Abstract
So far we have discussed problems that are independent of time and neglected inertial effects. It is therefore appropriate to extend the discussion of the theory and implementation to problems in dynamics. We have already seen that the Boundary Element Method has distinct advantages over the Finite Element Method for static problems involving infinite domains. This advantage is even more pronounced for dynamic problems since we will see that the fundamental solutions used in the BEM implicitly fulfil the radiation conditions. It is known that the FEM which requires the truncation of the mesh has the problem that waves may be reflected at truncation boundaries. In this Chapter we will only give an overview of the implementation of dynamic problems. For more details the reader is referred to relevant publications.
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References
Banerjee P.K. (1994) The Boundary Element Methods in Engineering, McGraw Hill Book Company, London.
Manolis G.D. and Beskos D.E. (1988) Boundary Element Methods in Elastodynamics. Unwin-Hyman, London.
Dominguez, J. (1993) Boundary Elements in Dynamics. Computational Mechanics Publications, Southampton.
Bonnet, M. (1995) Boundary Integral Equation Methods for Solids and Fluids, J.Wiley.
Chopra A.K. (2007) Dynamics of Structures. Pearson Prentice Hall.
Lubich (1988) Convolution quadrature and discretized operational calculus I. Numerische Mathematik. 52: 129–145.
Kreyszig, E. (1999) Advanced Engineering Mathematics. J. Wiley
Wheeler L.T and Sternberg E. (1968) Some theorems in classical elastodynamics. Arch. Rational Mech. Anal. 31:51–90.
Pereira A. (2006) A Duhamel integral approach based on BEM to 3-D elasto-dynamic multi-region problems. IABEM, Verlag der TU Graz, Austria, 71–74.
Pereira A. (2008) PhD thesis, Graz University of Technology, Austria.
Schanz M. (2001) Wave propagation in viscoelastic and poroelastic continua. Springer, Berlin
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(2008). Dynamic Analysis. In: The Boundary Element Method with Programming. Springer, Vienna. https://doi.org/10.1007/978-3-211-71576-5_14
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DOI: https://doi.org/10.1007/978-3-211-71576-5_14
Publisher Name: Springer, Vienna
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