Abstract
The second-order sensitivity analysis for a domain optimization problem is studied for a linear elastic structure. In the primary elastic structure considered, the surface traction, a part of the boundary conditions, depends not only on the position but also on the shape of the structure. The first variation and the second variation of the objective functional are calculated in terms of the solution, the first variation of the solution for the primal elastic system, and of the adjoint variable introduced. Moreover, the first-order and the second-order necessary optimality conditions are derived for the structure under a hydrostatic pressure. As an illustrative problem, a mean compliance design is treated.
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