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*NonLinear Model

Purpose

To specify a modelling approach for non-linear materials.

Theory

Refer to Tangent and Secant Stiffness and Curvature Slippage for further information on this feature.

Keyword Format

A single line specifying the modelling option.

METHOD=Method

Method can be either TANGENT or SECANT. Whichever option is invoked carries through to any or all subsequent restarts, until it is changed again. If the keyword is never invoked, the tangent method is used by default.

An optional line to adjust material properties for an element set.

EI=EI Type [, NONLINEAR=Nonlinear type] [, SET=Set Name]

This line may be repeated as often as required to redefine element properties.

EI Type can be LINEAR or NONLINEAR (the default). Nonlinear type can be ORIGINAL (the default) or CURVATURE_SLIPPAGE. Set Name defaults to ALL if omitted.

Whichever options are invoked, they carry through to any or all subsequent restarts, until subsequently altered.

Table Input

Non-linear Model – Solution Method

Non-linear Model – Bending Stiffness

Notes

(a)This option relates to non-linear structural properties, whether defined in the Flexible Riser or the Rigid Riser format, and non-linear elements. Under normal circumstances, both methods should produce exactly the same results, but the secant method may provide additional robustness occasionally. 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 nonlinear 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. Refer to Tangent and Secant Stiffness for further information.

(b)When the Linear option is invoked, Flexcom will use the linear bending stiffness specified under the *GEOMETRIC SETS keyword. When the Nonlinear option is invoked, Flexcom will use the non-linear moment-curvature relationship defined under the *MOMENT-CURVATURE keyword, and referenced under the *GEOMETRIC SETS keyword. The non-linear relationship may be consistent with the original data (see Note (c)), or modified automatically by the program (see Note (d)).

(c)If the Original option is specified, Flexcom will simply apply the (unmodified) user-defined moment-curvature relationship, as defined under the *MOMENT-CURVATURE keyword, to the specified element set.

(d)If the Curvature Slippage option is specified, Flexcom will automatically modify the user-defined moment-curvature relationship, as defined under the *MOMENT-CURVATURE keyword, and apply the modified data to the specified element set. Refer to Curvature Slippage for further information on this feature. The modification procedure may be summarised as follows.

•The program ascertains the bending moment and curvature at the element mid-point, at the end of the preceding analysis stage. These governing values, typically derived from a preceding static analysis, are termed Ms and Ks, respectively.

•For the purposes of determining the moment from a given curvature, the curvature is first adjusted, by subtracting the governing Ks value. The moment is then obtained from the non-linear moment-curvature relationship, and subsequently translated by the slip moment Ms.

•Note also that the non-linear relationship is mirrored about the {Ks, Ms} slip point, and that all points on the original non-linear moment-curvature relationship should be zero or positive (i.e. the original curve should be defined in the first quadrant).