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
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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