Displacement, Flexibility, and Mixed Beam–Column Finite Element Formulations for Distributed Plasticity Analysis

This paper presents several beam–column finite element formulations for full nonlinear distributed plasticity analysis of planar frame structures. The fundamental steps within the derivation of displacement-based, flexibility-based, and mixed elements are summarized. These formulations are presented using a total Lagrangian corotational approach. In this context, the element displacements are separated into rigid-body and deformational (or natural) degrees of freedom. The element rigid-body motion is handled separately within the mapping from the corotational to global element frames. This paper focuses on the similarities and differences in the element formulations associated with the element natural degrees of freedom within the corotational frame. The paper focuses specifically on two-dimensional elements based on Euler–Bernoulli kinematics; however, the concepts are also applicable to general beam–column elements for three-dimensional analysis. The equations for the consistent tangent stiffness matrices are presented, and corresponding consistent element state determination algorithms are explained. Numerical examples are provided to compare the performance of the above elements.