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Modelling contact with isotropic and anisotropic friction by the bipotential approach
Few remarks on the use of Love waves in non destructive testing
1. | Département d'ingénierie mathématique, Conservatoire National des Arts et Métiers, 292, rue saint Martin, 75003 Paris, France |
2. | Laboratoire de mathématiques d'Orsay, Univ. Paris-Sud, CNRS, Université Paris-Saclay, 91405 Orsay, France |
References:
[1] |
M. Amara, Ph. Destuynder and M. Djaoua, On a finite element schem for plane crack problems, Numer. Meth. in Frac. Mech., D.R.J. Owen and A.R. Luxmoore, Pinridge Press, Swansea, (1980), 41-50. |
[2] | |
[3] | |
[4] |
P. G. Ciarlet, The Finite Element Mehod for Elliptic Problems, Elsevier, Amsterdam, 1978. |
[5] |
Ph. Destuynder and C. Fabre, Singularities occuring in multimaterials with traPHDCF3nsparent boundary conditions, to appear in Quaterly of Applied Maths, (2016). |
[6] |
Ph. Destuynder and C. Fabre, On the Detection of Cracks in Linear Elasticity, research report CNAM, 2015. |
[7] |
Ph. Destuynder and M. Djaoua, Sur une interpretation mathématique de l'intégrale de Rice en mécanique de la rupture fragile, Mathematical Methods in the Applied Sciences, 3 (1981), 70-87.
doi: 10.1002/mma.1670030106. |
[8] |
G. Diot, A. Kouadri-David, L. Dubourg, J. Flifla, S. Guegan and E. Ragneau, Mesures de Défauts par Ultrasons Laser Dans Des Soudures D'alliage D'aluminium, Publications du CETIM, 2014. |
[9] |
M. Dobrowolski, Numerical Approximation of Elliptic Interface and Corner Problems, Habilitationsschrift, Bonn, 1981. |
[10] |
J.-C. Dumont-Fillon, Contrôle non Destructif Par Les Ondes de Love et Lamb, Editions Techniques de l'ingénieur, 2012. |
[11] |
A. Galvagni and P. Cawley, The reflection of guided waves from simple supports in pipes, AIP Conf. Proc., 105 (2011), p1335.
doi: 10.1063/1.3591845. |
[12] |
E. Holmgren, Über systeme von linearen partiellen differentialgleichungen, Öfversigt af kongl, Vetenskaps-Academien Förhandlinger, 58 (1901), 91-103. |
[13] |
M. J. S. Lowe, Characteristics of the reflection of Lamb waves from defects in plates and pipes, Review of Progress in Quantitative NDE, DO Thompson and DE Chimenti (eds), Plenum Pr ess, New-York, 17 (2002), 113-120.
doi: 10.1007/978-1-4615-5339-7_14. |
[14] |
S. G. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999. |
[15] |
P. M. Marty, Modelling of Ultrasonic Guided Wave Field Generated by Piezoelectric Transducers, Thesis at Imperial college of science, technology and medecine, university of London, (2002), http://www3.imperial.ac.uk/pls/portallive/docs/1/50545711.PDF |
[16] |
J. Necas, Les Méthodes Directes en Théorie des Équations Elliptiques, Masson, Paris, (1965). |
[17] |
P. A. Raviart and J. M. Thomas, Approximation des Équations aux Dérivées Partielles, Masson, Paris, 1986. |
[18] |
R. Ribichini, F. Cegla, P. Nagy and P. Cawley, Study and comparison of different EMAT configurations for SH wave inspection, IEEE Trans.UFFC, 58 (2011), 2571-2581.
doi: 10.1109/TUFFC.2011.2120. |
[19] |
G. Strang and G. Fix, Analysis of the Finite Elements Method, Prentice Hall; Edition: First Edition, 1973. |
[20] |
A. N. Tychonoff, Solution of incorrectly formulated problems and the regularization method, Soviet Math Dokl, 4 (2011), 1035-1038; English translation of Dokl Akad Nauk SSSR, 151 (1963), 501-504. |
[21] |
D. Zagier, The Dilog function, http://maths.dur.ac.uk/~dma0hg/dilog.pdf (2007). |
show all references
References:
[1] |
M. Amara, Ph. Destuynder and M. Djaoua, On a finite element schem for plane crack problems, Numer. Meth. in Frac. Mech., D.R.J. Owen and A.R. Luxmoore, Pinridge Press, Swansea, (1980), 41-50. |
[2] | |
[3] | |
[4] |
P. G. Ciarlet, The Finite Element Mehod for Elliptic Problems, Elsevier, Amsterdam, 1978. |
[5] |
Ph. Destuynder and C. Fabre, Singularities occuring in multimaterials with traPHDCF3nsparent boundary conditions, to appear in Quaterly of Applied Maths, (2016). |
[6] |
Ph. Destuynder and C. Fabre, On the Detection of Cracks in Linear Elasticity, research report CNAM, 2015. |
[7] |
Ph. Destuynder and M. Djaoua, Sur une interpretation mathématique de l'intégrale de Rice en mécanique de la rupture fragile, Mathematical Methods in the Applied Sciences, 3 (1981), 70-87.
doi: 10.1002/mma.1670030106. |
[8] |
G. Diot, A. Kouadri-David, L. Dubourg, J. Flifla, S. Guegan and E. Ragneau, Mesures de Défauts par Ultrasons Laser Dans Des Soudures D'alliage D'aluminium, Publications du CETIM, 2014. |
[9] |
M. Dobrowolski, Numerical Approximation of Elliptic Interface and Corner Problems, Habilitationsschrift, Bonn, 1981. |
[10] |
J.-C. Dumont-Fillon, Contrôle non Destructif Par Les Ondes de Love et Lamb, Editions Techniques de l'ingénieur, 2012. |
[11] |
A. Galvagni and P. Cawley, The reflection of guided waves from simple supports in pipes, AIP Conf. Proc., 105 (2011), p1335.
doi: 10.1063/1.3591845. |
[12] |
E. Holmgren, Über systeme von linearen partiellen differentialgleichungen, Öfversigt af kongl, Vetenskaps-Academien Förhandlinger, 58 (1901), 91-103. |
[13] |
M. J. S. Lowe, Characteristics of the reflection of Lamb waves from defects in plates and pipes, Review of Progress in Quantitative NDE, DO Thompson and DE Chimenti (eds), Plenum Pr ess, New-York, 17 (2002), 113-120.
doi: 10.1007/978-1-4615-5339-7_14. |
[14] |
S. G. Mallat, A Wavelet Tour of Signal Processing, Academic Press, 1999. |
[15] |
P. M. Marty, Modelling of Ultrasonic Guided Wave Field Generated by Piezoelectric Transducers, Thesis at Imperial college of science, technology and medecine, university of London, (2002), http://www3.imperial.ac.uk/pls/portallive/docs/1/50545711.PDF |
[16] |
J. Necas, Les Méthodes Directes en Théorie des Équations Elliptiques, Masson, Paris, (1965). |
[17] |
P. A. Raviart and J. M. Thomas, Approximation des Équations aux Dérivées Partielles, Masson, Paris, 1986. |
[18] |
R. Ribichini, F. Cegla, P. Nagy and P. Cawley, Study and comparison of different EMAT configurations for SH wave inspection, IEEE Trans.UFFC, 58 (2011), 2571-2581.
doi: 10.1109/TUFFC.2011.2120. |
[19] |
G. Strang and G. Fix, Analysis of the Finite Elements Method, Prentice Hall; Edition: First Edition, 1973. |
[20] |
A. N. Tychonoff, Solution of incorrectly formulated problems and the regularization method, Soviet Math Dokl, 4 (2011), 1035-1038; English translation of Dokl Akad Nauk SSSR, 151 (1963), 501-504. |
[21] |
D. Zagier, The Dilog function, http://maths.dur.ac.uk/~dma0hg/dilog.pdf (2007). |
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