Summation rules in critical self-buckling states of cylinders

Kanahama, Tohya; Sato, Motohiro

doi:10.1016/j.mechrescom.2022.103905

Cited by 5 publications

(4 citation statements)

References 26 publications

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“…This formula indicates that the greatest height of a solid cylinder against self-weight buckling is proportional to two-thirds of the power of its diameter ( 1 ), and McMahon demonstrated that the scaling law of height–diameter based on Greenhill’s theory is applicable to actual trees as well ( 2 , 3 ). Through these verification results, Greenhill’s achievements have been widely applied in the fields of ecology, forest science, and engineering ( 5 – 24 ).…”

mentioning

confidence: 94%

Mechanics-based classification rule for plants

Kanahama,

Sato

2023

Proc. Natl. Acad. Sci. U.S.A.

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The height of thick and solid plants, such as woody plants, is proportional to two-thirds of the power of their diameter at breast height. However, this rule cannot be applied to herbaceous plants that are thin and soft because the mechanisms supporting their bodies are fundamentally different. This study aims to clarify the rigidity control mechanism resulting from turgor pressure caused by internal water in herbaceous plants to formulate the corresponding scaling law. We modeled a herbaceous plant as a cantilever with the ground side as a fixed end, and the greatest height was formulated considering the axial tension force from the turgor pressure. The scaling law describing the relationship between the height and diameter in terms of the turgor pressure was theoretically derived. Moreover, we proposed a plant classification rule based on stress distribution.

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confidence: 94%

Mechanics-based classification rule for plants

Kanahama,

Sato

2023

Proc. Natl. Acad. Sci. U.S.A.

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“…While Equation 7 predicted a significantly greater length than was achieved, this assumed a perfect axial load on the robot. Our result is a better fit for models used to determine the critical height of cylinders under their own weight [24], which can be applied to plants in nature. This suggests we have reached the realistic limitation on collapse length for these robot parameters, even in our controlled setting.…”

Section: A Collapse Length For Various Launch Anglesmentioning

confidence: 86%

Collapse of Straight Soft Growing Inflated Beam Robots Under Their Own Weight

McFarland

Coad

2023

2023 IEEE International Conference on Soft Robotics (RoboSoft)

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Soft, growing inflated beam robots, also known as everting vine robots, have previously been shown to navigate confined spaces with ease. Less is known about their ability to navigate three-dimensional open spaces where they have the potential to collapse under their own weight as they attempt to move through a space. Previous work has studied collapse of inflated beams and vine robots due to purely transverse or purely axial external loads. Here, we extend previous models to predict the length at which straight vine robots will collapse under their own weight at arbitrary launch angle relative to gravity, inflated diameter, and internal pressure. Our model successfully predicts the general trends of collapse behavior of straight vine robots. We find that collapse length increases nonlinearly with the robot's launch angle magnitude, linearly with the robot's diameter, and with the square root of the robot's internal pressure. We also demonstrate the use of our model to determine the robot parameters required to grow a vine robot across a gap in the floor. This work forms the foundation of an approach for modeling the collapse of vine robots and inflated beams in arbitrary shapes.

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“…( 13 )), we obtain the greatest height equation as follows: where is the first zero point in the Bessel function of the first kind. Moreover, the greatest height of the non-tapering hollow cylinder is given by 26 …”

Section: Calculationmentioning

confidence: 99%

“…However, simply reducing the radius to reduce the weight results in a decrease in the bending rigidity. This problem can be solved by adopting a hollow cylindrical structure 24 – 26 . In fact, bamboos, which are smaller in diameter than trees, simultaneously possess both a tapered form and hollow structure; presumably, this allows them to grow as tall as trees.…”

Section: Introductionmentioning

confidence: 99%

Plant strategies for greatest height: tapering or hollowing

Kanahama,

Sato

2023

Sci Rep

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The tapered form and hollow cross-section of the stem and trunk of wild plants are rational mechanical approaches because they facilitate the plant simultaneously growing taller for photosynthesis and supporting its own weight. The purpose of this study is to clarify the advantages and disadvantages of tapering and hollowing from the perspective of the greatest probable height before self-buckling. We modelled woody plants using tapering or hollow cantilevers, formulated the greatest height before self-buckling, and derived a theoretical formula for the greatest probable height considering tapering and hollowing. This formula theoretically explains why almost all plants exhibit a tapered form: it allows for a greater height at an earlier growth stage than a hollow cross-section.

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Summation rules in critical self-buckling states of cylinders

Cited by 5 publications

References 26 publications

Mechanics-based classification rule for plants

Mechanics-based classification rule for plants

Collapse of Straight Soft Growing Inflated Beam Robots Under Their Own Weight

Plant strategies for greatest height: tapering or hollowing

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