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 |
\(\mathrm{N3}\) |
|
|
\(\mathrm{DX}\) |
—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).