Introduction:

Abaqus offers a range of linear and nonlinear capabilities for simulating the dynamic response of structures. This blog written by Matthew Knight (member of the UK technical team) focuses on some offshore applications which include Pipe and seabed interactions, pipe laying and particularly on pipe in pipe interactions. One of the major areas of modeling in such analyses is to get the contact definitions between the pipes working properly. These generally cannot be done with standard surface based contact like for example contact between two discrete points or contact between two pipelines or tubes. What follows is a list of recommended practices when setting up ITT elements to model large sliding contact between two pipes that slide within or next to each other. This is primarily done in Abaqus\\Standard and can be used for both two dimensional and three dimensional problems.

When using ITT elements to define contact between two pipes the elements are defined on one pipe and a slideline (The line along which these elements see contact and slide) is defined along the other pipe. Some rules about whether slideline should be defined on the inner or outer tube is covered in one of the commandments.

These commandments have been made from a trouble shooting viewpoint and in our experience of working with this class of problems they help in getting the solution to converge.

Commandment 1

Use B31H or PIPE31H elements:

Hybrid beam element types (B21H, B33H, etc.) are provided in Abaqus/ Standard for use in cases where it is numerically difficult to compute the axial and shear forces in the beam by the usual finite element displacement method. This problem arises most commonly in geometrically nonlinear analysis when the beam undergoes large rotations and is very rigid in axial and transverse shear deformation, such as a flexing long pipe or cable. The problem in such cases is that slight differences in nodal positions can cause very large forces, which, in turn, cause large motions in other directions. The hybrid elements overcome this difficulty by using a more general formulation in which the axial and transverse shear forces in the elements are included, along with the nodal displacements and rotations, as primary variables.

Although this formulation makes these elements more expensive, they generally converge much faster when the beam's rotations are large and, therefore, are more efficient overall in such cases. Furthermore, the model may experience more negative eigenvalue warnings, due to the hybrid formulation.

Commandment 2

Apply ITT elements to the inner (smaller diameter) pipe:

Use ITT21 elements with two-dimensional beam, pipe, or truss elements. Use ITT31 elements with three-dimensional beam, pipe, or truss elements. Each of these elements is defined by a single node which is attached to the inner pipe.

Commandment 3

Apply the slideline to the outer (larger diameter) pipe:

In the case of internal tube-to-tube contact, the slide line can be placed on the inner tube or the outer tube. Generally the slide line should be associated with the outer tube; however, if the inner tube is stiffer than the outer tube, the slide line should be attached to the inner tube.

Set TYPE=LINEAR to define a slide line made up of linear segments. This parameter should be used when first-order pipe or beam elements make up the model. Set TYPE=PARABOLIC to define a slide line made up of parabolic segments. This parameter should be used when second-order elements make up the model. In this case the slide line should consist of an odd number of nodes, where the odd nodes on the slide line are associated with the ends of parabolic segments.

Commandment 4

Add smoothing to the slideline:

Convergence is often improved by smoothing the discontinuities in surface tangents between slide line segments, thereby providing a smoothly varying tangent along the slide line. Typically a value of 0.5 is recommended, default is 0.

Commandment 5

Ensure a continuous slide line and check the radial clearance:

You specify the nodes that make up the slide line, and these must be in a sequence that defines a continuous slide line, i.e. the node list must follow a continuous sequence from one end of the pipe to the other.

You define the radial clearance between the pipes. Give a positive value to model contact between two pipes when one pipe (the one with the tube-to-tube contact elements) lies inside of the other pipe. The value given is the difference between the inner radius of the outer pipe and the outer radius of the inner pipe.

You can model external tube-to-tube contact by specifying a negative value for the radial clearance. The magnitude of the value must be the sum of the outer radii of the two pipes

Commandment 6

Non-default mechanical surface interactions:

By default, Abaqus/Standard uses “hard,” frictionless contact with tube-to-tube contact elements. You can assign optional mechanical surface interaction models. The following mechanical surface interaction models are available:

• Friction.
• Modified “hard” contact, softened contact, and viscous damping.

In certain situations, nonlinear penalty based contact can be beneficial to improve convergence.

Note, always check the levels of penetration (E11 < 0) to ensure the penalty stiffnesses are suitably high enough.

Commandment 7

Implicit Dynamics:

During the pull-in process the model can be unstable and convergence (equilibrium or contact, or both) can be slow. To overcome this issue, the model can be solved using the implicit dynamic solver, using the quasi-static option.

Note, if you use implicit dynamics, you must ensure that the kinetic energy are suitably kept low by applying loads slowly and applying velocity boundary conditions (rather than displacements). 

Commandment 8

Cable modelling (Truss or beam elements):

To model the pull-in process the pipe (or umbilical) is typically connected to a cable (or tether) which is then pulled through the J-riser. There are two ways to model the cable:

1)    Truss elements (T3D2H):  Models a flexible cable with no bending stiffness. Truss elements can become unstable unless they are prestressed in tension, which leads to convergence issues. This instability issue can be overcome using Implicit Dynamics.

2)    Beam elements (B31H) with a reduced bending stiffness: Models a flexible cable with reduced bending stiffness. Implemented using a generalised beam section, with lowered values of I11, I22 and J.

Note, lowering the bending stiffness too much can cause further convergence issues, i.e. the rotation correction has difficulties converging.

Commandment 9

Mesh refinement (snagging problems):

In certain situations where a pipe is being introduced into another pipe and these pipes are slightly misaligned, it may be necessary to refine the mesh such that more ITT elements are present at the entrance of the J-riser to model the contact. If the mesh is not suitably refined the model may suffer from contact issues were nodes become snagged as the pipe is pulled into the riser mouth.  

Commandment 10

Unsymmetric solver (optional):

If the model has highly curved slidelines or has friction between the pipes it may be necessary to use the unsymmetric solver to aid convergence.