The geometrical quantities to define the configuration of a riser in three-dimensional (3-D) space are thoroughly reviewed. The riser configuration is described by the position of the riser centroidal line and the twist of riser cross sections. The riser centroidal line is conventionally specified by the three displacement components along three fixed rectangular Cartesian coordinate system. However, in case to deal with the impact on the riser at the seabed, or the lateral vibration around the static equilibrium position, the use of the displacement components in the tangential, principal normal and binormal directions seems preferable. The twist is described by the orientation of riser cross sections. Based on the assumption that a plane section remains a plane and remains perpendicular to the displaced centroidal line, the orientation is given by one of the three means: three Euler's angles, the angle of a cross sectional radius relative to the principal normal of the centroidal line, and the angle rotated from any artificial unstrained position. The relative merits of each of the three means are presented. Finally, the cross sectional deformation is described by a radial movement and a sinusoidal displacement. The former governs the change in the cross sectional area, while the later describes the oval deformation which is usually neglected in ordinary analysis except until ovalization occurs.


In the analysis of a marine riser in three-dimensional space, it is necessary to express geometrical quantities to define the riser configuration in static and dynamic states. These quantities are, namely, centroidal line, orientation of a cross section, and deformation of a cross section. Bernitsas (1982), Bernitsas et al. (1985), and Kokarakis and Bernitsas (1987), O'Brien et al. (1988) used a centriodal line to define the 3-D riser configurations with axial and bending deformations.

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