Dynamic plastic behaviour of annular plates with transverse shear effects

The dynamic response of a rigid-plastic annular plate clamped at the outer edge and free at the inner edge is considered. The plate is subjected to initial impulsive loading so that at the initial moment of time all points of the plate have the uniform transverse velocity. It is assumed that the behaviour of a rigid perfectly plastic material is controlled by a cubic yield condition and the associated flow law in the space of bending moments and the transverse shear force. Theoretical predictions are developed and compared with an upper bound solution.