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Transparent boundary conditions for the harmonic diffraction problem in an elastic waveguide

✍ Scribed by V. Baronian; A.S. Bonnet-Ben Dhia; E. Lunéville

Publisher
Elsevier Science
Year
2010
Tongue
English
Weight
491 KB
Volume
234
Category
Article
ISSN
0377-0427

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✦ Synopsis

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 a 3D infinite elastic waveguide. The objective is to use modal representations to build transparent conditions on some artificial boundaries of the computational domain. This cannot be achieved in a classical way, due to non-standard properties of elastic modes. However, a biorthogonality relation allows us to build an operator, relating hybrid 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 2D case.

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