Aplicação do Método de Houbolt na formulação de Elementos de Contorno com Dupla Reciprocidade

Autores

  • Carlos Andrés Reyna Vera-Tudela Universidade Federal Rural do Rio de Janeiro

DOI:

https://doi.org/10.29215/pecen.v4i0.1558

Resumo

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

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Publicado

25-11-2020

Edição

Seção

CIÊNCIAS MATEMÁTICAS / MATHEMATICAL SCIENCES