For Example, 12.4, explicitly develop the stresses (12.8.25) from the complex potentials given by Eq. (12.8.23). Equation

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For Example, 12.4, explicitly develop the stresses (12.8.25) from the complex potentials given by Eq. (12.8.23).

Equation 12.8.23

Y(z) = A log z (2) = 4 (4/2 -A +1) +log z+1

Equation 12.8.25

Or de Tre || 1 Eaqa (a 2 k 1 Eaqa (a 2 k  (  + 1 Eaga (a 2 k r sin sine $7) cos#

Data from example 12.4

We now investigate the localized thermal stresses around a traction-free circular cavity in a plane of

which yields the actual temperature field (r. = 1/2 (r + /) si T(r,0) = 71 (12.8.20) This solution can also

with  (1 + k)k Using our previous polar coordinate stress combinations (10.2.12), we find or +00= Eaqa kr

I  a LI J X

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