Hydrodynamic shape optimization of thin floating plates

In this work, the problem of optimizing the shape of a thin floating plate (sometimes called a dock) to maximize radiation damping is investigated. The plate is modeled with zero draft and floats on the surface of an irrotational, incompressible ocean of infinite extent. For simplicity, only rigid heave motions are considered. The flow problem is analyzed using the Chen and Mei variational principle wherein the potential field inside a hemisphere surrounding the plate is represented using a spherical harmonic expansion and matched on the hemisphere to an outer field described by distributing sources on the hemisphere. The plate shape is parameterized using a Fourier series which is suitable for use with the variational principle. Gradients of the damping coefficient with respect to the shape parameters are developed by solving an adjoint flow problem whose potential is shown to be a scalar multiple of the original flow potential. Optimal plate shapes are determined using the well-known optimization code NPSOL which makes use of the damping coefficient calculation and gradients.