Previous sections have discussed use of a riser analysis in design, and modeling of environmental effects lead to applied loads and vessel motions. The objective of this section is to provide general guidance on analyses techniques and modeling practices typically used in industry. The treatment is intentionally generic, because many techniques apply to a wide variety of riser configurations and can be used to generate basic data from which further detailed results (e.g., component stress, tensioner stroke, riser clearance) can be derived. More detailed guidance for specific analyses and riser types is provided in subsequent sections.
The following presents the basic equation of motion fundamental to riser analysis and covers several key issues that need to be properly addressed in every riser analysis, including effective tension, stiffness, mass, buoyancy and hydrodynamic loads. Next, a discussion of typical boundary conditions is presented, followed by an introduction to various solution techniques. Finally, several special modeling considerations are discussed.
For simplicity in presentation, the following discussion is restricted to the case of planar, small angle, linear strain analysis of an initially straight riser modeled as a tensioned beam.
The static equilibrium equation for lateral displacement of a tensioned beam is:
...(35)
where
z = Spatial coordinate along the beam axis,
u = Transverse displacement in the direction of the load,
EI = Bending stiffness of cross section,
r = Applied lateral load, not including applied hydrostatic and pressures
Te = Effective tension.
The beam’s resistance to deformation is provided by flexural stiffness and more significantly, geometric stiffness arising from axial tension.
The dynamic equation of equilibrium can be obtained from Equation 35 by incorporating inertia forces and a mechanism for energy loss (damping). Applying D'Alembert's principle, assuming viscous damping, and simplifying leads to:
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