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Thickness-variation analog for nonhomogeneous plane-elasticity problems

The experimental stress analysis of isotropic, nonhomogeneous plane-elasticity problems can be accomplished by means of models whose thickness varies as the modulus

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Abstract

This investigation was undertaken to show that the experimental study of the stress distribution in plane nonhomogeneous bodies may be accomplished by using models of varying thickness. Fabrication of models makes the experimental analysis of heterogeneous plane bodies difficult. Equations of elasticity are given which show that models with thickness variation should give the same results as those with a comparable variation in Young's modulus. Experimental results are given for the thickness-variation analog of the classical inclusion problem of varying modulus. These results are compared with the known theoretical results of the classical problem.

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Abbreviations

a :

radius of inclusion

E :

Young's modulus

E i :

Young's modulus inside inclusion

E o :

Young's modulus outside inclusion

t :

thickness of plate

t i :

thickness inside inclusion

t o :

thickness outside inclusion

T :

uniform tension without inclusion

f :

1/Et=modulus-thickness function

ϕ:

stress function

σ:

normal stress

τ:

shearing stress

∇2 :

Laplace's operator

∇4 :

biharmonic operator

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Authors and Affiliations

  1. Kansas State University, Manhattan, Kan

    J. R. Kimzey (Graduate Student) & F. J. McCormick (Professor of Applied Mechanics)

Authors
  1. J. R. Kimzey
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  2. F. J. McCormick
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Kimzey, J.R., McCormick, F.J. Thickness-variation analog for nonhomogeneous plane-elasticity problems. Experimental Mechanics 7, 403–406 (1967). https://doi.org/10.1007/BF02326313

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