Optimized creasing pattern for maximizing natural frequencies of a thin elastic plate

Abstract

Crumpled or folded sheets tend to show higher flexural stiffness when compared to that of flat thin sheets. This is attributed to the Gaussian curvature due to the folds, and the increased energy needed for the sheets to then bend under the application of transverse loads. In this study, we motivate the optimization of an additively manufactured thin sheet which has crease lines resembling crumpling. The problem is posed as a constrained optimization problem. An optimal pattern of creasing within a thin square plate is examined that will maximize the minimum natural frequency of the structure.