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.
Abstract This study aims to determine the optimal design of fibers that can minimize circumferential bending stress from the morphology of “bamboo,” which is considered a “natural functionally graded material (FGM)” because vascular bundles are distributed unevenly across its cross-section. Further, vascular bundles are crucial for determining the mechanical properties of bamboo, and their distribution is not random. This study analyzes bias distribution from the viewpoint of structural mechanics. Longitudinal splitting is a dominant failure mode in both bamboo and fiber composites, it is mainly caused by circumferential bending tensile stress. The bamboo was modelled as a hollow cylinder, and a circumferential bending stress equation was formulated. As a result, the vascular bundles distribution of the bamboo minimized the circumferential bending stress on the inner surface of the cross-section throughout the culm. These suggest that bamboo is a smart plant that can control its distribution based on regions more prone to failure, e.g., where cracks occur first on the inner surface. This study can help obtain the optimal stress-controlled design of fiber-reinforced composites and understand the morphological design of bamboo.
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.
