Repeated Unit Cell (RUC) model with thinwall elements
The input to this model can be found in the example folder, under case E019.
A flexible pipe is modelled based on the RUC concept. The applied loads are combined tension and bending and external and internal pressure.
Model description
Basic assumptions of the RUC model is that the behaviour of the pipe is constant along the pipe, in the sense that the motion and strains of the components only depend on the circumferencial position in the cross section. Then by modelling a section with the element lengths adjusted such that the helical component ends match each other in the circumferential position. It is then possible to constrain the motion of the nodes at the same circumferential position to each other and hence reduce the degrees of freedom to a minimum.
With reference to the figure below, the yellow numer marks the position of 3 helix nodes at the same circumferential position. Node end 1 and 3 are constrained to behave identical to node number 2. The same applies for the 3 red nodes and all other groups of 3 nodes sharing the same circumferential position.
The present model, see Figure 1, consist of 9 different layers; thermal layers, tape, carcass, zeta spiral and tensile armours:
# name type ID Timeini ilaint ilaext ielbfl fimod content nelgr
CROSSECTION mypipe 353FLEXCROSS 101.6e-3 1.0 2 9 1 0 1000 9
1-1-flexbody
2-2-flexbarrier
3-3-flexloc
4-4-flexwear1-flexwear1contact
5-5-flexwear2inwardcontact-flextensile1
6-6-flexwear2
7-7-flextape1contact-flextensile2
8-8-flextape1
9-9-flexshield
#FLEXBODY A=5*12.7*.563 = 36.0, FLEXLOK A=6.4*14.1*.878 = 79.23
# CTYPE TH matname FRIC LAYANG RNUM TEMP nlmat CCODE CFATFL AREA IT INY IKS WIDTH
CARC 5.0e-3 steel_316 0.15 87.828 1 0.0 none MANUAL NONE 36.0e-6 0.000e+00 0.000e+00 0.000e+00 7.20e-3
THER 5.1e-3 plast_PVDF 0.15 0.000 0 0.0 none NONE NONE 0.00 0.000e+00 0.000e+00 0.000e+00 0.00
ZETA 6.4e-3 steel_110 0.15 87.813 1 0.0 none MANUAL NONE 79.23e-6 0.000e+00 0.000e+00 0.000e+00 12.38e-3
THER 2.0e-3 plast_PA11 0.15 0.000 0 0.0 none NONE NONE 0.00 0.000e+00 0.000e+00 0.000e+00 0.00
# 1st armour
TENS 2.00e-3 steel_190 0.15 -38 61 0.0 none FLEXTENSILE NONE 0.00 0.000e+00 0.000e+00 0.000e+00 0.00
THER 2.00e-3 plast_PA11 0.15 0.000 0 0.0 none NONE NONE 0.00 0.000e+00 0.000e+00 0.000e+00 0.00
# 2nd armour
TENS 2.00e-3 steel_190 0.15 37.8 65 0.0 none FLEXTENSILE NONE 0.00 0.000e+00 0.000e+00 0.000e+00 0.00
THER 0.3e-3 rubber 0.15 0.000 0 0.0 none NONE NONE 0.00 0.000e+00 0.000e+00 0.000e+00 0.00
THER 6.0e-3 rubber 0.15 0.000 0 0.0 none NONE NONE 0.00 0.000e+00 0.000e+00 0.000e+00 0.00
| Set timeini to a time after the axial load has been appliied, but before bending is initiated. In the present case full load is applied from the start, and bending is initiated from time 2. timeini 1.0 will then be the proper choise. |
The thinwall element hshear363 is applied to describe the concentric layers, and hshear353 is applied for the tensile armours.
# group elty material no n1 n2 n3 n4
Elcon flexbody hshear363 mypipe 1001 1 2 1001 repeat 2 1 1
Elcon flexbarrier hshear363 mypipe 2001 1 2 2001 repeat 2 1 1
Elcon flexloc hshear363 mypipe 3001 1 2 2001 repeat 2 1 1
Elcon flexwear1 hshear363 mypipe 4001 1 2 2001 repeat 2 1 1
Elcon flextensile1 hshear353 mypipe 30001 1 2 30001 30002
30061 1 2 30181 30182 repeat 2 61 1
Elcon flexwear2 hshear363 mypipe 6001 1 2 6001 repeat 2 1 1
Elcon flextensile2 hshear353 mypipe 40001 1 2 40001 40002
40065 1 2 40193 40194 repeat 2 65 1
Elcon flextape1 hshear363 mypipe 8001 1 2 8001 repeat 2 1 1
Elcon flexshield hshear363 mypipe 9001 1 2 8001 repeat 2 1 1
| If thinwall hshear363 elements are used, then the same model can not contain thickwall hshear364 elements. |
All the layers share the same center nodes: 1, 2 and 3. The thinwall hshear363 elements require one radial node, for storing the radius. The defined location (defined by nocoor) of these radial nodes are dummy.
Contact between layers
Several of the hshear363 layers share the same radial node. The layers sharing the same radial node can not separate.
| All layers could also be defined with separate radial nodes, in that case there is a need for contact elements between the layers. |
There are three contact groups working on the tensile armours:
-
contact from flexwear to inner tensile layer
-
direct contact between inner and outer tensile layer
-
contact from outer tensile layer to flextape
Elcon flexwear1contact hcont463 mypipe 53001 2001 30001 30002
53061 2001 30181 30182 repeat 2 61 1
Elcon flexwear2inwardcontact hcont453 mypipe 54001 30001 30002 40001 40002
54061 30181 30182 40181 40182 repeat 2 61 1
Elcon flextape1contact hcont463 mypipe 56001 40001 40002 8001
56065 40193 40194 8001 repeat 2 65 1
| The present model applies the old friction model. By applying elprop shearmodel for the contact groups, the new friction model can be switched on |
Constraints
The contstraints are a key point in the RUC model, and are applied using master-slave connection by the constr coneq concept.
# Constraint equations # CONSTR CONEQ GLOBAL 30002 3 0.0 30001 3 1.0 repeat 182 1 0 # CONSTR CONEQ GLOBAL 30001 1 0.0 30005 1 1.0 repeat 60 3 3 CONSTR CONEQ GLOBAL 30001 2 0.0 30005 2 1.0 repeat 60 3 3 CONSTR CONEQ GLOBAL 30001 5 0.0 30005 5 1.0 repeat 60 3 3 CONSTR CONEQ GLOBAL 30001 6 0.0 30005 6 1.0 repeat 60 3 3 # CONSTR CONEQ GLOBAL 30181 1 0.0 30002 1 1.0 CONSTR CONEQ GLOBAL 30181 2 0.0 30002 2 1.0 CONSTR CONEQ GLOBAL 30181 5 0.0 30002 5 1.0 CONSTR CONEQ GLOBAL 30181 6 0.0 30002 6 1.0 # CONSTR CONEQ GLOBAL 30006 1 0.0 30002 1 1.0 repeat 60 3 3 CONSTR CONEQ GLOBAL 30006 2 0.0 30002 2 1.0 repeat 60 3 3 CONSTR CONEQ GLOBAL 30006 5 0.0 30002 5 1.0 repeat 60 3 3 CONSTR CONEQ GLOBAL 30006 6 0.0 30002 6 1.0 repeat 60 3 3 # CONSTR CONEQ GLOBAL 30003 1 0.0 30182 1 1.0 CONSTR CONEQ GLOBAL 30003 2 0.0 30182 2 1.0 CONSTR CONEQ GLOBAL 30003 5 0.0 30182 5 1.0 CONSTR CONEQ GLOBAL 30003 6 0.0 30182 6 1.0
There is one set of constraint equations that restricts all the nodes in the helix layer to have identical motion in dof 3, which is the radial degree of freedom. This means that there is only one free radial degree of freedom for the helix layer, preventing any ovalization of the layer during bending.
The groups of 4 constr inputs, constraints the end node of one helix segment (slave) to the mid node (master) of the neighbouring wire, This is applied for dof 1,2,5,6 referring to axial, transverse and rotations respectively. All relative to the helical coordinate system.
| All the constrainst for one end, except for one, can be handeed by repeat and fixed increments for slave and master nodes. The last must be treated separatly, as seen below: |
Node 5 is master of slave node 1, node 8 is master of slave node 4, but node 2 is master of slave node 181.
| The connections will depend the sequence the nodes are defined in, and which lay direction the wire has. |
The only degree of freedom now left is 4. This is dummy in the thin wall modelling option, and should be constrained.
Symmetry spring
To prevent the layer from spinning or sliding axially before loads have create sufficient holding forces, a strong spring is connected to each of the layers. This spring works toward one node, and only in the axial and transverse (relative to the helix system) direction. This connection point should be at a point where no motion in their relevant dof 1 and 2 is expected during the loading process. At the intrados/extrados, this will be the case.
| The helix nodes must be defined such that there one mid-node from each layer is located exactly on the intrados (or extrados).- This node can be used for connecting the described symmetry spring. |
#extra node and element to ensure symmetry of the tensile armour behaviour
# additional node
Nocoor Coordinates
20001 0.0 0.0 0.0
# node fixed in alle dofs
BONCON gLObAL 20001 1
BONCON gLObAL 20001 2
BONCON gLObAL 20001 3
BONCON gLObAL 20001 4
BONCON gLObAL 20001 5
BONCON gLObAL 20001 6
# two spring elements, one pr. tensile layer
# group elty flexcrossname no n1 n2 n3 n4
Elcon symspring spring137 springmat 20001 20001 30002
20002 20001 40002
Elorient eulerangle 20001 0.0 0.0 0.0
20002 0.0 0.0 0.0
# turnofftransformation
ELPROP symspring genspring 0 0 0 0 0 0 1
MATERIAL springmat genspring belly belly zero zero zero zero
# name type alfa eps sig
#
MATERIAL belly hycurve -1000 -765e9
1000 765e9
#
MATERIAL zero hycurve -1000 0
1000 0
Loads
The center mid node is keept fixed, and the two end nodes are rotated by constr pdisp to obtain curvature.
Results
The moment curvature is obtained by nrplot from bflex2010post:
| To obtain these results, the model must be run longer than the present example file to obtan larger curvature values. |
Relevant files
Processing of files from command line
-
bflex2010 -n bflex2010_01
-
bflex2010post -n bflex2010post_01