Abstract
In this paper, 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 in contrast with the nonlinear adjoint systems introduced by Dems and Mróz, and by Dems and Haftka. From these results, the first-order and the second-order necessary conditions that an optimal domain should satisfy are immediately derived.
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Communicated by N. V. Banichuk
Portions of this paper were presented at the 5th IFAC Symposium on Control of Distributed Parameter Systems, Perpignan, France, 1989. The authors would like to express their sincere thanks to the referees for their critical readings.
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Masanao, T., Fujii, N. Second-order necessary conditions for domain optimization problems in elastic structures, part 1: Surface traction given as a field. J Optim Theory Appl 72, 355–382 (1992). https://doi.org/10.1007/BF00940523
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DOI: https://doi.org/10.1007/BF00940523