Abstract
Procedures based on group representation theory, allowing the exploitation of geometrical symmetry in symmetric Galerkin BEM formulations of 3D elastodynamic problems, are developed. They are applicable for both commutative and noncommutative finite symmetry groups and to partial geometrical symmetry, where the boundary has two disconnected components, one of which is symmetric.
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References
Allgower, E. L., Georg, K., Miranda, R., Tausch, J. Numerical Exploitation of Equivariance. Z. Angew. Math. Mech., 78, 795–806 (1998).
Bonnet, M. On the use of geometrical symmetry in the boundary element methods for 3D elasticity. In C.A. Brebbia (ed.), Boundary element technology VI, pp. 185–201. Comp. Mech. Publ., Southampton / Elsevier, Southampton, Boston (1991).
Bonnet, M., Maier, G., Polizzotto, C. On symmetric galerkin boundary element method. Appl. Mech. Rev., 51, 669–704 (1998).
Bossavit, A. Symmetry, groups and boundary value problems: a progressive introduction to noncommutative harmonic analysis of partial differential equations in domains with geometrical symmetry. Comp. Meth. in Appl. Mech. Engng., 56, 167–215 (1986).
Eringen, A. C., Suhubi, E. S. Elastodynamics (vol II — linear theory). Academic Press (1975).
Lobry, J., Broche, C.H. Geometrical symmetry in the boundary element method. Engng. Anal. with Bound. Elem., 14, 229–238 (1994).
Nedelec, J. C. Integral equations with non integrable kernels. Integral equations and operator theory, 5, 562–572 (1982).
Serre, J. P. Linear representations of finite groups. Springer-Verlag (1977).
Vinberg, E. B. Linear representations of groups. Birkhäuser (1989).
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© 2002 Springer-Verlag Berlin Heidelberg
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Bonnet, M. (2002). Exploiting Partial or Complete Geometrical Symmetry in Boundary Integral Equation Formulations of Elastodynamic Problems. In: Babuška, I., Ciarlet, P.G., Miyoshi, T. (eds) Mathematical Modeling and Numerical Simulation in Continuum Mechanics. Lecture Notes in Computational Science and Engineering, vol 19. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-56288-4_18
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DOI: https://doi.org/10.1007/978-3-642-56288-4_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42399-7
Online ISBN: 978-3-642-56288-4
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