An Optimal Design Problem for Submerged Bodies,
DELAWARE UNIV NEWARK APPLIED MATHEMATICS INST
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When a body, floating on the surface of an infinite, ideal, inviscid, irrotational fluid is subjected to a periodic vertical displacement, a wave pattern is created in the fluid and the problem of determining this pattern from a knowledge of the body geometry and applied forces is well known in fluid mechanics. In problems with both partially and fully submerged objects, quantities of physical interest are not only the wave patterns which may be derived from the velocity potential but also functionals of the potential such as added mass and damping factors which measure the distribution of energy in the fluid. These factors are, of course, dependent on the body geometry. The present paper is devoted to showing how these quantities may be optimized over restricted classes of body geometry. Specifically we study the problem of the optimal design of a floating body, totally submerged in a fluid of finite depth. In the terminology of optimal control, this is a problem of optimization of geometrical elements.
- Numerical Mathematics
- Fluid Mechanics