3 point bending of flexible pipe

The input to this model can be found in the example folder, under case E006.

A flexible pipe installed in a 3 point bend set-up is modelled. The modelling is based on thinwall elements.

Figure 1. Bflex model

The current model is shorter than probably would be realistic in a test set-up.

Model description

Flexible pipe

The pipe is modelled manually, and consists of the following layers:

Core - to represent everything internal of the pressure armour - modelled using hshear363
Pressure armour - modelled using the shear2helix option for element hshear363
Inner tensile armour - modelled using hshear353
Tape layer - modelled using hshear363
Outer tensile armour - modelled using hshear353
Outer tape - modelled using the shear2helix option for element hshear363
Dummy outer layer for contact towards test rig - modelled using pipe31 elements

In addtion, 4 sets of contacts are defined on the inside and outside of each tensile armour layer.

Friction models

3 different friction models can be found in the inputfile. By commenting in/out sections of the file:

New friction model with constant slope - this is the one that has been used when building the case

#MATERIAL MNAME FRICONTACT TYPE MUS  MUD  KEL   KEL2   RATIO  KDYN         C1  C2   DIM  kz
MATERIAL contmat fricontact   6 0.2  0.2  2e3  2e3   2e-15  10000.0E-6   1.0 1.0   -2  5e5

New fricvisc material

#MATERIAL MNAME      FRICVISC  KSTICK KTRANS   KSURF MU   C1      C2  A1
#MATERIAL  contmat    fricvisc 1e3    1e3      1.4e3 0.0  6.70E1  0.0 1.0

Coloumb friction based on spesific slip distance

#        Mname      Type        MuXY  XYName   ZName    
#MATERIAL contmat   isocontact  0.2   bellx    bellz
#
#        name      type     alfa   eps     sig
#MATERIAL bellx     epcurve  1      0       0
#                                   0.0001  1.0
#                                   1000    1.02                               
#MATERIAL bellz     hycurve       -1000   -1.4e12
#                                  1000    1.4e12

Tuning of parameters

To match results from a physical test the following parameters may be relevant to tune:

Friction coefficient and shear stiffness of the new friction model
Constants of the fricvisc material
Pre-straining of the outer tape layer

Test rig

The test rig consists of:

two pairs of rollers
a strong spring connected to fixed point at the loading point of the pipe (mid node)

Five nodes are defined and fixed in all dofs:

NOCOOR COORDINATES       100000      0.00000      0.00000    0.00000
NOCOOR COORDINATES       100001     -0.40000      0.00000    0.12800
NOCOOR COORDINATES       100002     -0.40000      0.00000   -0.12800
NOCOOR COORDINATES       100003      0.40000      0.00000    0.12800
NOCOOR COORDINATES       100004      0.40000      0.00000   -0.12800
#
BONCON GLOBAL 100000 1
REPEAT 5 1
BONCON GLOBAL 100000 2
REPEAT 5 1
BONCON GLOBAL 100000 3
REPEAT 5 1
BONCON GLOBAL 100000 4
REPEAT 5 1
BONCON GLOBAL 100000 5
REPEAT 5 1
BONCON GLOBAL 100000 6
REPEAT 5 1

Four of the nodes are used to attach roller elements onto:

ELCON spool01_01 cont164  rollermat1 100001  100001
ELCON spool01_02 cont164  rollermat1 100002  100002
ELCON spool02_01 cont164  rollermat1 100003  100003
ELCON spool02_02 cont164  rollermat1 100004  100004
#
ELORIENT EULERANGLES 100001 0 0 0
REPEAT 4 1 0 0 0
#
ELECC radius 100001 1 2 0.0 -0.3 0.0 0.0 0.3 0.0
ELECC radius 100002 1 2 0.0 -0.3 0.0 0.0 0.3 0.0
ELECC radius 100003 1 2 0.0 -0.3 0.0 0.0 0.3 0.0
ELECC radius 100004 1 2 0.0 -0.3 0.0 0.0 0.3 0.0
#
#	                 diam
ELPROP spool01_01 roller 0.1
ELPROP spool01_02 roller 0.1
ELPROP spool02_01 roller 0.1
ELPROP spool02_02 roller 0.1
#
CONTINT spool01_01 spool01_01 couter 7001 7040 1000.0 1000.0 0.0  40 -1
CONTINT spool02_01 spool02_01 couter 7001 7040 1000.0 1000.0 0.0  40 -1
CONTINT spool01_02 spool01_02 couter 7001 7040 1000.0 1000.0 0.0  40 -1
CONTINT spool02_02 spool02_02 couter 7001 7040 1000.0 1000.0 0.0  40 -1
#
MATERIAl rollx hycurve -10 -20e3
	                10  20e3
#			
MATERIAl rolly hycurve -10 -20e3
	                10  20e3
#			
MATERIAl rollz1 hycurve -1 -1e3
	 	         1  1e3

#
MATERIAL rollermat1 contact 0.3 0.3 rollx rolly rollz1

The rollers are only acting in their radial direction, this is done by switching the z-direction on at time 0, and x- and y-diretion iat a larger time than the simulation time in the contint section. No friction is hence included if the pipe slides on the rollers.

One node is positioned at the mid of the flexible pipe, and is used as a fix point to hook a spring onto:

ELCON  lspring1      spring137 lspringmat 100000 100000 21 
#
ELORIENT eulerangle 100000 0.0 0.0 0.0
 
ELPROP lspring1      genspring 0.0 0.0  0.0  0.0  0.0  0.0
#
MATERIAL lspringmat genspring springmat1 springmat1 springmat1 springmat1 springmat1 springmat1 

MATERIAl springmat1 hycurve -10 -1e10
	                    10  1e10

MATERIAL dummy hycurve  -10 -0.1
                         10  0.1

The spring has two purposes: to be able to apply vertical displacement at the mid of the pipe, and to keep the remaining degrees of freedom fixed for the pipe at that point. The latter could also be done by using boncon on the relevant node, but it is often more numerically stable to use a spring connection.

Using too strong spring may affect the numerical stability, using too soft spring will cause the pipe stiffness to influence the displacement signifficantly.

Boundary conditions

The boundary condisions can be split in two groups. One relates to the overall behaviour of the pipe:

The mid node of the pipe is fixed in all dofs except vertical motion, by applying the strong spring described above.
The roller pairs support the pipe at both sides

Then there are a set of boundary conditions that relates to the internal behaviour of the components within the pipe.

For all concentric layers, the radial node is fixed in dof 2 and 3. This is required for thinshell hshear363 layers, leaving only one radial displacement free.
For the helix nodes, one of the radial dofs (dof 3) in a layer is selected to be master, and all the remaining are linked to this node. This means that no ovalization can take place.
For the helix nodes dof 4 is fixed at all nodes. The twisting of the wire is governed by its position on the pipe surface on which it is sliding.
At the two pipe ends all dofs except dof 3 and 4 are attached to a spring to create an end fitting, see below:

ELCON  endspring11      spring137 lspringmat2 100101 10001 100101
                                              100116 10616 100116
ELCON  endspring12      spring137 lspringmat2 100201 10041 100201
                                              100216 10656 100216
ELCON  endspring21      spring137 lspringmat2 100301 20001 100301
                                              100316 20616 100316
ELCON  endspring22      spring137 lspringmat2 100401 20041 100401
                                              100416 20656 100416

ELORIENT eulerangle 100101 0.0 0.0 0.0
                    100116 0.0 0.0 0.0
ELORIENT eulerangle 100201 0.0 0.0 0.0
                    100216 0.0 0.0 0.0
ELORIENT eulerangle 100301 0.0 0.0 0.0
                    100316 0.0 0.0 0.0
ELORIENT eulerangle 100401 0.0 0.0 0.0
                    100416 0.0 0.0 0.0
 
ELPROP endspring11      genspring 0.0 0.0  1000.0  1000.0  0.0  0.0 1
ELPROP endspring12      genspring 0.0 0.0  1000.0  1000.0  0.0  0.0 1
ELPROP endspring21      genspring 0.0 0.0  1000.0  1000.0  0.0  0.0 1
ELPROP endspring22      genspring 0.0 0.0  1000.0  1000.0  0.0  0.0 1
#
MATERIAL lspringmat2 genspring springmat2 springmat2 springmat2 springmat2 springmat2 springmat2 
#
MATERIAl springmat2 hycurve -10 -1e8
                             10  1e8
#

Loads

Internal pressure is applied, which will create a tension in the pipe due to the end cap effect.
A vertical force is applied on the mid node of the pipe, but due to the strong spring the pipe will see this as a prescribed displacement A concentrated load cload is applied in this mmodel, but another option would be to use inistrain on the spring that connects the pipe and the fix-point.

Results

The moment results are obtained by nrplot from bflex2010post:

Figure 2. Moment-curvature plot for mid nodes

Figure 3. Moment-time plot

Figure 4. Moment profile plot for many time steps

Figure 5. Curvature profile plot

To obtain these results, the model must be run for longer time than the present example file.

Looking at stresses in Xpost, the curvature appears to be irregular. This may be due to the interpolation polynomials used in the contact elements, and will decrease with decreasing element lengths. The relevant curvature for a node should in this case be obtained based on the mean of the two element ends that connects the node. Be aware that the curvature gradient close to the nodal position where the load is applied is quite steep. The resolution in the current model can be gradually refined in this region to obtain more detailed curvature/moment results in the proximitry of the load point.

A general rule of thumb for BFLEX element resolution is that one pitch should have about 20 elements.

An example Python script for plotting results similar to the above figures can be found here:

Python file for plotting of mpf results

Relevant files

Go to bflex2010 file

Go to bflex2010post file

User manual for reference

Processing of files from command line

bflex2010 -n bflex2010_01
bflex2010post -n bflex2010post_01

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