Transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide
july, 2007
Publication type:
Conference without proceedings
Conference:
8th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'07), Reading
Abstract:
This work concerns the numerical finite element computation, in the frequency
domain, of the diffracted wave produced by a defect (crack, inclusion,
perturbation of the boundaries etc..) located in an infinite elastic waveguide.
The objective is to use modal representations to build transparent conditions on
the artificial boundaries of the computational domain. This cannot be achieved
in a classical way, due to non standard properties of elastic modes. In
particular, the derivation of a ``Dirichlet-to-Neumann'' operator (relating
the normal stress to the displacement) is not tractable. However, a
biorthogonality relation allows to build an operator, relating hybrids
displacement/stress vectors. An original mixed formulation is then derived and
implemented, whose unknowns are the displacement field in the bounded domain
and the normal component of the normal stresses on the artificial boundaries.
Numerical validations are presented in the two-dimensional case.
BibTeX:
@conference{Bar-Bon-Lun-2007-1, author={Vahan Baronian and Anne-Sophie Bonnet-BenDhia and Eric Lunéville }, title={Transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide }, publisher={8th International Conference on Mathematical and Numerical Aspects of Waves (WAVES'07), Reading }, year={2007 }, month={7}, }