Consistency and misconceptions in co-rotational 3D continuum finite elements: A zero-macrospin approach.

• Novel zero-macrospin co-rotational approach for 3D continuum finite elements. • Formulation simplicity via deformation gradient defined at macro element level. • Full derivation with symmetric geometric stiffness matrix arising naturally. • Exposition of misconceptions and errors in Crisfield's seminal asymmetric formulation. • Demonstration of computational superiority of proposed symmetric formulation. The seminal work of Crisfield on co-rotational finite elements came to a profound conclusion that the geometric stiffness matrix of 3D continuum finite elements is inherently asymmetric, though it becomes symmetric under equilibrium conditions. Contending that these outcomes are misconceptions, this paper presents a novel zero-macrospin co-rotational approach for 3D continuum elements in which the geometric stiffness matrix is always symmetric for work-conjugate conservative loads, suggesting that Crisfield's geometric stiffness is erroneously asymmetric and inconsistent. This contention is subsequently upheld by identifying crucial terms omitted in Crisfield's formulation which are responsible for the erroneous asymmetry, and the notion that symmetry is eventually recovered at equilibrium is shown to be a further misconception. Importantly, this critical appraisal of Crisfield's formulation, which has been adopted by numerous researchers, and the delineation of its underlying misconceptions exceed academic interest to real practical relevance. Several numerical examples are presented in the paper which highlight the superiority of the proposed approach, lending incontrovertible practical evidence that the consistent geometric stiffness matrix for co-rotational 3D continuum elements is always symmetric for work-conjugate conservative loads. [ABSTRACT FROM AUTHOR]