Abstract
A steady state harmonic solution of Navier equations of motion is presented using the symmetric Galerkin Boundary Element Method, which leads to a symmetric system of equations. For the integration, a two-step regularisation process is proposed to deal with the singularities of the involved kernels. It is also shown that the standard application of the symmetric Galerkin methodology for multiply connected bodies leads to the deterioration of the conditioning of the system for low frequencies. Two examples are presented comparing the solutions obtained with the proposed formulation with those obtained with the standard collocation method. A third example is presented to illustrate the behaviour of a simple multi-connected body.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Beskos, D.E., 'Boundary element methods in dynamic analysis: Part II (1986-1996)', Appl.Mech. Rev. 50(3) (1997) 149-196.
Sirtori, S., 'General stress analysis method by means of integral equations and boundary elements', Meccanica 14 (1979) 210-218.
Kane, J.H. and Balakrishna, C., 'Symmetric Galerkin boundary formulations employing curved elements', Int. J. Numer. Meth. Engng. 36 (1993) 2157-2187.
Bonnet, M., Maier, G. and Polizzotto, C., 'Symmetric Galerkin boundary element methods', Appl. Mech. Rev. 51(11) (1998) 669-704.
Maier, G., Diligenti, M. and Carini, A., 'A variational approach to boundary element elastodynamic analysis and extension to multidomain problems', Comput. Meth. Appl. Mech. Engng 92 (1991) 193-213.
Bielak, J., MacCamy, R.C., McGhee, D.S. and Barry, A., 'Unified symmetric BEM-FEM for site effects on ground motion - SH waves', J. Eng. Mech. ASCE 117 (1991) 2265-2285.
Davi, G. and Milazzo, A., 'A symmetric and positive definite variational BEM for 2-D free vibration analysis', Engng Anal. Bound. Elem. 14 (1994) 343-348.
Pérez-Gavilán, J.J. and Aliabadi, M.H., 'A symmetric Galerkin BEM for multi-connected bodies: a new approach', Engng Anal. Bound. Elem. 25 (2001) 633-638.
Dominguez, J., Boundary Elements in Dynamics, Computational Mechanics Publications, Elsevier Applied Science, 1993.
Dominguez, J. and Abascal, R., 'On fundamental solutions for the boundary integral equations method in static and dynamic elasticity', Engng Anal. 1(3) (1984) 128-134.
Telles, J.C. F. and Olivera, R.F., 'Third degree polynomial transformation for boundary element integrals: further improvements', Engng Anal. Bound. Elem. 13(2) (1994) 135-141.
Sirtori, S., Maier, G., Novati, G. and Miccoli, S., 'A Galerkin symmetric boundary element method in elasticity: formulation and implementation'. Int. J. Num. Meth. Eng. 35 (1992) 255-282.
Pérez-Gavilán, J.J. and Aliabadi, M.H., 'A Galerkin boundary element formulation with dual reciprocity for elastodynamics', Int. J. Num. Meth. Engng 48 (2000) 1331-1344.
Cruse, T.A. and Rizzo, F.J., 'A direct formulation and numerical solution for the general transient elastodynamic problem-I', J. Math. Anal. 22 (1968) 244-359.
Fedelinski, P., Aliabadi, M.H. and Rooke, D.P., 'Laplace transform DBEM for mixed-mode dynamic crack analysis', Comput. Struct. 59(6) (1996) 1021-1031.
Kane, J.H., Boundary Element Analysis in Engineering Continuum Mechanics, Prentice Hall, New York, 1994.
Pérez-Gavilán, J.J. and Aliabadi, M.H., 'A symmetric Galerkin boundary element method for dynamic frequency domain viscoelastic problems', Comput. Struct. (accepted).
Chen, G. and Zhou, J., Boundary Element Methods, Chap. 9, Academic Press, London, 1992.
Pérez-Gavilán, J.J. and Aliabadi, M.H., 'A symmetric Galercin BEMfor multi-connected bodies', Common. Numer.Meth. Engng (in press).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
PÉrez-GavilÁn, J., Aliabadi, M. A Symmetric Galerkin BEM for Harmonic Problems and Multiconnected Bodies. Meccanica 36, 449–462 (2001). https://doi.org/10.1023/A:1015049225649
Issue Date:
DOI: https://doi.org/10.1023/A:1015049225649