Plastic-Wave Propagation Effects in Transverse Impact of Membranes

Abstract

The paper is concerned with the plane motion of a rigid-strain-hardening membrane attached to two parallel fixed supports. The membrane is subjected to a uniformly distributed transverse impulse and the subsequent motion of the membrane is to be determined with the particular emphasis on the variation of thickness in the final deflected shape. It is first shown that two essentially different initial modes of deformation exist depending on the average rate of hardening. For both modes, the analysis can be based on two types of waves of discontinuity until the moment when the compressive membrane forces occur in the middle region of the membrane. The presence of compressive forces will generally preclude the existence of a unique solution for further motion. The bending rigidity will probably have to be included into the analysis in order to obtain a unique solution. However, for the technically important rates of hardening and velocities, the kinetic energy of the membrane at the moment of occurrence of compressive forces is small compared with the initial energy, so that significant information could be obtained from the present analysis about the variation of thickness and hardening throughout the membrane.