A Timoshenko finite element straight beam with internal degrees of freedom

Summary 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.

[1]  J. S. Przemieniecki.  Theory of matrix structural analysis , 1985 .

[2]  J. Kosmatka,et al.  An improved two-node timoshenko beam finite element , 1993 .

[3]  A. Ibrahimbegovic,et al.  Finite element analysis of linear and non‐linear planar deformations of elastic initially curved beams , 1993 .

[4]  J. Mazars,et al.  Using multifiber beams to account for shear and torsion: Applications to concrete structural elements , 2006 .

[5]  R. Cook,et al.  Concepts and Applications of Finite Element Analysis , 1974 .

[6]  Enrico Spacone,et al.  FIBRE BEAM–COLUMN MODEL FOR NON‐LINEAR ANALYSIS OF R/C FRAMES: PART I. FORMULATION , 1996 .

[7]  D. L. Thomas,et al.  Timoshenko beam finite elements , 1973 .

[8]  Michael N. Fardis,et al.  Load-Path Effects in Column Biaxial Bending with Axial Force , 1995 .

[9]  R. Nickel,et al.  Convergence of consistently derived Timoshenko beam finite elements , 1972 .

[10]  S. B. Dong,et al.  On a hierarchy of conforming timoshenko beam elements , 1981 .

[11]  Géraldine Casaux-Ginestet,et al.  Modélisation tridimensionnelle du comportement sismique d'ouvrages en béton armé : développement de méthodes simplifiées , 2003 .

[12]  B.A.H. Abbas,et al.  Finite element model for dynamic analysis of Timoshenko beam , 1975 .

[13]  Panagiotis Kotronis,et al.  SIMPLIFIED MODELLING STRATEGIES TO SIMULATE THE DYNAMIC BEHAVIOUR OF R/C WALLS , 2005 .

[14]  C. Borderie.  Phénomènes unilatéraux dans un matériau endommageable : Modélisation et application à l'analyse de structures en béton. , 1991 .

[15]  J. Jensen.  On the shear coefficient in Timoshenko's beam theory , 1983 .