Abstract
Previous works have demonstrated that the concepts introduced by Pian in the finite element method may be generalized in terms of boundary integrals, resulting in a variationally consistent formulation [1, 2]. As a matter of further generalization, De Oliveira [3] developed some basic formulations of the hybrid boundary element method (HBEM) for time dependent problems. He also demonstrated that too simple formulations, as arrived at from the static fundamental solution, in which the dynamic equilibrium is not explicitly ensured, yield bad numerical results related to high vibration frequencies. Such inaccuracies are also observed in the conventional boundary element formulation (BEM), in case of the double reciprocity with no internal points -and even in the finite element method (FEM), if one eliminates the internal degrees of freedom by means of a static condensation [4, 5].
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References
N. A. Dumont, The Hybrid Boundary Element Method, Boundary Elements IX, Vol 1: Mathematical and Computational Aspects, Brebbia C. A., Wendland W. L, Kuhn, G., eds., Computational Mechanics Publications, Springer-Verlag, pp 125–138 (1987)
N. A. Dumont, The Hybrid Boundary Element Method: an Alliance Between Mech. Consistency and Simplicity, Appl. Mech. Rev., Vol 42 (1980) Nr.11, pp S54–S63
R. de Oliveira, O Método Híbrido dos Elementos de Contorno para a Análise de Problemas Dependentes do Tempo, Ph.D. Thesis, PUC/RJ, Rio de Janeiro (1994)
N. A. Dumont and R. de Oliveira, The Hybrid Boundary Element Method Applied to Time-Dependent Problems, Boundary Elements XV, Vol. 2, pp 363–376, Comput. Mechanics Publications, Elsevier Applied Science (1993)
N. A. Dumont and R. de Oliveira, Mass Matrix Determination in Hybrid Boundary Element Method, XII COBEM, Brasília, Brazil, Vol 1, pp 233–236 (1993)
W. J. Mansur, A Time-Stepping Technique to Solve Wave Propagation Problems Using the Boundary Element Method, Ph.D. Thesis, University of Southampton (1983)
N. Kamiya, E. Andoh, and K. Nogae, Standard Eigenvalue Analysis by Boundary Element Method, Commun. Num. Meth. Eng. Vol 9 (1993) Nr. 6, pp 489–495
A. J. Novak, Temperature Fields in Domains with Heat Sources using Boundary only Formulations, Boundary Elements X, Comp. Mech. Pub., Vol.2, pp 233–247 (1988)
J. S. Przemieniecki, Theory of Matrix Structural Analysis, Dover Publications, Inc. New York (1968)
N. A. Dumont and R. de Oliveira, Urna Form. em Série de Freqüência no Mét. Híbrido dos Eiem. de Contorno, XIV CILAMCE, São Paulo, Vol 1, pp 335–344 (1993)
N. A. Dumont and R. de Oliveira, Sobre a Determinação Aproximada de matrizes de Massa Dependentes da Freqüência no Método Híbrido dos Elementos de Contorno, XV CILAMCE, Belo Horizonte, Brazil, Vol I, pp 591–600 (1994)
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Dumont, N.A., de Oliveira, R. (1995). On The Determination of Approximate Frequency-Dependent Mass Matrices in The Hybrid Boundary Element Method. In: Atluri, S.N., Yagawa, G., Cruse, T. (eds) Computational Mechanics ’95. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79654-8_506
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DOI: https://doi.org/10.1007/978-3-642-79654-8_506
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