Carol Lee Chalermsin

Ovalization of a cross-section is a dominant cause of failure in hollow plants subjected to bending. This study investigates the optimal spatial arrangement of fibers to maximize flexural rigidity during transverse bending by examining the morphology of bamboo. Bamboo, a hollow plant, exhibits self-adaptive properties that potentially account for its distinct vascular bundle distribution. By deriving the volume fraction of fibers in the longitudinal direction and equations for transverse flexural rigidity, the study identifies the optimal fiber distribution. The results indicate that a parabolic distribution of fibers is optimal for avoiding ovalization. Furthermore, a comparison with Moso bamboo reveals that this calculated optimal distribution matches the actual fiber arrangement near the bamboo's base, where the ovalization effect is significant. Moso bamboo behaves like a cylindrical shell, with high bending moments causing pronounced ovalization, while in other regions, it resembles a beam with lower bending moments.

Abstract Functionally graded materials (FGMs) have various mechanical advantages and are naturally occurring, such as bamboo. Although bamboo is hollow and tapered, it remains resilient under a wind load. Based on this mechanical rationale, this study focuses on a large deflection of a tapering structure and the hollowing effect of a functionally graded beam. A theoretical analysis is conducted on a nonlinear bending of a slender and tapered hollow beam made of an axially FGM subjected to a uniformly distributed load undergoing a large deflection. To this end, governing equations are derived and a parametric study is conducted to investigate the effect of the inhomogeneous material, load magnitude and tapering and hollowing ratios on the large deflection of the beam. A linear analysis is conducted to examine the bending stress of the tapered beam and sets of deflection curves and angles along the beam are obtained and compared with values obtained from previous studies. As a result, the hollow and inhomogeneous nature of the axially FGM improves its rigidity against a wind load. This study provides insights into the potential use of axially FGMs to obtain more efficient and sturdier structural designs.

Abstract In previous research on the mechanical instability of trees based on mechanical theory, wild tree has been modeled as a cantilever which was perfectly attached to the ground. However, experimental research has identified two failure modes, including root turnover and self-buckling of the trunk. This suggests that the imperfect fixation caused by root-soil interaction must be considered when discussing tree stability. The purpose of this study is to clarify the self-buckling characteristics of wild trees considering soil instability. To account for the resistance moment caused by the interaction between the root and soil, trees as cantilevers fixed to the ground by a rotational spring were modeled. In this model, the self-buckling problem was formulated considering the rotational rigidity of the spring, and the formula derived for the critical height and buckling mode. As a result, the formula for critical height considering rotational rigidity was obtained, and it was found that the buckling modes can be classified into the rigid-body mode and beam mode based on the rotational rigidity. By comparing this result with the statistical law based on the measurement of real trees reported in previous research, it was determined that real trees were designed based on beam mode. This suggests that the wild tree skillfully balances the moment of resistance caused by the interaction between the root and soil to prevent “uprooting,” which is extremely fatal for trees. Moreover, it was also found that the safety factor of trees for self-buckling is ensured enough to prevent the beam mode.