We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. The specific mixed form allows for an element-local, discontinuous approximation of rotations, which is key to a simple and efficient discretization framework. The concept of discrete curvature provides a mathematically consistent treatment of rotation discontinuities. For linear constitutive laws, the mixed form is derived via a Legendre transform of the curvature-related strain energy. Objectivity is retained at the discrete level by interpolating relative rotations through a multiplicative split of the rotation field; path-independence is inherent to the total Lagrangian setting and verified numerically. Several benchmarks demonstrate optimal rates of convergence and accuracy, irrespective of the beam's slenderness and order of approximation. Notably, the lowest-order element entirely avoids rotation interpolation by employing element-constant rotations only.
Multilevel Preconditioning of Discontinuous-Galerkin Spectral Element Methods, Part I: Geometrically Conforming Meshes
RWTH Aachen（亚琛工业大学）；CNRS, UMR 7598, Laboratoire Jacques-Louis Lions（法国国家科学研究中心，联合研究单位7598，雅克-路易·利翁斯实验室）；UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions（巴黎第六大学，联合研究单位7598，雅克-路易·利翁斯实验室）；Politecnico di Torino（都灵理工大学）
A rotation-based geometrically nonlinear spectral Reissner--Mindlin shell element
Rheinland-Pfälzische Technische Universität Kaiserslautern-Landau（莱茵兰-普法尔茨技术大学凯泽斯劳滕-兰道分校）；Brandenburgische Technische Universität Cottbus-Senftenberg（勃兰登堡科技大学科特布斯-森夫滕贝格分校）
A space-time finite element formulation for geometrically exact shear-deformable beams
Institute for Mathematics and Computer-Based Simulation (IMCS), University of the Bundeswehr Munich（联邦国防大学数学与计算机仿真研究所）；Institute of Technical Mechanics, Johannes Kepler University Linz（林茨约翰内斯·开普勒大学技术力学研究所）
