{"paper":{"title":"Mixed Finite Elements for Geometrically Exact Beams using Discontinuous Rotations and Discrete Curvature","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"A mixed finite-element formulation for geometrically exact beams treats moments as independent variables to allow discontinuous rotations per element.","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Alexander Humer, Astrid Pechstein, Ivo Steinbrecher","submitted_at":"2026-05-06T07:22:54Z","abstract_excerpt":"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 lev"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We propose a novel mixed finite-element formulation for geometrically exact (Simo--Reissner) beams that introduces the moment vector as additional independent field. 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