2ND-ORDER SHAPE SENSITIVITY ANALYSIS FOR NONLINEAR PROBLEMS

First- and second-older shape sensitivity analyses in a fully nonlinea r framework are presented in this paper. Using the fixed domain techni que and the adjoint approach, integral expressions over the domain are obtained. The Guillaume-Masmoudi lemma allows these expressions to be rewritten as integrals over the domain boundary. The formalism is the n applied to the steady creep of a bar in torsion, as an example of po wer-law nonlinearities that occur not only in creep problems but also in viscoplastic fluid flow. Finally, a problem with known analytical s olution is presented in older to show the equivalence between exact di fferentiation and the shape sensitivity approach.