عنوان مقاله [English]
The Counter-intuitive behavior which means that the permanent deflection of the elastic-plastic beam come to rest in opposite direction of the impulsive loading, normally appears and disappears abruptly, in certain small ranges of the loading and structural parameters. One of the most important issues in the study of this phenomenon is the determination of the influence of the different parameters on this behavior. This present paper studied the effects of hardening in the counter-intuitive dynamic behavior of the elastic-plastic pin-ended beams under impulsive loading, by developing the proposed Galerkin's numerical model and by presenting a novel algorithm. Galerkin's method as well as Finite element code ANSYS/LS-DYNA were applied to study this phenomenon and the results of these two methods have been compared. In order to regard the hardening effects in Galerkin's method, a new algorithm was proposed. To test the validity of our proposed algorithm, the response of the elastic-perfectly
plastic beam was firstly studied, and the hardening effects on the counter-intuitive response was investigated afterwards. The displacement-time history curves of mid-span of the beam were studied in detail and the region of the occurrence of the counter-intuitive behavior was determined. Furthermore, using the finite element code, energy diagrams of the beam were also investigated. It was been found out that the counter-intuitive response is a phenomenon which is very sensitive to loading so that it may appear with a little change in the amount of loading. The results also showed that when considering the hardening effects, both methods predicted two continuous and distinct regions of loading for the occurrence of this phenomenon where the first had a narrower band and occurred in the tight region of the impulsive loading while the next one had a wider band and occurred in the vast region of the impulsive loading. In addition, our investigations on the energy diagrams showed that, this anomalous behavior would occur in the proper proportions of kinetic to internal energy.