Numerical analysis ofthe counterintuitive dynamic behavior of the elastic-plastic fully-clamped beams under impulsive loading

摘要

In 1985, an interesting fact was discovered in the USA by a well-known specialist on the dynamics of elasto-plastic beams, Symonds and his colleague Yu [1]. Computations made by the two scholars showed that under certain conditions when a transverse pressure pulse of magnitude sufficient to cause plastic deformation is applied to a elastic-plastic beam whose ends are attached to smooth fixed pins, the permanent deflection of the beam may come to rest in opposite direction ofthe load rather than in its direction, as intuitively expccted and observed in many tests. This phenomenon was named "anomalous behavior" or "counter-intuitive behavior" ofthe beam. For the particular problem defined by Symonds & Yu [1], solutions were obtained by ten numerical codes of finite element or finite difference type. Some predicted a final elastic vibration between negative displacement limits (implying a final displacement in the direction opposite to the load), while others predicted positive limits. Although later further investigations are also carried out on counterintuitive behavior of pin-ended beams [2-4|, as it is shown by other studies [5-7], the pin-ended condition is not essential and similar behaviors of this sort may be expected to occur in calculations for elastic-plastic beams with fully clamped ends under impulsive loading. Occurrence of this anomalous response requires the beam to have boundary conditions which prevent the axial displacement so that the transverse displacement causes stretching of the middle surface and the plastic strains in effect convert the beam to an arch. The anomalous behavior dealt with here is a consequence of dynamic instabilities akin to snap-buckling.