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Experimental Mechanics

, Volume 7, Issue 4, pp 168–175 | Cite as

Moiré study of anticlastic deformations of strips with tapered edges

Principal objective of paper is to verify the theoretical deformations for optimally tapered strips by experiments using the moiré method
  • W. E. Nickola
  • H. D. Conway
  • K. A. Farnham
Article

Abstract

When a thin elastic strip is bent, anticlastic deforming of the cross section takes place, and the edges move away from the center of curvature. This effect can have serious consequences in several applications. However, it has been found that the magnitudes of the deformations can be very greatly reduced if the concave edges of the bent strip are tapered.

The proportions of the tapers have already been worked out theoretically so as to optimize the reduction in anticlastic deformation in any given strip bent to a known radius of curvature. The main purpose of the present paper is to verify the theoretical deformations for optimally tapered strips by experiments using the moiré method.

Keywords

Mechanical Engineer Fluid Dynamics Elastic Strip Tapered Edge Concave Edge 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

b

half-width of strip (Fig. 8)

b1

half-width of uniform portion of strip (Fig. 8)

b2

dimension defined in Fig. 8

p

radial pressure

rb

width ratiob1width ratio/b

rt

thickness ratiot1/t0

t0

thickness of uniform portion of strip (Fig. 8)

t1

thickness defined in Fig. 8

t2

thickness defined in Fig. 8

x, y

Cartesian coordinates

w

final deviation of middle surface fromx−y plane

w0

initial deviation of middle surface fromx−y plane

D

flexural rigidity=Et03/12 (1 −μ2)

E

Young's modulus

H

distance between strain-gage grids

M

bending moment per unit width

Q

shearing force per unit width

R

longitudinal radius of curvature

S

maximum lateral relative displacement of concave surface of strip [eq (2)]

strain

λ

b(Rt0)−1/2 [3(1 −μ2)]1/4

λ2

b(Rt2)−1/2 [3(1 −μ2)]1/4

μ

Poisson's ratio (0.35 for Plexiglas)

η

2 (1 −y/b2)1/2

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References

  1. 1.
    Timoshenko, S. P., andGoodier, J. N., “Theory of Elasticity,”McGraw-Hill, New York, 1951, 254.Google Scholar
  2. 2.
    Ashwell, D. G., “The Anticlastic Curvature of Rectangular Beams and Plates,”Jnl. Roy. Aeron. Soc.,54,708 (1950).Google Scholar
  3. 3.
    Hertrich, F. R., IBM Corp., San Jose, Calif., private communication.Google Scholar
  4. 4.
    Conway, H. D., andFarnham, K. A., “Anticlastic Curvatures of Strips of Variable Thickness,”Int. Jnl. Mech. Sci.,7,451 (1965).Google Scholar
  5. 5.
    Pao, Y. C., andConway, H. D., “An Optimum Study of the Anticlastic Deformations of Strips with Tapered Edges,”Int. Jnl. Mech. Sci.,8,65 (1966).Google Scholar
  6. 6.
    Duncan, J. P., and Brown, C. J. E., “Slope Contours In Flexed Elastic Plates by Salet-Ikeda Technique,” Printed in “Proceedings of First International Congress on Experimental Mechanics,” edited by B. E. Rossi, Pergamon Press (1963).Google Scholar
  7. 7.
    Duncan, J. P., andSabin, P. G., “Determination of Curvatures in Flexed Elastic Plates by the Martinelli-Ronchi Technique,”Proc. SESA,20 (2),285–293 (1963).Google Scholar
  8. 8.
    Theocaris, P. S., “Moiré Patterns of Slope Contours in Flexed Plates,” SESA Second International Congress on Experimental Mechanics, 56–61 (1965).Google Scholar
  9. 9.
    Wasil, B. A., andMerchant, D. C., “Plate-Deflection Measurement by Photogrammetric Methods,”Experimental Mechanics,4 (3),77–83 (1964).Google Scholar
  10. 10.
    Wasil, B. A., Merchant, D. C., andDelVecchio, J. J., “Photogrammetric Measurements of Dynamic Displacement,”Experimental Mechanics,5 (10),332–339 (1965).Google Scholar
  11. 11.
    Ligtenberg, F. K., “The Moiré Method—A New Experimental Method for the Determination of Moments in Small Slab Models,”Proc. SESA,12 (2),83–98 (1955).Google Scholar
  12. 12.
    Conway, H. D., andNickola, W. E., “Anticlastic Action of Flat Sheets in Bending,”Experimental Mechanics,5 (4),115–119 (1965).Google Scholar
  13. 13.
    Bellow, D. G., Ford, G., andKennedy, J. F., “Anticlastic Behavior of Flat Plates,”5 (7),227–232 (1965).Google Scholar
  14. 14.
    Fung, Y. C., andWittrick, W. H., “The Anticlastic Curvature of a Strip with Lateral Thickness Variation,”Jnl. Appl. Mech.,21,351 (1954).Google Scholar

Copyright information

© Society for Experimental Mechanics, Inc. 1967

Authors and Affiliations

  • W. E. Nickola
    • 1
  • H. D. Conway
    • 1
    • 2
  • K. A. Farnham
    • 1
  1. 1.Systems Development DivisionIBM Corp.Endicott
  2. 2.Dept. of Theor. & Applied MechanicsCornell UniversityIthaca

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