This paper describes the development of a computational system for determining the wave-induced loads and motions of semi submersible catamarans. The procedure is based upon a strip theory computation of the hydrodynamic forces and utilizes a modified Frank close-fit technique for obtaining sectional added mass and damping coefficients. By this procedure the flow interaction effects between the two hulls and the effects of the free surface are taken into consideration. A number of pilot studies have been undertaken to ascertain the importance and nature of these effects.
Example calculations for configurations having the proportions and other features typical of real semi submersibles have shown that the hydrodynamic forces on the vertical surface-piercing legs play an important role in determining platform motion response. The forces on these legs may be approximated by including the legs in the strip wise representation of the main hulls, or the legs may be treated separately. Neither method yields completely satisfactory predictions of the platform response in the case of legs of large cross section. For slender legs and deeply submerged hulls, however, the predicted motions are in good agreement with model test results.
Several "First generation" computational procedures for the prediction of wave-induced forces and motion response of semi submersible drilling platforms have been developed and described in recent years. Examples are contained in papers by Burke (1970), Pauling (1970), Hoof (1971) and others. These procedures all share several basic assumptions concerning the computation of the hydrodynamic forces exerted by the fluid on the structure including:
The structure may be subdivided into several elements of simple geometrical form, principally slender cylinders or small volumes.
The distances between elements are large compared to element cross sectional dimensions, thus the hydrodynamic interference or interaction between elements may be neglected, and the force on one element may be computed as though the other parts of the structure are not present.
The typical cross sectional dimension of each element, e.g. its diameter, is small compared to the length of waves causing the motion, thus the fluid pressures, velocities and accelerations on the surface of the element may be approximated by nominal values computed at the centerline of the element.
The principal part of all members is deeply submerged below the free surface and, therefore, infinite fluid values may be used for damping and added mass coefficients. By this assumption, drag forces due to wave dissipation are effectively neglected.
The so-called "Morison formula" is frequently used as a starting point in computing the fluid forces on a cylindrical member. Since the viscous drag is assumed to be proportional to the velocity squared in this representation, it is necessary to formulate an equivalent linear drag coefficient for inclusion in the final linear equations of motion of the structure. This resulting equivalent linear coefficient proves to be a function of the amplitude of motion, thus necessitating an iterative solution procedure for the equations of motion.