Cross-sectional performance of hollow square prisms with rounded edges

TL;DR

This paper introduces a mathematical model for describing polygonal cross-sections with rounded edges, aiding in the analysis of mechanical properties of hollow square prisms and plant-like structures.

Contribution

It proposes a novel mathematical method to accurately represent rounded polygonal cross-sections for mechanical analysis and design purposes.

Findings

The model effectively captures the shape of plant culms and stems.

It improves the accuracy of stability and buckling analysis.

The method facilitates the design of plant-mimicking structures.

Abstract

Hollow-section columns are one of the mechanically superior structures with high buckling resistance and high bending stiffness. The mechanical properties of the column are strongly influenced by the cross-sectional shape. Therefore, when evaluating the stability of a column against external forces, it is necessary to accurately reproduce the cross-sectional shape. In this study, we propose a mathematical method to describe a polygonal section with rounded edges and vertices. This mathematical model would be quite useful for analyzing the mechanical properties of plants and designing plant-mimicking functional structures, since the cross-sections of the actual plant culms and stems often show rounded polygons.