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from the paper in this link , which is the Belytscko beam. I could not figure out if it is a 3D beam or a 2D one.

if you don't have access to that paper, please check the page 73 on this link.

Beam schematic

what confused me was the schematics on the original paper and the second link. in the beginning the general movements start from 3D but I don't see all the DOFs in the above image

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    $\begingroup$ If you look at section 4.2 of the LS-Dyna manual (page 76), from the parameters used to represent its deformed state it is clearly a 3D beam including torsion. $\endgroup$ – alephzero Aug 30 at 15:50
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It is a 3D beam (6 degrees of freedom at each node). The figure is 2D just to make things simpler.

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