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Master's Dissertation
DOI
10.11606/D.18.2001.tde-17062001-095633
Document
Author
Full name
Valério Júnior Bitencourt de Souza
E-mail
Institute/School/College
Knowledge Area
Date of Defense
Published
São Carlos, 2001
Supervisor
Committee
Coda, Humberto Breves (President)
Lindenberg Neto, Henrique
Paiva, Joao Batista de
Title in Portuguese
Algoritmos de integração eficientes para o método dos elementos de contorno tridimensional.
Keywords in Portuguese
elasticidade tridimensional
elementos de contorno
técnicas de integração
Abstract in Portuguese
Neste trabalho é analisado o problema elástico tridimensional através do método dos elementos de contorno empregando a solução fundamental de Kelvin. São utilizadas duas formulações principais: a formulação clássica e a formulação hiper-singular. A primeira utiliza a solução fundamental de Kelvin clássica e a segunda aplica uma derivada direcional da solução fundamental de Kelvin. O contorno é discretizado utilizando-se elemento triangular plano com aproximações constante, linear e quadrática. As integrais singulares são desenvolvidas analiticamente para o elemento constante, e semi-analiticamente para os elementos linear e quadrático. São apresentadas técnicas de integração de contorno considerando-se a eficiência e a precisão para a integral quase singular. São apresentados vários exemplos numéricos, inclusive problemas esbeltos, e seus resultados são comparados com valores conhecidos pela teoria de elasticidade, ou ainda, comparados com valores disponíveis na literatura.
Title in English
Efficient integration algorithms for the three-dimensional boundary element method.
Keywords in English
boundary elements
integration techniques
three-dimensional elasticity
Abstract in English
In this work the three-dimensional elastic problem is analyzed by the boundary element method using the Kelvin fundamental solution. Two main formulations are applied. The first one uses the classical Kelvin fundamental solution and the other, hyper-singular, uses a derivative of the Kelvin fundamental solution. The boundary is discretized by flat triangular elements with constant, linear and quadratic approximations. The singular integrals are analytically developed for constant elements, while for linear and quadratic elements a semi-analytical process is employed. Different techniques to perform quasi-singular boundary integrals are presented and their efficiency and accuracy are compared. Several numerical examples are presented, including slender problems. The results are compared with known solutions given by the theory of elasticity, or with other results found in the literature.
 
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Publishing Date
2001-06-19
 
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