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An optimal design problem for submerged bodies
Author(s) -
Angell T. S.,
Hsiao G. C.,
Kleinman R. E.
Publication year - 1986
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670080105
Subject(s) - mathematics , shape optimization , boundary value problem , domain (mathematical analysis) , boundary (topology) , class (philosophy) , variational inequality , space (punctuation) , function (biology) , mathematical analysis , mathematical optimization , surface (topology) , optimization problem , finite element method , geometry , computer science , physics , artificial intelligence , evolutionary biology , biology , thermodynamics , operating system
The problem of finding the shape of a smooth body submerged in a fluid of finite depth which minimizes added mass or damping is considered. The optimal configuration is sought in a suitably constrained class so as to be physically meaningful and for which the mathematical problem of a submerged body with linearized free surface condition is uniquely solvable. The problem is formulated as a constrained optimization problem whose cost functional (e.g. added mass) is a domain functional. Continuity of the solution of the boundary value problem with respect to variations of the boundary is established in an appropriate function space setting and this is used to establish existence of an optimal solution. A variational inequality is derived for the optimal shape and it is shown how finite dimensional approximate solutions may be found.