Consider the unit disk problem with displacement boundary conditions u r + iu = h() on

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Consider the unit disk problem with displacement boundary conditions ur + iuθ = h(ς) on C: ς = e. Using Cauchy integral methods described in Section 10.5, determine the form of the potentials γ (z) and Ψ(z).

Data from section 10.5

We now develop some solutions of particular plane elastic problems involving regions of a circular domain.

R/ f(0) -1(e) X +

The fundamental stress combinations and displacements in polar coordinates were given in relations (10.2.12).

f(0) = Celke Ck k=- -2 21/1 16 16 f(0)e-ike do 2T 0 (10.5.5)

Matching (10.5.4) with (10.5.5) on the boundary and equating like powers of exponentials of 0 yields the

(r(2). Y(Z) ) + zy' (2) + (z))| where =z=1= ei and 5 =e-i around the boundary contour C (r = 1  "Y(S) = 1/5.

1 y(2) + 12 + 202 + V(0) = 2  3() ac c (10.5.9) We also find that an = 0 for n > 2, and so y(z) = a + a +

0,=-p

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