Characterization of the Buckling and Post-Buckling Response for Crumpled Plates

Abstract

The mechanics of flat plates have been well studied for decades, and engineers continue to push for thinner designs while maintaining a margin to prevent the onset of buckling. As such, one potential avenue to maximize the structural efficiency is to incorporate deterministic and stochastic creases to the design, increasing the flexural rigidity without sacrificing additional weight. This thesis characterizes the behavior of these crumpled plates, focusing on the transition between the pre-buckled and post-buckled states when subject to uniaxial compressive loads. Specifically, it is known that plates have the ability to be load-bearing beyond the onset of buckling, thus the reaction of crumpled plates past it's transitional or buckling load is observed and captured. Two such configurations are considered: one with uniform pyramidal crumples protruding in one out-of-plane direction only, and one with pyramidal crumples that alternate in its protrusion direction. Numerous case studies, including crumple height, half-sine imperfection magnitude, number of crumple per edge, and aspect ratios, were conducted to observe the load-displacement response. In addition, unlike perfect flat plates, the natural frequency increases in post-buckled plates at certain levels of preload, offering increased vibration resistance, so the frequency response in the post-buckled crumpled plates are also observed and characterized.