Abstract
The shadow-moiré method has been extended to study the large displacements of a uniformly loaded hyperbolic-paraboloid shell. The new technique employs a curved grating which is everywhere equidistant from the initial position of the surface, as in the application of a plane grating in the study of plates. The theory of the curved grating is developed. Experimental verification is reported and a significant increase in accuracy over the equivalent plane grating is observed. The proposed improvement can be applied to the study of any ruled surface.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Abbreviations
- a :
-
half length of hypar (mm)
- b :
-
half width of hypar (mm)
- c :
-
half height of hypar (mm)
- d :
-
vertical distance between model and grating in the initial state (curved grating) (mm)
- k :
-
index referring to a line of the grating (dimensionless)
- L :
-
horizontal distance between light source and edge of model (mm)
- l :
-
index referring to a line of the shadow of the grating (dimensionless)
- M :
-
vertical distance from grating to observer (plane grating) (mm); vertical distance from reference plane to observer (curved grating) (mm)
- N :
-
moiré-fringe order (dimensionless)
- p :
-
pitch of the grating (mm)
- T :
-
horizontal distance between the edge of the surface and the edge of the grating (mm)
- W :
-
vertical distance from the grating to the light source (plane grating) (mm); vertical distance from the reference plane to the light source (curved grating) (mm)
- x,y,z :
-
coordinates on the model surface (plane grating) (mm)
- x′,y′,z′ :
-
coordinates on the model surface (curved grating) (mm)
- x m ,y m :
-
coordinates measured in the grating plane (plane grating) (mm); coordinates measured in the reference plane (curved grating) (mm)
- γ:
-
angle between the vertical and the light rays from the observer to the model (rad)
- δ:
-
vertical distance between the grating and the point (x, y, z) (plane grating) (mm); vertical distance between the grating and the point (x′, y′, z′) (curved grating) (mm)
- θ:
-
angle between the vertical and the light ray from the source to the model (rad)
References
Dykes, B. C., “Analysis of Displacements in Large Plates by the Grid-Shadow Moiré Technique”,Experimental Stress Analysis and its Influence on Design (Proc. of the 4th Int. Conf. on Exp. Stress. Anal.)ed. by M. L. Meyer, Institution of Mechanical Engineers, London, 125–134 (1971).
Pirodda, L., “Principii e Applicazioni di un Metodo Fotogrammetrico basato sull'impiego del Moiré,”Rivista di Ingegneria,12,913–923 (December 1969).
Meadows, D. M., Johnson, W. O. andAllen, J. B., “Generation of Surface Contours by Moiré Patterns,”Applied Optics,9 (4),942–947 (April 1970).
Takasaki, H., “Moiré Topography,”Applied Optics,9 (6),1457–1472 (June 1970).
Collet, J. P., Marasco, J. andPflug, L., “Le Moiré d'Ombre: Une Méthode Expérimentale et ses Possibilités,”Le Bulletin Technique de la Suisse Romande,9 179–187 (April 1974).
Duncan, J. P., “The Optical Survey of Curved Surfaces,” Rep. of the Dept. of Mech. Engl., The University of British Columbia (May 1966).
Pahud, M., “Calcul des Courbes de Niveau d'une Surface Quelconque,”Le Bulletin Technique de la Suisse Romande,19,393–395 (September 1973).
Author information
Authors and Affiliations
Additional information
Work was performed while he was Research Associate, Swiss Federal Institute of Technology, Lausanne, Switzerland.
Rights and permissions
About this article
Cite this article
Marasco, J. Use of a curved grating in shadow moiré. Experimental Mechanics 15, 464–470 (1975). https://doi.org/10.1007/BF02318361
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02318361