Modelling bend restrictors

We begin by introducing some terminology. A bend restrictor is any device that controls, restricts or limits bending on a line. A bellmouth is a bend restrictor in the form of a curved surface which provides support and limits curvature. A bend limiter is a bend restrictor that has no effect below a certain curvature, but prevents curvature from exceeding that value. A bend stiffener is a bend restrictor that provides increased bend stiffness in order to distribute the bending more widely.

Modelling a bellmouth

A bellmouth is represented in OrcaFlex by a curved plate.

The principal design requirement is that the bellmouth angle should be greater than the maximum value of end force Ez angle. For cases where the bellmouth is not radially symmetrical, OrcaFlex reports components of end force angle in the local $xz$ and $yz$ planes. End force Ezx angle is the component in the local $xz$ plane; end force Ezy angle is that in the local $yz$ plane.

Modelling bend limiters

Bend limiters can be represented in OrcaFlex by nonlinear bend stiffness with

Typically the low stiffness value will be close to zero and the high value one or two orders of magnitude greater than the stiffness of the protected line. To avoid numerical instability, try to avoid using too large a stiffness value and aim for a smooth transition between low and high stiffness.

Commonly, bend limiters are modelled by a single combined line type object to represent both the protected line and the limiter. The bend stiffness for this combined line type must account for both the protected line and the limiter. You may choose also to account for mass, displacement and hydrodynamic properties but often these properties are of lesser importance.

An alternative is to represent the limiter as a separate object using the bend stiffener attachment (see below), with the attachment line type being of the general category and having the requisite nonlinear bend stiffness. This method maintains the separation of protected line data and limiter data, so may be more helpful for QA purposes.

Bend limiter design

There are two design requirements for bend limiters:

  1. The limiter length must be not less than $\theta r$, where $\theta$ is the end force Ez angle and $r$ the limiter locking radius.
  2. The limiter must be capable of withstanding the maximum bend moment $m$ given by $m = r\,p$ where $p$ is the bend restrictor load, sometimes called the pseudo-curvature.

Modelling bend stiffeners

Bend stiffeners are modelled in OrcaFlex by two separate lines, one representing the stiffener and the other the protected line. The region of the protected line which is covered by the stiffener is called the protected region.

Using separate lines in this way facilitates reporting of separate results for the protected line and stiffener. In particular, fatigue analysis of the protected line is straightforward, since the reported loads and stresses for the protected line do not include the contributions of the stiffener.

The bend stiffness of the protected line may take a linear, nonlinear elastic or hysteretic form. The stiffener is modelled as a profiled homogeneous pipe, and may have linear or nonlinear elastic material properties.

Data

Although the stiffener is modelled as a separate line, you do not create this line explicitly: OrcaFlex creates it automatically as an attachment. The procedure for setting up a bend stiffener is:

  1. Create a line type which defines the material, structural and hydrodynamic properties of the stiffener. Usually this will be a profiled homogeneous pipe.
  2. Create a stiffener type of this line type.
  3. Create a line attachment of this stiffener type.
  4. Set the line attachment position and the stiffener type connection arc length and relative to so that the stiffener is attached at the desired location on the protected line.

The stiffener profile uses the convention that profile arc length increases from end A towards end B of the stiffener. If you have a bend stiffener connected at end B of a line, then you will need to define the profile so that the arc length 0 refers to the tip of the stiffener. The modelling stress joints topic illustrates this issue in more detail: stress joints are also profiled homogeneous pipes, and the discussion there of profile direction is equally applicable to bend stiffeners.

We strongly recommend that you use the profile graph, available from the line data form, to check that the stiffener is connected at the correct location on the line with the profile defined as you intended.

If you have multiple protected lines using identical bend stiffeners, then you can create a single stiffener type which can be re-used on each protected line.

Segmentation

The stiffener line that OrcaFlex creates is modelled with uniform segment length – that is every segment in the stiffener has the same length. The segment length is determined by the segment length of the protected line in the protected region.

The stiffener modelling (see below) requires that each node on the stiffener line is associated with a node on the protected line. Each stiffener node is effectively clamped, at least partially (see below), to its associated protected node.

These constraints have the following implications for the segmentation of the protected line:

  1. The protected region must have uniform segment length.
  2. The stiffener length must be an exact multiple of the segment length.

One simple way to satisfy these requirements is to model the protected region as a single section with length equal to the stiffener length.

Note that it is not essential for the protected region to be a single section. The protected region could comprise multiple sections each using different line types, so long as you satisfy the two rules above.

Drawing and results

The stiffener line is drawn using the drawing data of the protected line to which it is attached.

Results are available for the stiffener line exactly as they are for any other OrcaFlex line.

OrcaFlex reports results separately for protected line and stiffener line and this does need some explanation. For example, consider bend moment at a particular location on the protected line and at the corresponding location on the stiffener line. Suppose that the bending stiffnesses are $EI_\mathrm{p}$ and $EI_\mathrm{s}$ for protected line and stiffener respectively (assuming linear bend stiffness for simplicity). The bend moment carried by the protected line and stiffener ensemble is given by $B\!M_\textrm{total} = c(EI_\mathrm{p}+EI_\mathrm{s})$, where $c$ is the curvature at this location. For the protected line OrcaFlex reports the local protected line bend moment $B\!M_\mathrm{p} = c\,EI_\mathrm{p}$; likewise for the stiffener line, OrcaFlex reports $B\!M_\mathrm{s} = c\,EI_\mathrm{s}$. It is straightforward to see that $B\!M_\textrm{total} = B\!M_\mathrm{p} + B\!M_\mathrm{s}$.

The total load is also split into separate protected line and stiffener loads for effective tension, wall tension, shear force, torque and stress results.

Modelling details

As described above, the stiffener is represented by a separate line which OrcaFlex creates automatically as an attachment. The stiffener line inherits a number of properties from its protected line, namely:

OrcaFlex calculates the loads and inertia on the stiffener line, then transfers them to the protected line. The components of load and inertia normal to the stiffener are transferred directly from each stiffener node to its associated protected node, thus enabling the stiffener to perform its job of spreading the bend loads over the protected region. The transfer of the axial components depends on the axial load/inertia transfer data of the stiffener type, as follows.

If the axial transfer is at the connection point, then components of axial load/inertia are transferred to the protected node at the connection point. Typically this connection point is at the end of the protected line and the axial loads and inertia are thus transferred to the protected line's end connection. Each stiffener node (other than the connecting node) has just one free translational degree of freedom, allowing it to slide axially along the protected line, and in addition, if torsion is included, one free rotational degree of freedom. allowing it to twist relative to the protected line. Axial friction due to contact between stiffener and protected line is thus neglected.

If, on the other hand, axial transfer is over the stiffener's full length, then components of axial load/inertia are transferred directly from each stiffener node to its associated protected node. Each stiffener node is, in effect, clamped to its associated protected node, and the stiffener line has no free degrees of freedom. In this case, the axial contact friction is assumed to be sufficient that there is no axial slipping. The axial load will be shared between protected line and stiffener as determined by their relative axial stiffnesses, just as the bend moment is shared.

Fluid loading

Because the protected line is shielded from the fluid by the stiffener, OrcaFlex suppresses fluid loading on the protected line. The protected line sees no drag, lift, added mass or fluid inertia loads.

Buoyancy forces are applied to both lines. The protected line has displacement calculated from its outer diameter in the standard manner. The stiffener line has a displacement determined by its annulus.

Bend stiffener design using OrcaFlex

The modelling approach described above applies to an existing bend stiffener design, and one of the objectives of the analysis is to confirm that the stiffener provides the required protection. However, in many cases the stiffener design does not yet exist and the analysis is needed in order to define design loads. In this case, you should run a preliminary analysis without a bend stiffener, and model the line with a pinned end (i.e. zero bending stiffness at the line end connection).

The load information required for the bend stiffener design then consists of paired values of force and angle at the pinned end. These can be obtained in the form of an X-Y graph showing end force against end force Ez angle for the first segment. In practice, it is often sufficient to consider just three points on this graph, corresponding to maximum tension, maximum angle and maximum bend restrictor load: these can be extracted as linked statistics. Recall that end force Ez angle is an absolute magnitude and therefore always takes a positive value. If a signed value is required (e.g. to define out-to-out load cycles for fatigue analysis), then use the end force Ezx or end force Ezy angle as appropriate.

It is usually necessary to combine results from several analyses to fully define the bend stiffener design loading. This is most conveniently done by exporting the end force vs end force Ez angle results as a table of values for each analysis case, combining them into a single Excel spreadsheet and generating a single Excel plot with all results superimposed. A simplified set of load cases representing the overall loading envelope can then be selected for use in stiffener design. The export to Excel can be done manually or automated through the results spreadsheet or OrcFxAPI.

Bend stiffener design using OrcaBend

The task of bend stiffener design is usually left to the manufacturer, since the actual stiffener shape selected is governed in part by the manufacturing process, availability of tooling, etc., as well as by the load cases. The Orcina program OrcaBend has been developed to assist this process. For further information on OrcaBend, contact Orcina.