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A numerical method for separation of stresses in photo-orthotropic elasticity

A method is suggested for separation of stresses in photo-orthotropic elasticity using the numerical solution of compatibility equation

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Abstract

A numerical method is suggested for separation of stresses in photo-orthotropic elasticity using the numerical solution of compatibility equation for orthotropic case. The compatibility equation is written in terms of a stress parameter S analogous to the sum of principal stresses in two-dimensional isotropic case. The solution of this equation provides a relation between the normal stresses. The photoelastic data give the shear stress and another relation between the two normal stresses. The accuracy of the numerical method and its application to practical problems are illustrated with examples.

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Abbreviations

E x ,E y :

modulus of elasticity with respect to principal axes of orthotropyx andy

f x ,f y ,f xy :

material stress-fringe constants with respect to principal axes of orthotropyx andy

G xy :

modulus of rigidity with respect to principal axes of orthotropyx andy

h :

finite-difference mesh spacing

i, j :

integer variables denoting position of a point

K 1,K 2 :

orthotropic constants

N :

isochromatic-fringe order

n :

refractive index

P :

concentrated load

q :

uniformly distributed load

S :

\(\sigma _y + K_2^2 \sigma _x \)

t :

thickness

x, y :

Cartesian coordinates

ε x ,ε y ,γ xy :

Cartesian strain components

λ:

wavelength of light

μ x ,μ xy :

Poisson's ratio with respect to principal axes of orthotropyx andy

σ x ,σ y ,τ xy :

Cartesian stress components

θ o :

average stress

θ′ :

isoclinic angle

σσ,θε :

principal-stress and principal-strain angles

References

  1. Pih, H. andKnight, C.E., Photoelastic Analysis of Anisotropic Fiber Reinforced Composites, J. Comp. Mats.,3,94 (1969).

    Google Scholar 

  2. Sampson, R.C., A Stress-Optic Law for Photoelastic Analysis of Orthotropic Composites,Experimental Mechanics,10 (5),210–215 (1970).

    Article  Google Scholar 

  3. Bert, C.W., Theory of Photoelasticity of Birefringent Composites, 1st St. Louis Symp. Advanced Comp. (Apr. 1971).

  4. Dally, J.W. andPrabhakaran, R., Photo-orthotropic-elasticity,Experimental Mechanics,11, (8),346–356 (1971).

    Google Scholar 

  5. Pipes, R.B. andRose, J.L., Strain-Optic Law for a Certain Class of Birefringent Composites,Experimental Mechanics,14 (9),355–360 (1974).

    Google Scholar 

  6. Prabhakaran, R. andDally, J.W., The Application of Photo-Orthotropic Elasticity, J. Strain Anal.,7 (4,253 (1972).

    Google Scholar 

  7. Prabhakaran, R., On the Stress-Optic Law for Orthotropic Model Materials in Biaxial Fields,Experimental Mechanics,15 (1),29–34 (1975).

    Google Scholar 

  8. Prabhakaran, R., Photoelastic Analysis of an Orthotropic Ring Under Diametral Compression, AAIA J.,11 (6),777 (1973).

    Google Scholar 

  9. Prabhakaran, R., Strain-Optic Law for Orthotropic Model Materials, AIAA J.,13 (6),723 (1975).

    Google Scholar 

  10. Cernosek, J., On Photoelastic Response of Composites,Experimental Mechanics,15 (9),354–357 (1975).

    Google Scholar 

  11. Prabhakaran, R., The Interpretation of Isoclinics in Photo-orthotropic-elasticity,Experimental Mechanics,16 (1),6–10 (1976).

    Google Scholar 

  12. Knight, Jr., C.E., Orthotropic Photoelastic Analysis of Residual Stresses in Filament-wound Rings,Experimental Mechanics,12 (2),107–112 (1972).

    Google Scholar 

  13. Chandrashekhara, K. and Abraham Jacob, K., An Experimental Numerical Hybrid Technique for Stress Analysis of Orthotropic Composites, Developments in Composite Materials, C.S. Holister, ed., (to be published).

  14. Abraham Jacob, K., An Experimental Numerical Hybrid Technique for Two and Three Dimensional Stress Analysis, PhD Thesis, Indian Inst. Sci. (Aug. 1976).

  15. Allen, D.N. De. G., Relaxation Methods, McGraw Hill Book Co., New York (1954).

    Google Scholar 

  16. Lekhnitskii, Anisotropic Plates, Trans. from 2nd Russian Edition by Tsai, S. W. and Cheron, T., Gordon and Breach (1968).

  17. Sundara Raja Iyengar, K.T. andChandrashekhara, K., On the Theory of the Indentation Test for the Measurement of Tensile Strength of Brittle Materials, Brit. J. Appl. Phys.,13,501 (1962).

    Article  Google Scholar 

  18. Sabodh, K.G., Vytas, S. andGerald, A.G., Analysis of Structural Composite Materials, Marcel Dekkar, Inc., New York (1973).

    Google Scholar 

  19. Kedward, K.T. andHindle, G.R., Analysis of Strain in Fiber Reinforced Materials, J. Strain Anal.,5 (4),309 (1970).

    Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Indian Institute of Science, 560012, Bangalore, India

    K. Chandrashekhara (Professor) & K. Abraham Jacob (Senior Research Assistant)

Authors
  1. K. Chandrashekhara
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  2. K. Abraham Jacob
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Chandrashekhara, K., Abraham Jacob, K. A numerical method for separation of stresses in photo-orthotropic elasticity. Experimental Mechanics 18, 61–66 (1978). https://doi.org/10.1007/BF02324501

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  • DOI: https://doi.org/10.1007/BF02324501

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