# Problem in CableANCF formulation ?

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### SoMdt

Jun 23, 2022, 5:05:06 AMJun 23
to ProjectChrono
Hi all,
I am simulating a very simple cable element under traction (I also tested pure flexion) : one node is fixed, and a force is applied to the end node.

For the code attached, the elongation of the beam is 9.61 mm, while, analytically, it should be 12.7 mm. I did the same simulation with BeamEuler element, and the result is indeed 12.73 mm.
With cable ANCF, even with lower force (divided by 10), the error is significant (1.11 mm vs 1.27 mm).

The problem is the same in flexion and the error does not seem to be linear.

When I increase the number of nodes in the builder, the error decreases but it remains significant (10.88 mm vs 12.7 mm with 1000 nodes instead of 1).

I am using these elements wrong ? I thought they were suitable for large displacement and could replace Beam Euler if no twisting or shear were present ?

Thanks a lot for the help,
Solenne
simBeam.cpp

### Mike Taylor

Jun 29, 2022, 11:04:07 PMJun 29
to ProjectChrono
Solenne,

Based on the theory behind the ANCF cable element, it should provide good results in a pure axial test.  See: "Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation" by Gerstmayr and Shabana for the full technical detail on this element (as well as more details on bending).

When using ANCF elements, it is important to keep in mind the meaning behind the nodal coordinates.  Taking the ANCF cable element in particular, the nodal coordinates for each of the two nodes are the position of the node as well as the position vector gradient along the local element "x" axis at that node (6 coordinates per node).  The position vector gradient along the local element "x" axis defines the tangent to the beam axis in global coordinates at that node as well as the stretch along the beam axis at that node.

When you fix an ANCF node, you fix all of its coordinates.  So for your axial test, you do not get a constant state of stress in the meshed beam due to this imposed boundary condition and that is why adding elements will help you get closer to the analytical solution which assumes that constant state of stress.

That being said, I'm not sure if the boundary conditions explain all of the difference between the static solution and the analytic solution.  I haven't had time to investigate that further, but I wanted to at least pass on this information.

Best regards,

Mike