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Stress separation from photoelastic data by a multigrid method

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1998-08
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IOP Publishing Ltd.
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An application of multigrid techniques for the separation of principal stresses in plane stress systems is presented. By establishing the equilibrium equations and determining the value of shear from photoelastic data a system of partial differential equations is obtained, which can be solved by applying a multigrid method. Multigrid methods are comparable to Fourier methods in efficiency and robustness and can be applied to processing areas of arbitrary shape.
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© 1998 IOP Publishing Ltd. We thank Professor Eusebio Bernabeu, director of the Optics Department of the Universidad Complutense for his help and continuous support. Also, we thank Hans Steinbichler, of Steinbichler Optotechnik GmbH, for his technical assistance. This work has been partially supported by project MAT 95-0767 of the CICYT (Comisión Interministerial de Ciencia y Tecnología).
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[1] Frocht M M 1941 and 1948 (volumes 1 and 2) Photoelasticity (New York: Wiley). [2] Theocaris P S and Gdoutos E E 1979 Matrix Methods in Photoelasticity (Berlin: Springer). [3] Brown G M and Sullivan J L 1990 The computer aided holophotoelastic method: theory and experiment Proc. SEM Conf. on Hologram Interferometry and Speckle Metrology (Baltimore, MD, 5–8 November 1990) (Bethel, CN: Society for Experimental Mechanics) pp 102–9. [4] Press W H, Teukolsky S A, Vetterling W T and Flannery B P 1992 Numerical Recipes in C. The Art of Scientific Computing 2nd edn (Cambridge: Cambridge University Press). [5] Servín M, Malacara D and Marroquín J L 1996 Wave-frontrecovery from two orthogonal sheared interferograms Appl. Opt. 35 4343–8. [6] van Brug H 1997 Zernike polynomials as a basis for wave-front fitting in lateral shearing interferometry Appl. Opt. 36 2788–90. [7] Grèdiac M 1997 Method for surface reconstruction from slope or curvature measurements of rectangular areas Appl. Opt. 36 4823–9. [8] Loheide S 1997 General evaluation technique for shearing experiments Fringe ’97. Automatic Processing of Fringe Patterns ed W J¨uptner and W Osten (Berlin: Akademie) pp 92–4 [9] Rivera M, Marroquín J L, Servín M and Rodríguez-Vera R 1997 Fast algorithm for integrating inconsistent gradient fields Appl. Opt. 36 8381–90. [10] Haake S J, Patterson E A and Wang Z F 1996 2D and 3D separation of stresses using automated photoelasticity Exp. Mech. 36 269–76. [11] Freischlad K 1992 Wavefront integration from difference data Proc. SPIE 1755 212–18. [12] Mahfuz H, Wong T L and Case R O 1990 Separation of principal stresses by SOR technique over arbitrary boundaries Exp. Mech. 30 319–27 1209. [13] Briggs W L 1987 A Multigrid Tutorial (Philadelphia, PA: SIAM) [14] Pritt M D 1996 Phase unwrapping by means of multigrid techniques for interferometric SAR IEEE Trans. Geosci. Remote Sensing 34 728–38 [15] Takajo H and Takahashi T 1988 Least-squares phase estimation from the phase difference J. Opt. Soc. Am. A 5 416–25. [16] Asundi A 1993 Phase shifting in photoelasticity Exp. Tech. 17 19–23. [17] Nurse A D 1997 Full-field automated photoelasticity by use of a three-wavelength approach to phase stepping Appl. Opt. 36 5781–6. [18] Quiroga J A and González-Cano A 1997 Phase measuring algorithm for extraction of isochromatics of photoelastic fringe patterns Appl. Opt. 36 8397–402.
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