Skip to main content
Erschienen in: Experimental Mechanics 8/2012

01.10.2012

Photoelastic Tomography with Linear and Non-linear Algorithms

verfasst von: H. Aben, A. Errapart

Erschienen in: Experimental Mechanics | Ausgabe 8/2012

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Tomography is a powerful method for the investigation of the internal structure of 3D objects from human bodies to atomic reactors. Classical tomography has been elaborated for the determination of scalar fields, i.e. fields, each point of which is characterized by a scalar. Due to that, algorithms of classical tomography can not be directly applied by investigating stress fields since stress is a tensor. In this paper it is shown that photoelastic tomography can be based on the equations of integrated photoelasticity. In the linear approximation the problem of stress field tomography is decomposed into a number of problems of scalar field tomography for single components of the stress tensor. In the non-linear case the axisymmetric stress field can be determined using a genetic algorithm. The paper is illustrated by several examples.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Kobayashi AS (ed) (1993) Handbook on experimental mechanics. VCH Publishers, New York Kobayashi AS (ed) (1993) Handbook on experimental mechanics. VCH Publishers, New York
2.
Zurück zum Zitat Tokuoka T, Morikawa K (1986) Acoustoelasticity in a weakly anisotropic monoclinic elastic material. Wave Motion 8:65–75MATHCrossRef Tokuoka T, Morikawa K (1986) Acoustoelasticity in a weakly anisotropic monoclinic elastic material. Wave Motion 8:65–75MATHCrossRef
3.
Zurück zum Zitat Norris AN, Sinha BK, Kostek S (1994) Acoustoelasticity of solid/fluid composite systems. Geophys J Internat 118:439–446CrossRef Norris AN, Sinha BK, Kostek S (1994) Acoustoelasticity of solid/fluid composite systems. Geophys J Internat 118:439–446CrossRef
4.
Zurück zum Zitat Dike JJ, Johnson GC, Flower EC (1995) Acoustoelasticity using longitudinal waves for residual stress evaluation. NDT E Intern 28:117–118 Dike JJ, Johnson GC, Flower EC (1995) Acoustoelasticity using longitudinal waves for residual stress evaluation. NDT E Intern 28:117–118
5.
Zurück zum Zitat Paroni R, Man CHI-SING (2008) Two micromechanical models in acoustoelasticity: a comparative study. J Elast 59:145–173CrossRef Paroni R, Man CHI-SING (2008) Two micromechanical models in acoustoelasticity: a comparative study. J Elast 59:145–173CrossRef
6.
Zurück zum Zitat Kuske A, Robertson G (1974) Photoelastic stress analysis. John Wiley and Sons, London, UK Kuske A, Robertson G (1974) Photoelastic stress analysis. John Wiley and Sons, London, UK
7.
Zurück zum Zitat Desailly R (1976) Visualization of isoclinics and isochromatics in a birefringent slice optically singeled out in a three-dimensional model. Opt Comm 19:61–64CrossRef Desailly R (1976) Visualization of isoclinics and isochromatics in a birefringent slice optically singeled out in a three-dimensional model. Opt Comm 19:61–64CrossRef
8.
Zurück zum Zitat Dupré JC, Lagarde A (1997) Photoelastic analysis of a 3D specimen by optical slicing and digital image processing. Exp Mech 37:393–397CrossRef Dupré JC, Lagarde A (1997) Photoelastic analysis of a 3D specimen by optical slicing and digital image processing. Exp Mech 37:393–397CrossRef
9.
Zurück zum Zitat Germaneau A, Peyruseigt F, Miston S, Dalvemy O, Doumelin P, Dupré J-C (2008) Verification of a spherical plain bearing finite-element model using scattered light photoelasticity tests. J Eng Tribol 222:647–656CrossRef Germaneau A, Peyruseigt F, Miston S, Dalvemy O, Doumelin P, Dupré J-C (2008) Verification of a spherical plain bearing finite-element model using scattered light photoelasticity tests. J Eng Tribol 222:647–656CrossRef
10.
Zurück zum Zitat Lochegnies D, Romero E, Anton J, Errapart A, Aben H (2005) Measurement of complete residual stress fields in tempered glass plates. Proc Glass Processing Days, Tampere, Finland, pp 88–91 Lochegnies D, Romero E, Anton J, Errapart A, Aben H (2005) Measurement of complete residual stress fields in tempered glass plates. Proc Glass Processing Days, Tampere, Finland, pp 88–91
11.
Zurück zum Zitat Aben H, Anton J, Errapart A, Hödemann S, Kikas J, Klaassen H, Lamp M (2009) On complete non-destructive residual stress measurement in architectural glass panels and automotive glazing. Proc Glass Performance Days, Tampere, Finland. 923–925 Aben H, Anton J, Errapart A, Hödemann S, Kikas J, Klaassen H, Lamp M (2009) On complete non-destructive residual stress measurement in architectural glass panels and automotive glazing. Proc Glass Performance Days, Tampere, Finland. 923–925
12.
Zurück zum Zitat Herman CT (1980) Image reconstruction from projections. Academic, New YorkMATH Herman CT (1980) Image reconstruction from projections. Academic, New YorkMATH
13.
Zurück zum Zitat Natterer F (1986) Mathematics of computerized tomography. Teubner, StuttgartMATH Natterer F (1986) Mathematics of computerized tomography. Teubner, StuttgartMATH
14.
Zurück zum Zitat Proc 1st World Congress on Industrial Process Tomography (1999) Baxton. Derbyshire, England Proc 1st World Congress on Industrial Process Tomography (1999) Baxton. Derbyshire, England
15.
Zurück zum Zitat Anderson DL, Dziewonski AM (1984) Mapping the Earth’s mantle in three dimensions. Sci American 251:60–68CrossRef Anderson DL, Dziewonski AM (1984) Mapping the Earth’s mantle in three dimensions. Sci American 251:60–68CrossRef
16.
Zurück zum Zitat Grewing M, Praderie F, Reinhard R (eds) (1989) Exploration of Halley’s comet. Springer-Verlag Grewing M, Praderie F, Reinhard R (eds) (1989) Exploration of Halley’s comet. Springer-Verlag
17.
Zurück zum Zitat Sharafutdinov VA (1994) Integral geometry of tensor fields. VSP, Utrecht, The NetherlandsCrossRef Sharafutdinov VA (1994) Integral geometry of tensor fields. VSP, Utrecht, The NetherlandsCrossRef
18.
Zurück zum Zitat Aben H (1966) Optical phenomena in photoelastic models by the rotation of principal axes. Exp Mech 6:13–22CrossRef Aben H (1966) Optical phenomena in photoelastic models by the rotation of principal axes. Exp Mech 6:13–22CrossRef
19.
Zurück zum Zitat Aben H (1979) Integrated photoelasticity. McGraw-Hill, New York Aben H (1979) Integrated photoelasticity. McGraw-Hill, New York
20.
Zurück zum Zitat Mangal SK, Ramesh K (1999) Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique. Opt Lasers Eng 31:263–278CrossRef Mangal SK, Ramesh K (1999) Determination of characteristic parameters in integrated photoelasticity by phase-shifting technique. Opt Lasers Eng 31:263–278CrossRef
21.
Zurück zum Zitat Tomlinson RA, Patterson EA (2002) The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity. Exp Mech 42:43–50CrossRef Tomlinson RA, Patterson EA (2002) The use of phase-stepping for the measurement of characteristic parameters in integrated photoelasticity. Exp Mech 42:43–50CrossRef
22.
Zurück zum Zitat Andrienko YA, Dubovikov MS (1994) Optical tomography of tensor fields. J Opt Soc Am A 11:1628–1631CrossRef Andrienko YA, Dubovikov MS (1994) Optical tomography of tensor fields. J Opt Soc Am A 11:1628–1631CrossRef
23.
Zurück zum Zitat Berezhna SYu, Berezhnyi IV, Vlokh OG (1994) Optical tomography of anisotropic inhomogeneous medium. Proc. 10th Internat Confer Exp Mech, Lisboa, Balkema, Rotterdam, 1:431–435 Berezhna SYu, Berezhnyi IV, Vlokh OG (1994) Optical tomography of anisotropic inhomogeneous medium. Proc. 10th Internat Confer Exp Mech, Lisboa, Balkema, Rotterdam, 1:431–435
24.
Zurück zum Zitat Wijerathne MLL, Oguni K, Hori M (2002) Tensor field tomography based on 3D photoelasticity. Mech Mater 34:535–545CrossRef Wijerathne MLL, Oguni K, Hori M (2002) Tensor field tomography based on 3D photoelasticity. Mech Mater 34:535–545CrossRef
25.
Zurück zum Zitat Puro AE (1996) On tomographic magnetophotoelasticity. Optics Spectrosc 81:119–125 Puro AE (1996) On tomographic magnetophotoelasticity. Optics Spectrosc 81:119–125
26.
Zurück zum Zitat Aben H, Idnurm S, Josepson J, Kell K-J, Puro A (1991) Optical tomography of the stress tensor field. In: Levin GG (ed.) Analytical methods for optical tomography. Proc SPIE 1843:220–229 Aben H, Idnurm S, Josepson J, Kell K-J, Puro A (1991) Optical tomography of the stress tensor field. In: Levin GG (ed.) Analytical methods for optical tomography. Proc SPIE 1843:220–229
27.
Zurück zum Zitat Aben H, Guillemet C (1993) Photoelasticity of glass. Springer, BerlinCrossRef Aben H, Guillemet C (1993) Photoelasticity of glass. Springer, BerlinCrossRef
28.
Zurück zum Zitat Davin M (1969) Sur la composition des petites biréfringences subies par un rayon traversant un modèle photoélastique faiblement contraint. C R Acad Sci A269:127–129 Davin M (1969) Sur la composition des petites biréfringences subies par un rayon traversant un modèle photoélastique faiblement contraint. C R Acad Sci A269:127–129
29.
Zurück zum Zitat Doyle JF, Danyluk HT (1978) Integrated photoelasticity for axisymmetric problems. Exp Mech 18:215–220CrossRef Doyle JF, Danyluk HT (1978) Integrated photoelasticity for axisymmetric problems. Exp Mech 18:215–220CrossRef
30.
Zurück zum Zitat Aben HK, Josepson JI, Kell K-J (1989) The case of weak birefringence in integrated photoelasticity. Opt Lasers Eng 11:145–157CrossRef Aben HK, Josepson JI, Kell K-J (1989) The case of weak birefringence in integrated photoelasticity. Opt Lasers Eng 11:145–157CrossRef
31.
Zurück zum Zitat Aben H, Anton J, Errapart A (2003) Automatic measurement of residual stress in glass articles of complicated shape. Verre 9:30–35 Aben H, Anton J, Errapart A (2003) Automatic measurement of residual stress in glass articles of complicated shape. Verre 9:30–35
32.
Zurück zum Zitat Sharafutdinov V (1989) On integrated photoelasticity in case of weak birefringence. Proc Estonian Acad Sci Phys Math 38:379–389MathSciNet Sharafutdinov V (1989) On integrated photoelasticity in case of weak birefringence. Proc Estonian Acad Sci Phys Math 38:379–389MathSciNet
33.
Zurück zum Zitat Shupp D (1999) Optische Tensortomographie zur Bestimmung räumlicher Spannungsverteilungen. Tech Mess 66:54–60 Shupp D (1999) Optische Tensortomographie zur Bestimmung räumlicher Spannungsverteilungen. Tech Mess 66:54–60
34.
Zurück zum Zitat Schupp D (2000) Optische Tensortomographie zur Untersuchung räumlicher Spannungsverteilungen. Fortschritt-Berichte VDI, Reihe 8, “Mess-, Steuerungs- und Regelungstechnik” No. 858 Schupp D (2000) Optische Tensortomographie zur Untersuchung räumlicher Spannungsverteilungen. Fortschritt-Berichte VDI, Reihe 8, “Mess-, Steuerungs- und Regelungstechnik” No. 858
35.
Zurück zum Zitat Aben H, Idnurm S, Puro A (1990) Integrated photoelasticity in case of weak birefringence. Proc 9th Internat Confer Exp Mech, Copenhagen. 2:867–875 Aben H, Idnurm S, Puro A (1990) Integrated photoelasticity in case of weak birefringence. Proc 9th Internat Confer Exp Mech, Copenhagen. 2:867–875
36.
Zurück zum Zitat Dash CJ (1992) One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods. Appl Opt 31:1146–1152CrossRef Dash CJ (1992) One-dimensional tomography: a comparison of Abel, onion-peeling, and filtered backprojection methods. Appl Opt 31:1146–1152CrossRef
37.
Zurück zum Zitat Aben H, Ainola L, Errapart A (2010) Application of the Abel inversion in case of a tensor field. Inverse Probl Sci Eng 18:241–249MathSciNetMATHCrossRef Aben H, Ainola L, Errapart A (2010) Application of the Abel inversion in case of a tensor field. Inverse Probl Sci Eng 18:241–249MathSciNetMATHCrossRef
38.
Zurück zum Zitat Cormack AM (1963) Representation of a function by its line integrals, with radiological applications. J Appl Phus 34:2722–2727MATHCrossRef Cormack AM (1963) Representation of a function by its line integrals, with radiological applications. J Appl Phus 34:2722–2727MATHCrossRef
39.
Zurück zum Zitat Mason JC (2002) Chebyshev polynomials. Chapman & Hall/CRC Press, Roca Baton, FLCrossRef Mason JC (2002) Chebyshev polynomials. Chapman & Hall/CRC Press, Roca Baton, FLCrossRef
40.
Zurück zum Zitat Born M, Wolf E (1986) Principles of optics. Pergamon Press, New York Born M, Wolf E (1986) Principles of optics. Pergamon Press, New York
41.
Zurück zum Zitat Ajovalasit A, Barone S, Petrucci G (1998) A review of automated methods for the collection and analysis of photoelastic data. J Strain Anal 33:75–91CrossRef Ajovalasit A, Barone S, Petrucci G (1998) A review of automated methods for the collection and analysis of photoelastic data. J Strain Anal 33:75–91CrossRef
42.
Zurück zum Zitat Aben H, Ainola L, Anton J (1999) Half-fringe phase-stepping with separation of the principal stress directions. Proc Estonian Acad Sci Eng 5:198–211 Aben H, Ainola L, Anton J (1999) Half-fringe phase-stepping with separation of the principal stress directions. Proc Estonian Acad Sci Eng 5:198–211
44.
Zurück zum Zitat Ainola L, Aben H (2004) A new relationship for the experimental-analytical solution of the axisymmetric thermoelasticity problem. ZAMM 84:211–215MathSciNetMATHCrossRef Ainola L, Aben H (2004) A new relationship for the experimental-analytical solution of the axisymmetric thermoelasticity problem. ZAMM 84:211–215MathSciNetMATHCrossRef
45.
Zurück zum Zitat Bartenev GM (1970) The structure and mechanical properties of inorganic glasses. Wolters-Nordhoff, Groingen Bartenev GM (1970) The structure and mechanical properties of inorganic glasses. Wolters-Nordhoff, Groingen
47.
Zurück zum Zitat Aben H, Anton J, Errapart A (2008) Modern photoelasticity for residual stress measurement in glass. Strain 44:40–48CrossRef Aben H, Anton J, Errapart A (2008) Modern photoelasticity for residual stress measurement in glass. Strain 44:40–48CrossRef
48.
Zurück zum Zitat Aben H, Errapart A (2007) A non-linear algorithm of photoelastic tomography for the axisymmetric problem. Exp Mech 47:821–830CrossRef Aben H, Errapart A (2007) A non-linear algorithm of photoelastic tomography for the axisymmetric problem. Exp Mech 47:821–830CrossRef
49.
Zurück zum Zitat Price KV, Storn RM (2005) Differential evolution, a practical approach to global optimization. Springer, BerlinMATH Price KV, Storn RM (2005) Differential evolution, a practical approach to global optimization. Springer, BerlinMATH
50.
Zurück zum Zitat Theocaris PS, Gdoutos EE (1979) Matrix theory of photoelasticity. Springer, Berlin Theocaris PS, Gdoutos EE (1979) Matrix theory of photoelasticity. Springer, Berlin
Metadaten
Titel
Photoelastic Tomography with Linear and Non-linear Algorithms
verfasst von
H. Aben
A. Errapart
Publikationsdatum
01.10.2012
Verlag
Springer US
Erschienen in
Experimental Mechanics / Ausgabe 8/2012
Print ISSN: 0014-4851
Elektronische ISSN: 1741-2765
DOI
https://doi.org/10.1007/s11340-011-9575-z

Weitere Artikel der Ausgabe 8/2012

Experimental Mechanics 8/2012 Zur Ausgabe

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.