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Alleviation of the stress concentration with analogue reinforcement

Stress concentration around a hole in a plate is reduced by placement of reinforcement following stress trajectories

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Abstract

In order to reduce the stress concentration around a hole in a plate, new, “analogue” reinforcements instead of reinforcing rings were used in this investigation. In two of these specimens, reinforcements with different volume fractions were arranged to coincide with the stress trajectories for an infinite plate with a hole under uniaxial tension. Two other specimens containing straight rectangular-grid-type reinforcements were made by using a photofabrication method. Specimens were then prepared by sandwiching these reinforcements between two epoxy-resin plates. Plane specimens, i.e., without reinforcement, were also made of the same epoxy resin for comparison.

The stress concentrations at the edge of the hole under uniaxial tension were determined by photoelastic techniques. The measured stress-concentration factors were compared with well-known values for an infinite, isotropic, homogeneous plate containing a hole. Results were also compared with published data on [90/0/90/0]s 7-ply laminated composite plates, and on plates strengthened with reinforcing rings.

A definite reduction in stress concentration was observed on specimens containing analogue reinforcement.

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Abbreviations

a :

radius of hole

b :

half width of plate

f :

material-fringe value

n max,n a :

fringe order at edge of hole; at remote location

r :

radial coordinate

v f, vm :

volume fraction of reinforcement; of matrix

x,y :

longitudinal and transverse coordinates

E, E L, ET, E45 :

moduli of elasticity: isotropic, longitudinal, transverse; at 45 deg

E f, Em :

moduli of elasticity for reinforcement; matrix

G, G LT :

shear moduli: isotropic, orthotropic

K ti, Kz :

stress-concentration factors: isotropic, orthotropic

α:

angle formed by longitudinal axis and slope of stress trajectory

ννLT :

Poisson's ratios: isotropic, orthotropic

ϕ:

tangential coordinate

σ,σ θτγθ :

stress components in cylindrical coordinates

σ x,σyτx,y :

stress components in Cartesian coordinates

τmax,σa :

maximum longitudinal stress; at remote location

References

  1. Kirsh, G., VDI,42 (1898); See also Timoshenko, S. and Goodier, Theory of Elasticity, 3rd ed., McGraw-Hill Book Co., New York, 90 (1970).

  2. Howland, R. C. J., “On the Stresses in the Neighbourhood of a Circular Hole in a Strip under Tension,”Philo. Trans. of the Royal Soc. of London, Series A,229,49–86 (1930).

    MATH  Google Scholar 

  3. Lekhnitskii, S. G., “Theory of Elasticity of an Anisotropic Elastic Body,”trans. by P. Fern, Holden-Day, Inc., San Francisco, 1701 (1963).

    Google Scholar 

  4. Timoshenko, S., “On the Stresses in a Plate with a Circular Hole,”J. of the Franklin Inst.,197,505–516 (1942).

    Google Scholar 

  5. Sezawa, K. and Kubo, K., “Stresses in a Plate with a Flanged Circular Hole,” Report of the Aeron. Res. Inst., Tokyo Imperial Univ., Tokyo, Japan, (84) (Sept. 1932).

  6. Gurney, G., “An Analysis of the Stresses in a Flat Plate with a Reinforced Circular Hole under Edge Forces,” British Rep. Memo No. 1834 (Feb. 1938).

  7. Beskin, L., “Strengthening of Circular Holes in Plates under Edge Loads,”J. of Appl. Mech.,11 (3),140–148 (Sept. 1944).

    Google Scholar 

  8. Levy, S., McPherson, A. E. andSmith, F. C., “Reinforcement of a Small Circular Hole in a Plane Sheet under Tension,”J. of Appl. Mech. 22 (2),249–254 (June 1955).

    Google Scholar 

  9. Radok, J. R. M., “Problems of Plane Elasticity for Reinforced Boundaries,”J. of Appl. Mech. 15 (2),160–168 (June 1948).

    Google Scholar 

  10. Muskhelishvili, N. I., “Some Basic Problems of the Mathematical Theory of Elasticity,”N.V.P. Noordhoff, Gronigen, Holland (1953).

    Google Scholar 

  11. Shimada, H., “Influence of Breadth in Bars with Reinforced Circular Holes under Tension,”Experimental Mechanics,1 (7),33–39 (1961).

    Article  Google Scholar 

  12. Suzuki, S., “Stress Measurements in a Plate Containing a Reinforced Circular Hole Using a Photoelastic Method,”Int. J. Mech. Sci.,6,473–477 (1964).

    Google Scholar 

  13. Suzuki, S., “Stress Measurements in an Infinite Plate with a Hole Reinforced by Different Materials,”Experimental Mechanics,9 (7),332–336 (1969).

    Article  Google Scholar 

  14. Seika, M. andIshii, M., “Photoelastic Investigation of the Maximum Stress in a Plate with a Reinforced Circular Hole under Uniaxial Tension,”J. of Appl. Mech., Trans. ASME,31 (4),Series E,701–702 (Dec. 1964).

    Google Scholar 

  15. Seika, M. andAmano, A., “The Maximum Stress in a Wide Plate with a Reinforced Circular Hole under Uniaxial Tension—Effects of a Boss with Fillet,”J. of Appl. Mech., Trans. ASME,34 (1),Series E.,232–233 (March 1967).

    Google Scholar 

  16. Daniel, I. M. andRowlands, R. E., “Determination of Strain Concentration in Composites by Moiré Techniques,”J. of Comp. Mat.,5,250–254 (April 1971).

    Google Scholar 

  17. Hyman, B. I., De Turk, A., Diaz, R. andDiGiovanni, G., “Exploratory Tests on Fiber-Reinforced Plates with Circular Holes under Tension,”AIAA J.,7 (9),1820–1821 (Sept. 1969).

    Google Scholar 

  18. Lackman, L. M. and Ault, R. M., “Mollifying Stress Field by Using Filamentary Composite Materials,” 12th Nat. SAMPE Symp., D-3 (1967).

  19. “An Introduction to Photofabrication Using KODAK Photosensitive Resists,” Kodak Publication No. P-79 (1970).

  20. “Chemical Milling with KODAK Photosensitive Resists,” Kodak Publication No. P-131 (1968).

  21. Chiba, T. and Heller, R. A., “Alleviation of Stress Concentration with Analogue Reinforcement,” Virginia Polytechnic Inst. and State Univ. Report No. VPI-E-72-4 (April 1972).

  22. Dally, J. W. andRiley, W. F., “Experimental Stress Analysis,”McGraw-Hill Book Co., New York (1965).

    Google Scholar 

  23. Savin, G. N., “Stress Concentration Around Holes,”Pergamon Press Inc., New York (1961).

    Google Scholar 

  24. Cooper, A.A.G., “Trajectorial Fiber Reinforcement of Composite Structures,”PhD Dissertation, Washington Univ., Saint Louis (Dec. 1972).

    Google Scholar 

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Authors and Affiliations

  1. Department of Engineering Science and Mechanics, Virginia Polytechnic Institute and State University, 24061, Blacksburg, VA

    R. A. Heller (Professor)

  2. Musushi Institute of Technology, Tokyo, Japan

    T. Chiba

Authors
  1. R. A. Heller
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  2. T. Chiba
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Heller, R.A., Chiba, T. Alleviation of the stress concentration with analogue reinforcement. Experimental Mechanics 13, 519–525 (1973). https://doi.org/10.1007/BF02322340

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