Efficient Pulse Shapes to Plastically Deform Beams

Abstract

The transient motion of a simply supported, rigid-plastic beam in response to uniformly distributed pressure pulses of arbitrary shape is considered. The objective is to determine the pulse shape that will maximize the residual deflection at the center of the beam subject to certain load constraints. Results for two constraints are determined. When a specified impulse is applied to the beam an impulsive load causes the largest deflection. When a specified amount of work is done on the beam the deflection is maximized by limiting the maximum pressure so only the static collapse deformation mode occurs. This result is independent of pulse shape. These conclusions are supported by comparisons of the deformation due to triangular, exponentially decreasing and double rectangular pressure pulses.