A novel method for 3-dimensional dynamic analysis of marine slender structures such as risers and pipelines is developed using Euler parameters. The Euler parameter rotation, which is widely used in kinematics of rigid body motion, is applied to elastic structure analysis. Large deformation of flexible slender structures is described by means of Euler parameters. Euler parameter method is implemented effectively in an incremental-iterative algorithm for 3D dynamic analysis. The normalization constraint of Euler parameters is efficiently satisfied by means of a sequential updating method.


It is the large deformation response to external loads that distinguishes marine slender structures such as risers, pipelines, cables and moorings from other offshore structures. Flexible risers, tether cables of remotely operated vehicles and flexible conduit for deep ocean mining are the representative examples. Euler angles systems are frequently used in the mathematical modeling of the geometric nonlinearity of slender structures (Bernitsas 1982, Patrikalakis 1986, Hong 1992, 1995, 1997a, 1997b). The Euler angles, which have been investigated in kinematics of rigid body motion (e.g. Goldstein, 1980), are convenient for description of body rotation. However, they are difficult to use in numerical computation because of the large number of trigonometric functions involved and some singular orientations. Four Euler parameters are preferred in aerodynamics, mechanical systems, multi-body dynamics and so on, since the transformation matrix is expressed by algebraic terms and no singular orientation exists. However, the four Euler parameters are not independent each other, but related by the normalization constraint, which is represented by an algebraic equation. Thus, the equations system to be solved becomes differential- algebraic equations (DAE). Bae (1994) proposed a sequential update method satisfying the normalization constraint, in which the normalization constraint of Euler parameters is involved implicitly in Newton's method and the Euler parameters are corrected during the iteration.

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