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Differentiation along arbitrary orientations

Methods are presented for numerically differentiating photomechanical-fringe patterns along arbitrarily curved and straight directions

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Abstract

A prevalent problem of mechanics is the differentiation of experimental information with respect to various directions, including the determination of cross derivatives. Simple methods for evaluating such derivatives along straight and curved directions are described. The concepts are demoinstrated at boundary and internal locations of in-plane and transversely loaded plates.

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Abbreviations

f, F :

general function or dependent variable

x, y, s, y, h :

coordinates

Δξ:

arc length along ξ-direction

u, v, w :

displacements

θɛ, θη :

tangent angles to the ξ- and ν-coordinates and measured counterclockwise from the positive x-axis

r, θ :

polar coordinates

a :

radius of plate

i, 1,2:

denote directions as subscripts

ϕ, ψ:

angles

N :

fringe order

N :

fringe order

λ:

wavelength

References

  1. Theocaris, P.S., Moiré Fringes in Strain Analysis, Pergamon Press, (1969).

  2. Bradley, W.A., “laterally Loaded Flat Plates,” J. Engrg. Mech. Div., ASCE, 77-107 (Oct. 1959).

  3. Hung, Y.Y., Daniel, I.M. andRowlands, R.E., “Full-field Optical Strain Measurement Having Postrecording Sensitivity and Direction Selectivity,”Experimental Mechanics,18 (2),56–60 (Feb. 1978).

    Google Scholar 

  4. Rowlands, R.E., Daniel, I.M. andWhiteside, J.B., “Stress and Failure Analysis of a Glass-Epoxy Composite with a Circular Hole,”Experimental Mechanics,13 (1),31–37 (Jan. 1973).

    Google Scholar 

  5. Rowlands, R.E., Winters, K.E. and Jensen, J.A., “Full-Field Numerical Differentiation,” presented at 14th Int. Cong. Theo. & Appl. Mech., Delft (1976).

  6. Rowlands, R.E., Liber, T., Daniel, I.M. andRose, P.G., “Stress Analysis of Anisotropic Plates,”AIAA J.,12 (7),903–908 (Jul.1974).

    Google Scholar 

  7. Timoshenko, S.P. andWoinsowsky-Kreiger, S., Theory of Plates and Shells, McGraw-Hill Co., New York (1959).

    Google Scholar 

  8. Perry, C.C., Plane-shear Measurement with Strain Gages, Experimental Mechanics,9 (1),19N-22N (Jan. 1969)

    Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Mechanics, University of Wisconsin, 53706, Madison, WI

    R. E. Rowlands, J. A. Jensen & K. D. Winters

Authors
  1. R. E. Rowlands
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  2. J. A. Jensen
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  3. K. D. Winters
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Rowlands, R.E., Jensen, J.A. & Winters, K.D. Differentiation along arbitrary orientations. Experimental Mechanics 18, 81–86 (1978). https://doi.org/10.1007/BF02325001

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  • DOI: https://doi.org/10.1007/BF02325001

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