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©2012 Civil-Comp Ltd |
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J.A.G. Sánchez and H.B. Coda
Department of Structural Engineering, São Carlos School of Engineering, University of São Paulo, São Carlos SP, Brazil
Keywords: finite element method, riser, surge motions, heave motions, nonlinear dynamic analysis.
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In this paper, the finite element method is applied to obtain the nonlinear dynamic behaviour of risers using bi-dimensional Reissner frame elements. This methodology is based on the minimum potential energy theorem written regarding nodal positions and was proposed by Coda and Greco [1].
The external actions considered are self-weight, buoyancy load, pretension in the top, added mass, drag force and vessel motions. The added mass and drag forces are modelled using the modified Morison equation. The current properties in the surface region follow the linear Airy theory for waves. The vessel movements are applied as displacement boundary conditions at the top. The temporal integration is performed using Newmark's method.
Extensive tests of the basic formulation are performed in order to identify its limitations for riser applications. Various strategies are proposed in order to overcome the detected limitations, including the distribution of the imposed displacement with the aid of an exponential decay technique.
The first example explores the validation of hydrostatic forces. This is a cantilever beam under self-weight and buoyancy forces. Another example is a riser connected to a frictionless ball-joint at the upper and lower end containing mud. Waves are assumed to act in the direction of the positive offset, and the upper end is forced by vessel motion in the surge or heave direction. The vessel motion is sinusoidal with the same period as the wave. Top tension is assumed constant.
The finite element formulation based in positions together with the exponential decay strategy enables the modelling with accuracy the dynamic and static behaviour of riser structures. The results compare well with the ones presented in the literature. It is noted that displacement boundary conditions in the heave direction may cause compression and an increase in the bending stress, especially in the near vertical risers. It is important to the optimal design that structural numerical analysis tools are able to provide the response under these movements.
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- 1
- H.B. Coda, M. Greco, "A simple FEM formulation for large deflection 2D frame analysis based on position description", Computer Methods in Applied Mechanics and Engineering, 193, 3541-3557, 2004.
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