Dynamic Analysis of Elastoplastic Shakedown of Structures

This paper deals with the dynamics of a single-degree-of-freedom elastoplastic oscillator. The model adopted herein is useful for understanding the dynamic behavior of civil engineering structures, such as steel structures, especially when plastic inelasticity is of concern. Using appropriate internal variables, the dynamic hysteretic system can be written as a singular autonomous system. The free vibration of such a nonlinear system reduces to periodic motion. The harmonic forced oscillator can exhibit periodic or quasi-periodic behaviors. A bifurcation diagram is numerically computed, which indicates that periodic elastoplastic limit cycles exist for some ranges of structural parameters. The bifurcation boundary separates the shakedown from other alternating plasticity phenomena.