Tangent and Secant Stiffness |
 
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Tangent and Secant Stiffness |
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Traditionally, Flexcom has employed a tangent method for modelling non-linear materials. An alternative secant approach is now also available. This may be helpful in situations where the default tangent method leads to solution robustness issues. The option relates to non-linear structural properties, whether defined in the Flexible Riser or the Rigid Riser format, and non-linear bend stiffener elements. Both methods are illustrated graphically in the figure below for a sample moment-curvature relationship.
Secant Stiffness Method
Under normal circumstances, both methods should produce exactly the same results, but the secant method may occasionally provide additional robustness. For example, the tangent method generally requires that the slope should either monotonically increase or monotonically decrease with increasing displacement. Otherwise, there may be more than one location along the non-linear relationship which results in the same restoring force, and this may contribute to solution instability. The tangent method is still retained as the default option, as the secant method should, in theory at least, typically require a slightly larger number of iterations for solution convergence.
•The secant stiffness option is available for Static Analysis and Time Domain Analysis only, and does not apply to Frequency Domain Analysis.
•The secant stiffness method applies to Non-Linear Elastic material properties and non-linear Bend Stiffeners.
•Many other non-linear modelling features, such as Spring Elements, Pipe-in-Pipe Connections, Seabed Embedment etc. still employ the tangent stiffness method even if secant stiffness is specified.
•P-y curves used in Soil Modelling are an exception in that they are always modelled using the secant method (where the secant approach typically provides greater numerical stability).
•*GEOMETRIC SETS is used to assign geometric properties to element sets.
•*STIFFENER is used to define the properties of a conical bend stiffener positioned on a flexible riser or pipe.
•*NONLINEAR MODEL is used to specify a modelling approach for non-linear materials.