Aplicação do Método de Houbolt na formulação de Elementos de Contorno com Dupla Reciprocidade
DOI:
https://doi.org/10.29215/pecen.v4i0.1558Resumo
Neste trabalho, a formulação da dupla reciprocidade no método dos elementos de contorno é revisitada numa aplicação a problemas de campo vetorial como são os problemas elastodinâmicos. São estudados problemas onde a resposta dinâmica é resolvida utilizando o esquema de Houbolt para a integração temporal. Dois exemplos são apresentados, resolvidos e o desempenho deles é comparado com soluções analíticas. Finalmente é analisado o efeito da introdução de pontos internos no domínio do corpo.
Palavras chave: Esquema de Houbolt, método dos elementos de contorno, dupla reciprocidade.
Referências
Bathe K.J. (1996) Finite Element Procedures. New Jersey: Prentice Hall. 1037 p.
Brebbia C.A. & Dominguez J. (1994) Boundary Elements: An Introductory Course. Southampton: WIT. 322 p.
Brebbia C.A., Telles J.C.F. & Wrobel L.C. (2012) Boundary Element Techniques. Berlin: Springer. 464 p.
Burden R.L. & Faires J.D. (2008) Análise Numérica. São Paulo: Cengage do Brasil. 736 p.
Cheng A.H.D., Cheng C.S., Goldberg M.A. & Rashed Y.F. (2001) BEM for thermoelasticity and elasticity with body force - a revisit. Engineering Analysis with Boundary Elements, 25: 377–387. https://doi.org/10.1016/S0955-7997(01)00032-7
Guendelman T. (2008) Análise estático y dinámico de estruturas. La Serena: Universidad de la Serena. 236 p.
Hetenyi M. (1971) Beams on elastic foundation: theory with application in the fields of civil and mechanical engineering. Michigan: University of Michigan Press. 264 p.
Houbolt J. C. (1950) A recurrence matrix solution for the dynamic response of elastic aircraft. Journal of the Aerospace Sciences, 17: 540–550. https://doi.org/10.2514/8.1722
Katsikadelis J. (2002) Boundary Elements: Theory and Applications. Oxford: Elsevier Science. 448 p.
Klaseboer E., Sun Q. & Chan D.Y.C. (2019) Helmholtz decomposition and boundary element method applied to dynamic linear elastic problems. Journal of Elasticity, 137: 83–100. https://doi.org/10.1007/s10659-018-09710-y
Lei J., Yun L. & Zhang C. (2017) An interaction integral and a modified crack closure integral for evaluating piezoelectric crack-tip fracture parameters in BEM. Engineering Analysis with Boundary Elements, 79: 88–97. https://doi.org/10.1016/j.enganabound.2017.04.001
Li J., Shi Z. & Liu L. (2018) A unified scaled boundary finite element method for transient two-dimensional vibro-acoustic analysis of plate-like structures. Computers and Structures, 202: 105–128. https://doi.org/10.1016/j.compstruc.2018.03.004
Li C., Ooi E.T., Song C. & Natarajan S. (2015) SBFEM for frature analysis of piezoelectric composites under thermal load. International Journal of Solids and Structures, 52: 114–129. https://doi.org/10.1016/j.ijsolstr.2014.09.020
Malvern L.E. (1969) Introduction to the Mechanics of a Continuous Medium. New Jersey: Prentice-Hall. 771 p.
Meirovitch L. (1975) Elements of Vibration Analysis. USA: McGraw-Hill Int. 495 p.
Morovati V. & Malek A. (2015) Solving inhomogeneous magnetohydrodynamic flow equations in an infinite region using boundary element method. Engineering Analysis with Boundary Elements, 58: 202–221. https://doi.org/10.1016/j.enganabound.2015.04.021
Mukhtar F.M. (2017) Relative performance of the three mesh-reduction methods in predicting mode III crack-tip singularity. Latin American Journal of Solids and Structures, 14: 1226–1250. https://doi.org/10.1590/1679-78253656
Nardini D. & Brebbia C.A. (1983) A new approach to free vibration analysis using boundary elements. Applied Mathematical Modelling, 7: 157–162.
https://doi.org/10.1016/0307-904X(83)90003-3
Nogueira F.C. & Loeffler C.F. (1991) Resposta dinâmica com o Método dos Elementos de Contorno utilizando Superposição Modal. Revista Militar de Ciência e Engenharia, 8: 36–49.
Partridge P.W., Brebbia C.A. & Wrobel L.C. (1991) The Dual Reciprocity Boundary Element Method. Berlin: Computational Mechanics Publications. 276 p.
Parvanova S., Vasilev G. & Dineva P. (2020) Hybrid modelling of multi-layered geological structure under seismic excitation. Journal of Seismology, 24: 183–202.
https://doi.org/10.1007/s10950-019-09896-1
Rama B.B. & Rao V.D. (2001) Advanced Dynamics. Pangbourne: CRC Press. 395 p.
Sayyad A.S. & Ghugal Y.M. (2016) Single variable refined beam theories for the bending, buckling and free vibration of homogenous beam. Applied and Computational Mechanics, 10: 123–138.
Trevelyan J. (1994) Boundary Elements for Engineers: Theory and Applications. Southampton: WIT. 228 p.
Vera-Tudela C.A.R. (2003) Formulações Alternativas do MEC para Problemas Elastodinâmicos de Mecânica da Fratura com o uso da Função de Green Numérica. Tese (Programa de Pós-Graduação em Engenharia Civil). Instituto Alberto Luiz Coimbra de Pós-Graduação e Pesquisa de Engenharia, Universidade Federal do Rio de Janeiro, Rio de Janeiro.
Wang W., Ye W. & Jiang Y. (2019) A scaled boundary finite element method for bending analysis of fiber-reinforced piezoelectric laminated composite plates. International Journal of Mechanical Sciences, 161–162: 105011. https://doi.org/10.1016/j.ijmecsci.2019.105011
Ye W., Liu J., Lin G., Xu B. & Yu L. (2018) Application of scaled boundary finite element analysis for sloshing characteristics in an annular cylindrical container with porous structures. Engineering Analysis with Boundary Elements, 97: 94–113.
https://doi.org/10.1016/j.enganabound.2018.09.013
Yee K.S. (1966) Numerical solution of initial boundary value problems involving Maxwell’s equations in isotropic media. IEEE Transactions on Antennas and Propagation, 14(3): 302–307. https://doi.org/10.1109/TAP.1966.1138693
Zhao C., Ailor M. & Gray L.J. (1994) Interior point evaluation in the boundary element method. Engineering Analysis with Boundary Elements, 13: 201–208. https://doi.org/10.1016/0955-7997(94)90022-1
Downloads
Publicado
Edição
Seção
Licença
Autores que publicam nesta revista concordam com os seguintes termos / Authors who publish in this journal agree to the following terms:
A) Autor(es) e o periódico mantêm os direitos da publicação; os autores concedem ao periódico o direito de primeira publicação, sendo vedada sua reprodução total ou parcial sob qualquer caráter de ineditismo; qualquer utilização subsequente de trechos de manuscritos (e.g., figuras, tabelas, gráficos etc.) publicados na Pesquisa e Ensino em Ciências Exatas e da Natureza deve reconhecer a autoria e publicação original / Author (s) and the journal maintain the rights of publication; the authors grant the journal the right of first publication, being prohibited their total or partial reproduction in any character of novelty; any subsequent use of excerpts from manuscripts (e.g., figures, tables, graphics, etc.) published in Research and Teaching in Exact and Natural Sciences must acknowledge the original authorship and publication.
B) Autores tem o direito de disseminar a própria publicação, podendo, inclusive disponibilizar o PDF final do trabalho em qualquer site institucional ou particular, bem como depositar a impressão da publicação em bibliotecas nacionais e internacionais / Authors have the right to disseminate the publication itself, and may also make available the final PDF of the work in any institutional or private site, as well as depositing the printing of the publication in national and international libraries.