Optimal design of bamboo under transverse bending

Abstract

Bamboo, a natural functionally graded material (FGM), exhibits self-adaptive properties that are potentially responsible for its distinct vascular bundle distribution. This study explores the optimal spatial distribution of vascular bundles to maximize flexural rigidity during transverse bending. We compared the expression for volume fraction of fibers with a verified volume fraction expression and utilized the Halpin-Tsai equation to derive expressions for transverse Young's modulus and flexural rigidity. The optimal distribution was consistent with the actual distribution in Moso bamboo, which exhibits significant ovalization of the cross section due to pure bending. Bamboo behaves as a cylindrical shell near its base where the ovalization effect is significant and as a beam at other regions. Furthermore, the spatial distribution of flexural rigidity from pure bending is optimized at all positions in wild bamboo, demonstrating its potential as a versatile FGM that can adjust its distribution under both pure and transverse bending.