Dynamics of ideal fibre-reinforced rigid-plastic beams

A mechanism is proposed by which discontinuities in slope can propagate along an ideal fibr-ereinforced beam which is inextensible in the direction of its axis. The equations of motion of the beam are formulated, including the dynamical conditions which must be satisfied at the discontinuity. Constitutive equations for a rigid-plastic fibre-reinforced beam are established, and it is shown that slope discontinuities may propagate in a strain-hardening material, but are stationary in a perfectlyplastic beam. The theory is illustrated by its application to the problem of a beam moving in a direction normal to its axis brought to rest by striking a rigid stop at its mid-point. It is shown that in the subsequent motion slope discontinuities travel outwards from the centre of the beam. A complete explicit solution is obtained for the case of a beam with linear strain-hardening.