Question: 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 Equation 12.8.25 Data from example 12.4 Y(z)

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

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

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The potentials from Example 124 where given by Y Alog v A 1 02Y7 4ReY 4Re 0 08 24e2is 0 ... View full answer

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