A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries
The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applicatio...
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Published in | Ultrasonics Vol. 40; no. 1; pp. 177 - 180 |
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Main Authors | , |
Format | Journal Article Conference Proceeding |
Language | English |
Published |
Amsterdam
Elsevier B.V
01.05.2002
Elsevier Science |
Subjects | |
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Abstract | The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials.
In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge–Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE. |
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AbstractList | The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge-Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE. The use of ultrasound to measure elastic field parameters as well as to detect cracks in solid materials has received much attention, and new important applications have been developed recently, e.g., the use of laser generated ultrasound in non-destructive evaluation (NDE). To model such applications requires a realistic calculation of field parameters in complex geometries with discontinuous, layered materials. In this paper we present an approach for solving the elastic wave equation in complex geometries with discontinuous layered materials. The approach is based on a pseudospectral elastodynamic formulation, giving a direct solution of the time-domain elastodynamic equations. A typical calculation is performed by decomposing the global computational domain into a number of subdomains. Every subdomain is then mapped on a unit square using transfinite blending functions and spatial derivatives are calculated efficiently by a Chebyshev collocation scheme. This enables that the elastodynamic equations can be solved within spectral accuracy, and furthermore, complex interfaces can be approximated smoothly, hence avoiding staircasing. A global solution is constructed from the local solutions by means of characteristic variables. Finally, the global solution is advanced in time using a fourth order Runge–Kutta scheme. Examples of field prediction in discontinuous solids with complex geometries are given and related to ultrasonic NDE. |
Author | Hesthaven, J.S. Nielsen, S.A. |
Author_xml | – sequence: 1 givenname: S.A. surname: Nielsen fullname: Nielsen, S.A. email: srn@force.dk organization: Risø National Laboratory, Department of Optics and Fluid Dynamics, OFD-128, DK-4000 Roskilde, Denmark – sequence: 2 givenname: J.S. surname: Hesthaven fullname: Hesthaven, J.S. organization: Brown University, Division for Applied Mathematics, Providence, RI 02912, USA |
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Cites_doi | 10.1002/nme.1620070405 10.1016/0045-7825(95)00896-9 10.1137/S1064827596299470 10.1190/1.1442319 10.1137/0719047 10.1016/S0041-624X(99)00069-4 10.1785/BSSA0760041115 10.1190/1.1442885 |
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Keywords | Multi-domain Pseudospectral Complex geometries Elastic scattering Wave equation Stress analysis Spectral method Acoustic measurement Time domain method Chebyshev polynomial Material testing Elastic wave Collocation method Non destructive test Modeling |
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References | Nielsen, Toftegaard (BIB1) 2000; 38 Carcione (BIB6) 1996; 130 Nielsen, Bjørnø (BIB2) 1997; vol. 23 Achenbach (BIB7) 1975 Hesthaven (BIB9) 1999; 20 Bayliss, Jordan, LeMesurier, Turkel (BIB3) 1986; 76 Kosloff (BIB5) 1990; 55 Fornberg (BIB4) 1987; 52 Gordon, Hall (BIB8) 1973; 7 Gottlieb, Gunzburger, Turkel (BIB10) 1982; 19 Bayliss (10.1016/S0041-624X(02)00133-6_BIB3) 1986; 76 Gordon (10.1016/S0041-624X(02)00133-6_BIB8) 1973; 7 Nielsen (10.1016/S0041-624X(02)00133-6_BIB2) 1997; vol. 23 Fornberg (10.1016/S0041-624X(02)00133-6_BIB4) 1987; 52 Kosloff (10.1016/S0041-624X(02)00133-6_BIB5) 1990; 55 Hesthaven (10.1016/S0041-624X(02)00133-6_BIB9) 1999; 20 Achenbach (10.1016/S0041-624X(02)00133-6_BIB7) 1975 Carcione (10.1016/S0041-624X(02)00133-6_BIB6) 1996; 130 Nielsen (10.1016/S0041-624X(02)00133-6_BIB1) 2000; 38 Gottlieb (10.1016/S0041-624X(02)00133-6_BIB10) 1982; 19 |
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SubjectTerms | Acoustical measurements and instrumentation Acoustics Complex geometries Cross-disciplinary physics: materials science; rheology Elastic scattering Exact sciences and technology Fundamental areas of phenomenology (including applications) Materials science Materials testing Multi-domain Nondestructive testing: ultrasonic testing, photoacoustic testing Physics Pseudospectral Structural acoustics and vibration |
Title | A multi-domain Chebyshev collocation method for predicting ultrasonic field parameters in complex material geometries |
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