2D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle

•A new model is proposed for 2D elastic wave diffraction by a stress-free wedge.•The developed spectral functions method is valid for any wedge angle.•The numerical scheme for the spectral functions method is detailed.•The proposed model has been validated against two different numerical models. 2D...

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Bibliographic Details
Published in:Journal of computational physics Vol. 394; pp. 532 - 558
Main Authors: Chehade, Samar, Darmon, Michel, Lebeau, Gilles
Format: Journal Article
Language:English
Published: Cambridge Elsevier Inc 01.10.2019
Elsevier Science Ltd
Elsevier
Subjects:
Acoustics
Collocation methods
Computational physics
Elastic wedge
Mathematical analysis
Mechanics
Numerical methods (spectral and related methods)
Physics
Plane waves
Wave diffraction
Wave scattering
Wedges
Numerical methods (spectral and related methods)
Wave scattering
Elastic wedge
ISSN:0021-9991, 1090-2716
Online Access:Get full text
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Summary:•A new model is proposed for 2D elastic wave diffraction by a stress-free wedge.•The developed spectral functions method is valid for any wedge angle.•The numerical scheme for the spectral functions method is detailed.•The proposed model has been validated against two different numerical models. 2D elastic plane wave diffraction by a stress-free wedge is a canonical problem of interest to researchers in many different fields. To our knowledge, no fully analytical resolution has been found and semi-analytical evaluations of asymptotic approximations have therefore become a common approach. In this paper, a method called the spectral functions method is developed in the aforementioned 2D configuration. This method has the advantage of being valid for wedge angles lower and higher than π. The diffracted displacement field is expressed as an integral in terms of two unknown functions called the spectral functions. These functions are decomposed into two parts: one which can be computed analytically and the other which is approached numerically using a collocation method. The details of the corresponding numerical scheme are given and the method is validated numerically for all wedge angles.
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ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2019.06.016