A consistent Timoshenko hysteretic beam finite element model. (March 2020)

• Record Type: Journal Article
• Authors: Amir, M.; Papakonstantinou, K.G.; Warn, G.P.
• Is Part Of: International journal of non-linear mechanics. Volume 119(2020)
• Publication Date: 2020-03
• Subjects: Hysteretic finite element -- Multiaxial interactions -- Distributed plasticity -- Interpolation functions -- ODEs/DAEs; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.07.003
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: A parametrized Timoshenko hysteretic beam finite element model is developed, using consistent two-node elements, to efficiently simulate the nonlinear behavior of structures. New displacement interpolation functions are derived that satisfy both the exact equilibrium and kinematic conditions. Therefore, nodal strain field continuity is achieved, resulting in a consistent formulation without shear locking effects. Multiaxial interactions are considered through yield/capacity functions and distributed plasticity is accounted for by appropriate hysteretic interpolation functions. The suggested interpolation functions yield constant element matrices that do not require updating throughout the analysis, and the nonlinearities are captured in terms of hysteretic curvatures, axial and shear deformations, which are set to evolve through ordinary differential equations. A computationally efficient solution scheme is also suggested, without requiring any linearization, to straightforwardly solve the resulting system of equations for quasi-static problems. The consistency, efficiency, versatility and validity of the suggested model is explained in detail and demonstrated through several numerical examples and comparisons with experimental data from available tests. Highlights: A general consistent hysteretic beam finite element model is developed. New displacement interpolation functions are introduced to satisfy exact equilibrium conditions. Strain continuity is achieved without any shear-locking effects. A new computationally efficient solution scheme is suggested. Axial-moment-shear interactions and distributed plasticity are considered.