BEM/OQM Formulation to Simulate Crack Problems
DOI:
https://doi.org/10.5540/tema.2008.09.02.0363Resumo
Over the last few years the Boundary Element Method (BEM) has been successfully applied to linear elastic fracture mechanics problems (LEFM), involving static and dynamic cases. An approach to solve LEFM problems is presented in this work. The Numerical Green’s Function is used at the fundamental solution together with the Operational Quadrature Method. Proceeding this way, there is no need to discretize the unloaded crack surface and the convolution integral is substituted bya Quadrature formula whose weights are computed using the Laplace transform of the fundamental solution and a linear multistep method. This solution strategy is here implemented to deal with problems associated with the scalar wave equation.Referências
[1] A.I. Abreu, J.A.M. Carrer, W.J. Mansur, Scalar wave propagation in 2-D: a BEM formulation based on the operational quadrature method, Engineering Analysis with Boundary Elements, 27, No. 2 (2003), 101-105.
L.P.S. Barra, J.C.F. Telles, A hyper-singular numerical Green’s function generation for BEM applied to dynamic SIF problems, Engineering Analysis with Boundary Elements, 23, (1999), 77-87.
G.E. Blandford, A.R. Ingraffea, J.A. Ligget. Two-dimensional stress intensity factor computation using the boundary element method, Int. J. Numer. Methods Eng., 17 (1981), 387-404.
C.A. Brebbia, J.C.F. Telles, L.C. Wrobel, “Boundary Elements Techniques: Theory and Applications”, Springer-Verlag, Berlin, 1984.
S. Guimar˜aes, J.C.F. Telles, On the hyper-singular boundary element formulation for fracture mechanics applications, Engineering Analysis with Boundary Elements, 13, (1994), 353-363.
C. Lubich, Convolution quadrature and discretized operational calculus II, Numer. Math., 52 (1988), 413-425.
C. Lubich, Convolution quadrature and discretized operational calculus I, Numer. Math. , 52 (1988), 129-145.
C. Lubich, On the multistep time discretization of linear initial-boundary value problems and their boundary integral equation, Numer. Math., 67 (1994), 365-389.
W.J. Mansur, “A Time-stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method”, Ph.D. Thesis, University of Southampton, England, 1983.
P.M. Morse, H. Feshbach, “Methods of Theoretical Physics”, McGraw-Hill, New York, 1953.
J.C.F. Telles, G.S. Castor, S. Guimar˜aes, A numerical Green’s function approach for boundary elements applied to fracture mechanics, International Journal for Numerical Methods in Engineering, 38 (1995), 3259-3274.
J.C.F. Telles, S. Guimar˜aes, Green’s function: a numerical generation for fracture mechanics problems via boundary elements, Comput. Methods Appl. Mech. Eng., 188 (2000), 847-858.
Downloads
Publicado
Como Citar
Edição
Seção
Licença
Direitos Autorais
Autores de artigos publicados no periódico Trends in Computational and Applied Mathematics mantêm os direitos autorais de seus trabalhos. O periódico utiliza a Atribuição Creative Commons (CC-BY) nos artigos publicados. Os autores concedem ao periódico o direito de primeira publicação.
Propriedade Intelectual e Termos de uso
O conteúdo dos artigos é de responsabilidade exclusiva dos autores. O periódico utiliza a Atribuição Creative Commons (CC-BY) nos artigos publicados. Esta licença permite que os artigos publicados sejam reutilizados sem permissão para qualquer finalidade, desde que o trabalho original seja corretamente citado.
O periódico encoraja os Autores a autoarquivar seus manuscritos aceitos, publicando-os em blogs pessoais, repositórios institucionais e mídias sociais acadêmicas, bem como postando-os em suas mídias sociais pessoais, desde que seja incluída a citação completa à versão do website da revista.