Optimal Design of Composite Granular Protectors

Abstract

We employ an evolutionary algorithm to investigate the optimal design of composite protectors using one-dimensional granular chains composed of beads of various sizes, masses, and stiffnesses. We define a fitness function using the maximum force transmitted from the protector to a “wall” that represents the body to be protected and accordingly optimize the topology (arrangement), size, and material of the chain. We obtain optimally randomized granular protectors characterized by high-energy equipartition and the transformation of incident waves into interacting solitary pulses. We consistently observe that the pulses traveling to the wall combine to form an extended (long-wavelength), small-amplitude pulse.

Keywords:

• granular protectors
• optimal design
• solitary waves
• pulse disintegration and reflection
• thermalization
• evolutionary algorithms

ACKNOWLEDGEMENTS

We thank Dr. Antonio Della Cioppa from the Department of Information and Electrical Engineering of the University of Salerno for providing the BGA code. F.F. greatly acknowledges the support of the Province of Salerno and the University of Salerno through a grant for international mobility. FF and MAP thank the Graduate Aerospace Laboratory at Caltech (GALCIT) for hospitality during their visits, and CD acknowledges support from Caltech startup funds and from the Army Research Office, Grant Number 54272-E6.

Notes

¹In the absence of gravity and precompression, a loose state is reached after a sufficiently long time because the granular chain is constrained only at one end. The dynamics evolve so that the interactions go to zero.