Reference solution
=====================

Calculation method used for the reference solution
--------------------------------------------------------

The curvature of a highly rotating beam subjected to a bending moment :math:`M` is: :math:`\frac{1}{R}=\frac{M}{\mathrm{EI}}`

Since the moment is constant along the beam, the deformation is circular and its radius has the value, taking into account the data: :math:`R=\frac{l}{2\pi }`, the deformation is a complete circle.


Benchmark results
----------------------

.. csv-table::

    "KNOT", ":math:`\mathrm{N3}` "," :math:`\mathrm{N4}` "," :math:`\mathrm{N6}`"
    ":math:`\mathrm{DX}` ", "—0.30645", "—0.69355", "—1.0"



Bibliographical references
---------------------------

J.C. SIMO and L. VU QUOC, A three-dimensional finite strain rod model. Part II: computational aspects. Compute. Meth. Call. Mech. Engrg.58, 79‑116 (1986).