@inbook{a3f81eda6d4f4b94a428d98b8883fcd2,
title = "The absolute nodal coordinate formulation",
abstract = "The key idea of the absolute nodal coordinate formulation (ANCF) is to use slope vectors in order to describe the orientation of the cross-section of structural mechanics components, such as beams, plates or shells. This formulation relaxes the kinematical assumptions of Bernoulli–Euler and Timoshenko beam theories and enables a deformation of the cross-sections. The present contribution shows how to create 2D and 3D structural finite elements based on the ANCF by employing different sets of slope vectors for approximating the cross-sections{\textquoteright} orientation. A{\^A} specific aim of this chapter is to present a unified notation for structural mechanics and continuum mechanics ANC formulations. Particular focus is laid on enhanced formulations for such finite elements that circumvent severe issues like Poisson or shear locking. The performance of these elements is evaluated and a detailed assessment comprising the convergence order, the number of iterations, and Jacobian updates for large deformation benchmark problems is provided.",
keywords = "Absolute Nodal Coordinate Formulation, Flexible Multibody System, Local Frame, Shear Correction Factor, Virtual Work",
author = "Johannes Gerstmayr and Alexander Humer and Peter Gruber and Karin Nachbagauer",
note = "Publisher Copyright: {\textcopyright} 2016, CISM International Centre for Mechanical Sciences. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.",
year = "2016",
doi = "10.1007/978-3-319-31879-0_4",
language = "English",
series = "CISM International Centre for Mechanical Sciences, Courses and Lectures",
publisher = "Springer",
pages = "159--200",
booktitle = "CISM International Centre for Mechanical Sciences, Courses and Lectures",
address = "Germany",
}