Taking the total complementary dissipation energy as the cost function and the compatibility as the state equation, the first and second order shape sensitivity analysis for steady-state creep torsion problems are presented in this paper. Using the variational formulation, the fixed domain technique and the adjoint approach, integral expressions over the domain are obtained. Moreover, a particular case with known analytical solution is analyzed in order to show the equivalence between exact differentiation and the shape sensitivity approach. Finally, this example is also used to stress that the extension of the velocity field to the interior of the domain is irrelevant.

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