A Timoshenko finite element straight beam with internal degrees of freedom |
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| Authors: | Denis Caillerie Panagiotis Kotronis Robert Cybulski |
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| Institution: | 1. Univ. de Grenoble Alpes ‐ L3SR CNRS ‐ L3SR Domaine Universitaire, Grenoble Cedex, France;2. L'UNAM Université Ecole Centrale de Nantes, Université de Nantes, CNRS UMR 6183, GeM (Institut de Recherche en Génie Civil et Mécanique), Nantes, CEDEX 3, France;3. Department of the Theory of Building Structures, Silesian University of Technology, Gliwice, Poland |
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| Abstract: | We present hereafter the formulation of a Timoshenko finite element straight beam with internal degrees of freedom, suitable for nonlinear material problems in geomechanics (e.g., beam type structures and deep pile foundations). Cubic shape functions are used for the transverse displacements and quadratic for the rotations. The element is free of shear locking, and we prove that one element is able to predict the exact tip displacements for any complex distributed loadings and any suitable boundary conditions. After the presentation of the virtual power and the weak form formulations, the construction of the elementary stiffness matrix is detailed. The analytical results of the static condensation method are provided. It is also proven that the element introduced by Friedman and Kosmatka in 1 , with shape functions depending on material properties, is derived from the new beam element. Validation is provided using linear and material nonlinear applications (reinforced concrete column under cyclic loading) in the context of a multifiber beam formulation. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | beam shear locking Timoshenko multifiber |
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