General time-dependent analysis with the frequency-domain hybrid boundary element method

  • Ney Augusto Dumont Pontifίcia Universidade Catόlica do Rio de Janeiro
  • Ricardo A. P. Chaves Pontifίcia Universidade Catόlica do Rio de Janeiro

Abstract

The paper presents an attempt to consolidate a formulation for the general analysis of the dynamic response of elastic systems. Based on the mode-superposition method, a set of coupled, higher-order differential equations of motion is transformed into a set of uncoupled second order differential equations, which may be integrated by means of standard procedures. The first motivation for these theoretical developments is the hybrid boundary element method, a generalization of T. H. H. Pian's previous achievements for finite elements which, requiring only boundary integrals, yields a stiffness matrix for arbitrary domain shapes and any number of degrees of freedom. The method is also an extension of a formulation introduced by J. S. Przemieniecki, for the free vibration analysis of bar and beam elements based on a power series of frequencies, that handles constrained and unconstrained structures, non-homogeneous initial conditions given as nodal values as well as prescribed domain fields (including rigid body movement), forced time-dependent displacements, and general domain forces (other than inertial forces).

Keywords

References

[1] J. S. Przemieniecki. Theory of Matrix Structural Analysis. Dover Pubis., New York, 1968.
[2] T. H. H. Pian. Element stiffness matrices for boundary compatibility and for prescribed boundary stresses. In: Proc. Conf. on Matrix Meths. in Struct. Mech., AFFDL-TR-66-80, pages 457-477, Wright Patterson Air Force Base, Ohio, 1966.
[3] N. A. Dumont, D. R. L. Nunes, R. A. P. Chaves. Analysis of general transient problems with the hybrid boundary element method. In: Proceedings Third Joint Conference of Italian Group of Computational Mechanics and IberoLatin American Association of Computational Methods in Engineering, Giulianova, Italy, 2002. 10 pp in CD.
[4] N. A. Dumont, R. A. P. Chaves. Analysis of general time-dependent problems with the hybrid boundary element method. In: BETECH 15 - 15th International Conference on Boundary Element Technology, Detroit, USA, 2003.
[5] N. A. Dumont, R. A. P. Chaves. Simplified hybrid boundary element method applied to general time-dependent problems. In: S. Valliappan and N. Khalili, editors, Computational Mechanics - New Frontiers for the New
Millenium (Proceedings of the First Asian-Pacific Congress on Computational Mechanics), Sydney, Australia, 2001. Elsevier Science Ltd.
Published
Jan 26, 2023
How to Cite
DUMONT, Ney Augusto; CHAVES, Ricardo A. P.. General time-dependent analysis with the frequency-domain hybrid boundary element method. Computer Assisted Methods in Engineering and Science, [S.l.], v. 10, n. 4, p. 431- 452, jan. 2023. ISSN 2956-5839. Available at: <https://cames.ippt.gov.pl/index.php/cames/article/view/1056>. Date accessed: 13 nov. 2024.
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Articles