Finite Element Based Elasto-Plastic Analysis of Classical and First Order Beams With Armstrong–frederick Kinematic Hardening Model

Abstract

This investigation is focused on the elasto-plastic behavior of classical and first order Timoshenko beams by a finite element formulation under two major kinematic hardening models. The approach consists of proposing a finite element formulation with variable stiffness matrix and optimized solution for the Armstrong–Frederick theory together with the Ziegler–Prager model under cyclic flexural and deformation controlled loading conditions. In symmetrical cyclic deformation and flexural controlled states of the first order beams, it was concluded that after several cycles, the total stress-strain curves tend to be coincident. It also corroborates that the anisotropic characteristic cases with symmetric loading exhibit a ratcheting response for both beam models.