The dynamic response of a strain-softening beam

The dynamic response of a strain-softening beam subjected to a transverse impulsive on its tip is investigated. A softening moment-curvature relation is assumed for the beam and a closed form solution is obtained for a special kind of load, which shows that there exists a softening region in the beam and this region propagates along the beam. This result indicates that, except for the possible discrete softening points with rotation discontinuity caused by the deformation localization^1], the existence of the softening region and its travelling along the beam are the essential features of the dynamic response of a strain-softening beam. The results also show that the failure of the beam should take place under a special load and the critical condition on which the dynamic failure occurs is given. The project supported by National Natural Science Foundation of China