Simplified Large Deflection Mode Solutions for Impulsively Loaded, Viscoplastic, Circular Membranes

The title problem is solved by estimating the maximum strain rate field in a circular membrane associated with a modal velocity condition when one-half the kinetic energy in the system has been dissipated. The radial stress may only vary in the radial direction, but is taken as a constant with time at any given location. Internal plastic energy absorbed during the large deformation is found by integrating while accounting for rate sensitivity effects; this absorbed energy is equated to the initial kinetic energy in the system to obtain the final deformed configuration. Correlation of analytically determined results with a series of experiments reported elsewhere is very good. The procedure described here is potentially extendable to any planform membrane shape as well as to axisymmetric shells. The method is applicable to plate problems when membrane effects dominate over bending, that is for deformations of the order of two thicknesses or more. A simple general formula for final plate deformation is devised and also agrees well with experimental results.