A new Hermite finite element for nonlinear Kirchhoff rods: The plane case

This article presents the formulation of a finite element method for nonlinear Kirchhoff rods, based on a interpolation of the rod's geometry in terms of Hermite shape functions. The critical use of the same interpolation scheme for both the geometry and the kinematics of the rod is shown to lead to the correct invariant properties of the final numerical formulation, thus leading to the correct resolution of the fundamental equilibrium relations along it (balance of forces and moments). The so‐called “self‐straining” is completely avoided. Several numerical examples are presented illustrating the adequacy of the proposed formulation for the analysis of thin rods undergoing large finite deformations.