Dynamic Analysis of Risers and Caissons by the Element Method
Authors: Gardner T.N. , Kotch M.A 
Published: October 2008

ABSTRACT
The finite element formulation leads to an efficient and accurate solution for the dynamic response of caissons and risers. The governing equations are derived including intermediate ball joints with nonlinear stiffness, periodic excitation due to surface vessel surge, sway and heave motion, the hydrodynamic excitation of a periodic wave, and multidirectional current. Parametric results based on the method are presented-with emphasis on a deep water riser design having distributed buoyancy material. Or-particular interest is the sensitivity of bending stresses near the bottom of the-riser to periodic top surge and wave forces and the importance of maintaining adequate tension.

INTRODUCTION
The diminishing unit cost, over the past decade, of high speed mass storage digital computer capability has encouraged the wide spread use of the finite element method. Whereas the early structural analysis computer programs were simply computerized versions of techniques previously performed by hand, the stiffness method of finite element analysis became practical only through implementation on digital computer. The melding of the method and the tool has been so successful that the finite element stiffness method has virtually eclipsed all others for large scale structural analysis. Although several finite element riser programs are known to have been developed, formulation of the riser analysis problem by this method has not yet appeared in the published literature.
Over the years, riser design analysis has received considerable attention. Early investigations of riser structural analysis [1, 2] provided the insight necessary for successful design of shallow water risers. More recently, Burke [3] studied riser response sensitivity to the frequency content of the excitation by developing a linearized method of riser dynamic analysis in the frequency domain. This approach has particular value in establishing riser fatigue life. In a series of articles' still being published, Morgan [4, 5] has discussed numerous problems relating to the environment, analysis, and design criteria of marine risers with particular emphasis on deep water.
The objective of this paper is to add to the published literature a reasonably complete. Formulation of the riser dynamic response problem by the finite element method. Questions relating to environmental excitation are given only cursory attention. For example, a periodic wave is mentioned as the source of excitation. A more appropriate description of deep sea environment, however, is a random, multi-directional sea state. Methods have been demonstrated in the literature [6, 7] for converting such a random spectral definition to a time history excitation which can be employed in nonlinear dynamic analysis. Similarly, the method described in the next section could be readily converted to linearized, frequency domain methods. Such extensions, and others, are left fox subsequent efforts.

MATHEMATICAL MODEL

Basic Assumptions
Before embarking on the theoretical development it is appropriate to establish the underlying assumptions.