Abstract

A computer-based technique is described for direct determination of bending strains in beam and plate structures. First a displacement-related phase-change map is constructed by digital holography and computer-vision techniques. Subsequently the computer generates an exact replica of the phase-change map, then overlays the two identical maps and, finally, rotates one of the maps through 180° relative to the other in their planes about a point of interest. The local curvatures and the local twist of the bent surface at the point of interest are determined from the conic sections that are reconstructed from the algebraic sum of the phase changes at the vicinity of this point, thus permitting further calculation for determination of the local bending strains. When the need arises, bending moments and stresses may be determined concurrently. As the optical setup is simple, with computer-based data acquisition and processing, the entire system is user friendly, and rapid measurement is achieved.

© 2001 Optical Society of America

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References

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  1. S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959).
  2. C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).
  3. D. Post, “The moire grid-analyzer method for strain analysis,” Exp. Mech. 5, 368–377 (1965).
    [CrossRef]
  4. K. A. Stetson, “Moire method for determining bending moments from hologram interferometry,” Opt. Laser Technol. 2, 80–84 (1970).
  5. Y. Y. Hung, S. K. Cheng, N. K. Loh, “A computer vision technique for surface gaging with projected grating,” IEEE Trans. Indust. Electron. IE-32, 156–161 (1986).
  6. Y. Y. Hung, “Three-dimensional computer vision techniques for full-field surface shape measurement and surface flaw inspection,” in 1992 SAE International Congress and Exposition, Detroit, 24–28 February 24–28 1992 (Society of Automotive Engineers, Warrendale, Pa. 15096), Paper 920246.
  7. W. W. Macy, “Two-dimensional fringe pattern analysis,” Appl. Opt. 22, 3898–3901 (1983).
    [CrossRef]

1986 (1)

Y. Y. Hung, S. K. Cheng, N. K. Loh, “A computer vision technique for surface gaging with projected grating,” IEEE Trans. Indust. Electron. IE-32, 156–161 (1986).

1983 (1)

1970 (1)

K. A. Stetson, “Moire method for determining bending moments from hologram interferometry,” Opt. Laser Technol. 2, 80–84 (1970).

1965 (1)

D. Post, “The moire grid-analyzer method for strain analysis,” Exp. Mech. 5, 368–377 (1965).
[CrossRef]

Cheng, S. K.

Y. Y. Hung, S. K. Cheng, N. K. Loh, “A computer vision technique for surface gaging with projected grating,” IEEE Trans. Indust. Electron. IE-32, 156–161 (1986).

Hung, Y. Y.

Y. Y. Hung, S. K. Cheng, N. K. Loh, “A computer vision technique for surface gaging with projected grating,” IEEE Trans. Indust. Electron. IE-32, 156–161 (1986).

Y. Y. Hung, “Three-dimensional computer vision techniques for full-field surface shape measurement and surface flaw inspection,” in 1992 SAE International Congress and Exposition, Detroit, 24–28 February 24–28 1992 (Society of Automotive Engineers, Warrendale, Pa. 15096), Paper 920246.

Loh, N. K.

Y. Y. Hung, S. K. Cheng, N. K. Loh, “A computer vision technique for surface gaging with projected grating,” IEEE Trans. Indust. Electron. IE-32, 156–161 (1986).

Macy, W. W.

Post, D.

D. Post, “The moire grid-analyzer method for strain analysis,” Exp. Mech. 5, 368–377 (1965).
[CrossRef]

Stetson, K. A.

K. A. Stetson, “Moire method for determining bending moments from hologram interferometry,” Opt. Laser Technol. 2, 80–84 (1970).

Timoshenko, S. P.

S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959).

Vest, C. M.

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Woinowsky-Krieger, S.

S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959).

Appl. Opt. (1)

Exp. Mech. (1)

D. Post, “The moire grid-analyzer method for strain analysis,” Exp. Mech. 5, 368–377 (1965).
[CrossRef]

IEEE Trans. Indust. Electron. (1)

Y. Y. Hung, S. K. Cheng, N. K. Loh, “A computer vision technique for surface gaging with projected grating,” IEEE Trans. Indust. Electron. IE-32, 156–161 (1986).

Opt. Laser Technol. (1)

K. A. Stetson, “Moire method for determining bending moments from hologram interferometry,” Opt. Laser Technol. 2, 80–84 (1970).

Other (3)

S. P. Timoshenko, S. Woinowsky-Krieger, Theory of Plates and Shells (McGraw-Hill, New York, 1959).

C. M. Vest, Holographic Interferometry (Wiley, New York, 1979).

Y. Y. Hung, “Three-dimensional computer vision techniques for full-field surface shape measurement and surface flaw inspection,” in 1992 SAE International Congress and Exposition, Detroit, 24–28 February 24–28 1992 (Society of Automotive Engineers, Warrendale, Pa. 15096), Paper 920246.

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Figures (7)

Fig. 1
Fig. 1

Optical layout for digital holography.

Fig. 2
Fig. 2

Distribution of maximum flexural strain along an end-loaded cantilever beam.

Fig. 3
Fig. 3

Holographic fringe pattern of a centrally loaded square plate.

Fig. 4
Fig. 4

Concentric circular fringes in the inset show equibiaxial flexural strains at the center of the plate.

Fig. 5
Fig. 5

Hyperbolic fringes in the inset show flexural strains with opposite signs at the top right-hand corner of the plate.

Fig. 6
Fig. 6

Elliptical fringes in the inset show flexural strains with the same sign along the reference (horizontal) x axis.

Fig. 7
Fig. 7

Elliptical fringes in the inset show flexural strains with the same sign along the reference (vertical) y axis.

Equations (13)

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ε=-z d2wdx2,
εx=-z 2wx2, εy=-z 2wy2, γxy=-2z 2wxy.
I1=a0x, y+b0x, ycos α,  I2=a0x, y+b0x, ycosα+ϕ,
ϕx, y=-4πλ wx, y,
wx, y=λ4 N,  N=0, ±1, ±2, ±3, ±4,.
ϕχ, η=ϕP+χϕxP+ηϕyP+12χ22ϕx2P+2χη2ϕxyP+η22ϕy2P+16χ33ϕx3P+3χ2η3ϕx2yP+3χη23ϕxy2P+η33ϕy3P.
ϕχ, η=ϕP+χϕxP+ηϕyP+12χ22ϕx2P+2χη2ϕxyP+η22ϕy2P+16χ33ϕx3P+3χ2η3ϕx2yP+3χη23ϕxy2P+η33ϕy3P+,
χ=χ cos ξ+η sin ξ, η=-χ sin ξ+η cos ξ.
ΔSϕχ, η+ϕ-χ, -η=2ϕP+χ22ϕx2P+2χη2ϕxyP+η22ϕy2P.
ε=h2D1+νP4π1+νloge2a sinπξ/aπc+1-0.565,
P=Dwmax0.0116a2.
ε=h2D1+νP4π1+νloge2a sinπξ/aπc+1-0.565+4π0.0536,
P=Dwmax0.0056a2.

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