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*Bending Hysteresis

Purpose

To define hysteresis moment-curvature backbone curves for non-linear materials.

Theory

Refer to Hysteretic Bending for further information on this feature.

Keyword Format

A block of lines which define a moment-curvature relationship. The block begins with a line defining its name, followed by as many lines as necessary to define each point on the moment-curvature curve. The block can be repeated as often as necessary.

Line defining curve name:

CURVE=Curve Name

Line defining a point on the curve:

Moment, Curvature

Each curve must have at least two points defined. The hysteresis curve may not be associated with non-linear beam elements which are defined using the rigid riser format for geometric properties specification.

Table Input

Notes

(a)Use as many lines as you need to completely define a particular moment-curvature curve. Simply leave Column 1 blank for second and subsequent lines. For subsequent moment-curvature curves, put the curve name in Column 1 and specify the moment-curvature data in the same way.

(b)The points defining the non-linear moment-curvature curve may be specified in any order. Flexcom subsequently sorts the data pairs into ascending order of curvature.

(c)Two to ten segments normally capture the essential characteristics of the hysteresis response.  Two segments give a bi-linear curve, while a larger number of segments can be used to represent a smoother hysteresis curve.  The hysteresis curve is required to be such that the (positive) bending stiffness decreases as the loading increases, that is, the curve softens and does not harden.

(d)Flexcom converts the hysteresis curve into a multiple component system of elasto-plastic stiffnesses and a linear elastic stiffness.  The linear elastic bending stiffness equals the slope on the last segment of the hysteresis curve. The last slope must be positive and usually equals the bending stiffness when hysteresis is not included in the model, for example, a depressurised flexible pipe.

(e)When hysteresis is included in the model, the bending stiffness is assumed symmetric about the local-y and local-z axes.