingular formulation developed in this work was implemented through the Intel Visual Fortran compiler. Some problems were analyzed and the obtained results were compared with those of analytical solution or through the Finite Element Method. The results achieved were satisfactory validating the proposed formulation
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SANTOS, Claudia Gomes de Oliveira. Formulação hipersingular do método dos elementos de contorno para a solução de problemas bidimensionais de elastostática. 2013. 98 f. Dissertação (Mestrado em Engenharia Civil) - Universidade Federal de Goiás, Goiânia, 2013.