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Topological Asymptotic Expansion of the Shape Functional
Now we are in position to establish the asymptotic expansion of the shape functional and obtain its topological derivative. After introducing the first ansatz in the shape functional associated to the perturbed problem, we have
Ąus) = -J (u + f(e)g + = - u- e-f(e) • ue
(70)
= Ąu)-f(e)Jge + o(f(e]).
J. Sokołowski (IECL) Topological Derivatives October 6, 2015 62 / 110
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