We present a numerical formulation and computational results for the hydrodynamic loads on bottom-mounted thin-shell vertical cylinders of arbitrary cross-sectional shapes, including open bodies. Such cylinders may undergo prescribed or free motion or may be subjected to a wave load. The formulation is based on linear theory and a hypersingular integral-equation results from sectional contours of zero thickness. The method reduces the fully three-dimensional problem into a number of two-dimensional ones in the horizontal plane and is therefore much faster than the usual boundary integral method used for water wave problems. This traditional method of solution is also known to become ill-conditioned as the body thickness decreases. As an example of the current method, radiation and diffraction loads are presented for the cases of a circular and square closed and opened cylinders with the effect of the increased opening size discussed at different frequencies. The free-surface elevation associated with this method of solution is presented for some cases as well.

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