Precise High Speed Stochastic Fatigue Evaluation of Risers Applying 2D Hysteresis Models
Authors: Arnholm Carsten , Hoen-Sorteberg Christopher , Gundersen Paul 
Published: June 2014

Abstract
Dynamic global displacement response of risers subjected to irregular waves is commonly simulated by time-domain Finite Element methods. This captures the non-linearity in wave and drag loading, and includes geometric non-linear effects, while material behaviour often is assumed linear. Segments of flexible risers experiencing large curvatures may respond non-linearly with respect to armour friction behaviour, but the effects on the global displacement responses are minor. However, the armour wire stresses are significantly influenced by such local friction, causing hysteresis effects that influence estimated fatigue life. In such simulations, stress levels can be obtained as an integral part of the simulation procedure, or by post-processing the global response time series using a local-global approach where global response to stress transfer functions are generated once through a local analysis with a detailed FE model. Similar approaches have previously been demonstrated, but with significant limitations in stress precision and computational speed. This limited the practical use of such methods.
A general methodology that overcomes these issues has been developed. The methodology is applied for risers with tension-dependent hysteresis relationships for 2D curvature to stress. Almost exact replication of the stresses calculated by detailed 3D FE-models, even when loaded by irregular global response time series, is obtained.
The high computational speed allows for fatigue estimation applying irregular wave loading over the complete wave scatter diagram. The calculation of one stress time series is performed at approximately 1/7500 of the time used for the global analysis of a typical flexible riser configuration. The fatigue accumulation for a stress time-series is performed at 1/10 of the time used for the stress computation.
The methodology and implementation allows for full stochastic fatigue evaluation of flexible risers with acceptable total computational effort. This results in more accurate and in many cases significantly increased fatigue lives due to elimination of the inherent conservatism in regular wave based methods. The generic aspects of the methodology promises similar advances in related areas, e.g. threaded and bolted connectors in wellhead casings, top-tensioned risers and umbilicals.
This paper demonstrates through a working implementation that the methodology is practical and sound.

Introduction
Fatigue evaluation of tensile armour wires in flexible risers is an important part of the design and evaluation process for flexible risers. This requires sufficiently accurate determination of the stress cycles experienced by the riser armour wires over their design life.
The computation of armour stresses can in principle be performed either as a post-processing step to a global riser analysis based on a beam finite element model or the stresses can be computed as an integral part of the global response simulation. The first approach was presented by Doynov et al (Doynov 2007), while Majed et al (Majed 2013) present a variant of the second approach based on a nonlinear dynamic substructuring technique.
A major advantage with the approach of Doynov et al (Doynov 2007) is that it does not require modification of already well-tested and verified riser global response simulation software. Furthermore, riser global analysis software normally have the option to include hysteresis material models for the beam elements in case this is found necessary to reduce conservatism in the stochastic global response simulation. However, it is our experience that a linear material model is sufficient for simulation of global stochastic response time series without being overly conservative.