Plastic deformations of impulsively loaded, rigid-plastic beams

Rigid body dynamics is used to determine the deformation of a fixed-end, ri gid-plastic beam subjected to uniformly distributed impulsive loading. The proposed solution methodology allows calculations of deformations at plasti c hinges and can be used to establish rigid-plastic fracture criteria for r igid-plastic beams. Unlike previous solutions to this problem, rotary inert ia and the shear deformations at the support are considered. The solution f or beam deformations is described in three phases: shear, bending, and memb rane. Each phase ends when the corresponding component of the strain rate v ector vanishes. The initial shear phase is completed when the transverse sh ear velocity at the support vanishes. The beam then undergoes only rigid bo dy rotation and axial stretching at plastic hinges in the bending phase. Th e bending phase ends when the angular velocity vanishes. In the membrane ph ase, the beam acts like a string until the transverse velocity vanishes. It has been found that beams subjected to low impulse velocity attain permane nt deformation in the bending phase, while beams subjected to high impulse velocity reach permanent deformation in the membrane phase. The predictions of the beam deflections using the proposed methodology are within 15% of t he experimental results.