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Abbreviations
- a :
-
inner radius of the inclusion i.e. radius of cavity
- b :
-
outer radius of the inclusion
- X :
-
b/a
- G :
-
shear modulus
- g :
-
G 2/G 1
- l :
-
couple-stress constant
- λ:
-
a/l
- ⋎:
-
Poisson's ratio
- γ, θ:
-
polar coordinates
- ϱ:
-
r/l
- \(\left. {\begin{array}{*{20}c} {\sigma _r ,\sigma _\theta } \\ {t_{r\theta } ,t_{\theta r} } \\ \end{array} } \right\}\) :
-
stresses in polar coordinates
- M r ,M 0 :
-
couple-stresses in polar coordinates
- u r ,u 0 :
-
displacements in polar coordinates
- \(\omega _{\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle\cdot}$}}{r} \theta } \) :
-
rotation in polar coordinates
- I 1,I 2 :
-
modified Bessel's function of 1st kind, order one and two respectively
- K 1,K 2 :
-
modified Bessel's function of second kind, order one and two respectively
- Φ:
-
airy stress function
- Ψ:
-
couple-stress function
- T :
-
magnitude of uniaxial tension
References
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Parhi, H.K., Das, A.K. The effect of couple-stresses on stress concentration of a ring inclusion. Acta Mechanica 14, 219–227 (1972). https://doi.org/10.1007/BF01184860
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DOI: https://doi.org/10.1007/BF01184860