Bend Stiffeners |
 
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Bend Stiffeners |
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Bend stiffeners are typically positioned at the termination of a flexible riser to prevent excessive bending occurring. Like tapered stress joints, they are assumed to be conical in shape. The user inputs include the external diameters at the two ends of the stiffener, the Young’s modulus of the stiffener material, the total mass of the stiffener, and the stiffener internal diameter. These properties are assigned to a named element set, and the elements comprising the set are defined separately. One important point to note about a bend stiffener is that it provides additional bending resistance to the elements over which it is positioned. So the elements of the bend stiffener set must also be assigned properties appropriate to normal beam-column elements. The order in which the elements are specified in defining the bend stiffener element set is very important. The first element specified is assumed to be at the free end (smaller diameter) of the bend stiffener and the last element is assumed to be at the fixed end (larger diameter). Intermediate elements must be specified in order from free end to fixed end.
Flexcom uses the specified bend stiffener properties as follows. The external diameters at stiffener interior nodes are found by linear interpolation between the stiffener start and end values. If the external diameters at the ends of a particular stiffener element are 
and 
, and the stiffener internal diameter is 
, then the moments of inertia at the element ends 
and 
can be calculated in the usual way - for example:
(1)
An average value for the element 
is calculated as:
(2)
The user-specified bending stiffnesses EIyy and EIzz for the element are augmented by the addition of EBSIav, where EBS is the Young’s modulus of the stiffener material. The bend stiffener is assumed to provide no additional axial or torsional stiffness to the riser. Note that you have the option to specify a non-linear material model for your bend stiffener, which is defined in terms of a direct stress-strain curve. If you invoke that option, then the value of EBS will be an instantaneous rather than a constant value.
In earlier versions of Flexcom, when you specified a mass for a bend stiffener this mass was distributed between the elements protected by the stiffener, which therefore had a mass increased from that specified by the user. Likewise the buoyancy diameter for these elements was increased to add the volume of water displaced by the bend stiffener to the volume displaced by the riser elements themselves. The current modelling approach differs in two respects. Firstly, by default (that is, unless you specify otherwise), the mass and buoyancy of the bend stiffener are not now included in the analysis loading. The rationale for this is that these loads are rarely transferred to the riser itself, but are in fact carried by an end fitting. You do though have the option to override this: if you exercise this option, the second change in program operation occurs. Instead of the weight and buoyancy of the stiffener being distributed over the enclosed elements, these are now applied as point loads at the stiffener end where the outer diameter is a maximum. (In fact Flexcom positions a point buoy with zero hydrodynamic coefficients at this location, which is effectively the same thing.) The program does apply one check as follows: if you specify a stiffener mass but do not change from the default program mode of operation, then you are warned that the weight of the stiffener will not in fact be included in the analysis.
To summarise, a bend stiffener specification is similar to that of a tapered stress joint described earlier, but differs in a couple of aspects:
(i)The properties assigned to the bend stiffener are additional to the properties defined for the standard beam element which it encloses. Flexcom automatically increases the bending stiffness of the elements where the bend stiffener is positioned, using the relevant bend stiffener properties.
(ii)Bend stiffeners can be either linear or non-linear. Young’s Modulus can be defined using a single (constant) value, or characterised in terms of a non-linear direct stress-strain relationship.
•*STIFFENER is used to define the properties of a conical bend stiffener positioned on a flexible riser or pipe.
•*NONLINEAR STIFFENER is used to define a stress-strain curve for a non-linear bend stiffener.
If you would like to see an example of how these keywords are used in practice, refer to C01 - Free Hanging Catenary.