SubDyn: Improved force outputs at member end nodes/joints

[luwang00]

This PR is not ready to be merged.

Feature or improvement description

This PR aims to improve the force outputs from SubDyn.

Currently, the axial and shear forces at the interior nodes of a member are averaged/interpolated from the forces over the two neighboring elements. This generally provides accurate results. However, for member end nodes, we only have a single element connecting to the node, and it is not possible to perform averaging. This can lead to large errors in the reported forces if the member discretization is coarse.

To address this issue, the forces at the end nodes are now computed using linear extrapolation from the forces over the first and second elements from the member end. This should provide significantly more accurate force estimates at the end nodes in most cases. If NDiv=1, each member only has a single element. In this case, no extrapolation is performed.

This change affects both user requested load outputs and the outputs obtained with the AllOuts option. However, the seabed reaction load outputs are not modified. Lastly, note that the change implemented only affects the timeseries printout from SubDyn. It does not affect SubDyn's internal states and module inputs/outputs.

Effectively, we are assuming the internal force over the two elements at the end of a member to be continuous and vary linearly. Correspondingly, the applied force on the two elements is approximated as a distributed and piecewise constant load instead of lumped forces at the nodes. The existing SubDyn formulation for the forces at member interior nodes based on averaging the forces of the two neighbor elements implicitly relies on the same assumption/approximation.

Note that this method for estimating end-node forces can result in significant errors if there is a large lumped force applied at the first interior node next to the end node, such as mooring fairlead forces. This lumped force creates a jump in the internal force at the second node, causing the extrapolation to overshoot. This situation should be avoided when setting up the model. It is recommended to always map loads and motion between mooring fairleads and SubDyn user-defined joints instead of interior nodes.

Example results
TBD

Related issue, if one exists
This PR is complementary to the self-weight equivalent moment correction implemented in PR #3356. The current plan is to remove the force correction from PR #3356 while retaining only the moment correct. The force correction from this PR will be used instead.

Impacted areas of the software
SubDyn

Test results, if applicable
Some SubDyn r-test results have changed.

• r-test branch merging required