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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| Veröffentlicht in: | Journal of computational physics Jg. 394; S. 532 - 558 |
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| Abstract | •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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| AbstractList | 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. •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. |
| Author | Chehade, Samar Lebeau, Gilles Darmon, Michel |
| Author_xml | – sequence: 1 givenname: Samar orcidid: 0000-0002-4879-735X surname: Chehade fullname: Chehade, Samar email: samar.chehade@cea.fr organization: CEA LIST, Department of Imaging & Simulation for Nondestructive Testing, CEA-Saclay, DIGITEO LABs, bat 565, 91191 Gif-sur-Yvette, France – sequence: 2 givenname: Michel orcidid: 0000-0002-8209-3225 surname: Darmon fullname: Darmon, Michel email: michel.darmon@cea.fr organization: CEA LIST, Department of Imaging & Simulation for Nondestructive Testing, CEA-Saclay, DIGITEO LABs, bat 565, 91191 Gif-sur-Yvette, France – sequence: 3 givenname: Gilles surname: Lebeau fullname: Lebeau, Gilles email: lebeau@unice.fr organization: Laboratoire J.A. Dieudonné, UMR CNRS 7351, Université de Nice Sophia-Antipolis, Parc Valrose, 06108 Nice, France |
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| Keywords | Numerical methods (spectral and related methods) Wave scattering Elastic wedge |
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| Snippet | •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... 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... |
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| SubjectTerms | Acoustics Collocation methods Computational physics Elastic wedge Mathematical analysis Mechanics Numerical methods (spectral and related methods) Physics Plane waves Wave diffraction Wave scattering Wedges |
| Title | 2D elastic plane-wave diffraction by a stress-free wedge of arbitrary angle |
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