OrcaFlex Manual - Orcina

Theory, Line Theory
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Figure: Elastic Non-linear Bend Stiffness
Hysteretic
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The hysteretic model includes hysteresis effects, i.e. effects of the history of curvature applied. The data is taken to
specify the bend moment that results when the line is bent with slowly increasing curvature. But that if the
curvature reduces again then the bend moment does not come back down the same curve. Instead when the
curvature reduces again the bend moment comes down the curve that is obtained by first undoing and reversing the
first bit of curvature (i.e. the first increment of curvature that was applied), then the second bit of curvature, etc. In
other words the hysteretic model treats curvature as being made up of a series of curvature increments and
corresponding moment increments, and it undoes them on a first in first out basis, as opposed to the last in first out
basis that non-hysteretic bend stiffness uses.
The effect of this hysteretic model is that the bend moment follows a hysteresis curve, as shown in the following
diagrams. The left hand diagram shows the bend moment that results from a sinusoidal curvature history; the
arrows on the curve show the direction of change of the curvature and moment. The right hand diagram shows what
happens if a small curvature cycle is followed by another curvature cycle of greater amplitude.
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Figure: Hysteretic Non-linear Bend Stiffness
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