Second-order necessary conditions for domain optimization problems in elastic structures. I: Surface traction given as a field (Q1321156)

Domain optimization problems for both linear and nonlinear elastic structures are studied. The first variation and the second variation of the objective function are calculated in terms of the solution, of the first variation of the solution for the primal elastic system, and of the adjoint variables introduced. The adjoint variables obey a (fictitious) linear elastic system. From these results, the first-order and the second-order necessary conditions that an optimal domain should satisfy are immediately derived.