2. Reference solution#

2.1. Calculation method used for the reference solution#

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

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

2.2. Benchmark results#

KNOT

\(\mathrm{N3}\)

\(\mathrm{N4}\)

\(\mathrm{N6}\)

\(\mathrm{DX}\)

—0.30645

—0.69355

—1.0

2.3. 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).