Free vibration of thin, creased elastic plates: Optimization and scaling laws

Creasing, crumpling, and folding help to increase the flexural rigidity of thin elastic plates. In this study, the fundamental frequency is used as a measure of improvement in flexural stiffness. Firstly, an analysis of an orderly, creased, thin elastic plate with nine separate pyramidal crumples is presented. Such a plate shows an increase of 124% in the fundamental frequency with only a 0.5% increase in the total mass/ surface area when compared to that of a flat configuration. Further, scaling laws are introduced for such ordered creased structures for three separate cases-scaling based on (i) the total surface area of the structure, (ii) the amplitude/ height of the ordered pyramidal crumples, and (iii) the number of unit cells within a given edge length of the plate. Further, an optimization problem is posed to achieve maximum flexural stiffness under given constraints for an additively manufactured thin, elastic plate supported on all four edges. The objective is posed as a constrained optimization problem maximizing the fundamental frequency of the structure compared to that of a flat sheet. The results are promising, with a 176% increase in stiffness with only a 0.84% increase in the total mass/ surface area.