Abstract
The basic equation for fringe formation in the case of reflection moiré applied to surfaces of arbitrary curvatures is derived. A practical point-by-point solution for the application of this method is introduced, and the corresponding simplified equations are given. The technique is applied to an industrial problem, the stress analysis of a shell-shaped door.
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Abbreviations
- P o :
-
projected point of the grating
- P :
-
point of the initial shell surface where the beam coming fromP o is reflected
- Q :
-
point of the deformed shell surface where the beam coming fromP o is reflected
- R :
-
point of the image plane corresponding to pointP o before deformation
- P′:
-
point of intersection of plane π with the normal from pointP
- Q′:
-
point of intersection of plane π with the normal from, pointQ
- T :
-
point of the image plane corresponding toP o after deformation
- rP :
-
position vector of pointP
- rQ :
-
position vector of pointQ
- rR :
-
position vector of pointR
- rT :
-
position vector of pointT
- rPR :
-
unit vector that defines the linePR
- rPP′ :
-
unit vector that defines the lineP P′
- rQQ′ :
-
unit vector that defines the lineQ Q′
- rQT :
-
unit vector that defines the lineQT
- Io :
-
unit vector that defines the direction of illumination
- nP :
-
normal to the inital surface at pointP
- nQ :
-
normal to the deformed surface at pointQ
References
Ligtenberg, F.K., “The Moiré Method: A New Experimental Method for the Determination of Moments in Small Slab Models,”Proceedings of the Society for Experimental Stress Analysis,12,83–98 (Feb. 1954).
Reider, G. andRitter, R., “Krummungs messung an belasteten Platten nach den Ligtenbergschen Moiré Verfahren,”Forschung im Ingenieurwesen,31 (3),33–34 (1965).
Pedretti, M., “Nouvelle Methode de Moiré Pour L'Anlyse des Plaques Flechies,” Doctoral diss., Ecole Polytechnique Federale de Lausanne (1974).
Theocaris, P., Moiré Fringes in Strain Analysis, Pergamon Press, London, 2620278 (1969).
Sciammarella, C.A. andCombel, O., “Interferometric Reflection Moiré,”Proceedings of the International Society for Optical Engineers: Interferometry VII, Applications, J. Pryputniewicz, G. Brown andW.P. Jupner, eds., SPIE, Bellingham, WA, 72–85 (1995).
Theocaris, P., Moiré Fringes in Strain Analysis, Pergamon Press, London, 1969, p:330–337.
Osgerby, C., “Application of the Moiré Method for Use with Cylindrical Surfaces,” EXPERIMENTAL MECHANICS,7,313–320 (1967).
Kamaritova, M., “The Solution of Shells by the Moiré Method,” Acta Technica, Csav., No. 2 (1969).
Gambarova, P., Giovani, E., and Ronca, P., “La deformazione di modelli a doppia curvatura con il metodo del, moiré per riflessione,” Istituto di Scienza e Tecnica Delle Costruzioni del Politecnico di Milano Pub. No. 698 (1975).
Ritter, R. andSchulte, U., “Vibration Analysis by the Time Average Reflection Grating Principle,”Optik,75 (4),130–134 (1987).
Sciammarella, C.A. andBhat, G., “High Resolution Computer Aided Moiré,”SPIE Proceedings: Part I. Moiré Techniques, Holography, Interferometry, Optical NDT and Application to Fluid Mechanics,1554B,F.-P. Chiang,ed.,SPIE,Bellingham, WA,162–173 (1991).
Sciammarella, C.A. andDavies, D., “Gap, Effect in Moiré Fringes Observed with Coherent Monochromatic Collimated Light,” EXPERIMENTAL MECHANICS,8,459–466 (1968).
Sciammarella, C.A. andBhat, G., “Two Dimensional Fourier Transform Methods for Fringe Pattern Analysis,”Proceedings of the Seventh International Congress on Experimental Mechanics,12,Bethel, CT,1530–1538 (1992).
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Sciammarella, C.A., Trentadue, B. & Sciammarella, F.M. Measurement of bending stresses in shells of arbitrary shape using the reflection moiré method. Experimental Mechanics 40, 282–288 (2000). https://doi.org/10.1007/BF02327501
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DOI: https://doi.org/10.1007/BF02327501