Analysis of second order steady hydrodynamic forces on floating bodies in regular waves by finite element method

This paper is concerned with the computation of second order steady hydrodynamic forces experienced by floating bodies exposed to regular waves. A finite element method developed earlier for the linear diffraction-radiation problem of floating bodies in the frequency domain has been extended to build the capability for calculating second order mean hydrodynamic forces employing the first order potentials. The fluid domain is modeled using isoparametric hexahedron and/or pentahedron elements and the far field boundary condition is imposed by the use of boundary dampers. Expressions derived for second order force based on the direct integration of pressure on the submerged surface of the body have been used in this work. The adaptability of the finite element method for second order force calculation is demonstrated by computing both horizontal and vertical components of the second order steady force on a hemisphere, a semi-circular cylinder in beam sea and a floating square box.