New Equation for Bending Development of Arbitrary Rods and Application to Palm Fronds Bending

TL;DR

This paper introduces a new general equation for modeling the bending of arbitrary rods, overcoming limitations of classical equations, and demonstrates its application to palm fronds with experimental validation.

Contribution

A novel, versatile equation for rod bending that simplifies analysis and extends applicability beyond classical constraints.

Findings

The new equation accurately predicts bending behavior in experiments.

It simplifies calculations by avoiding iterative procedures.

Application to palm fronds demonstrates practical utility.

Abstract

A new general equation to explain bending of arbitrary rods (from arbitrary materials, cross sections, densities, strengthnesses, bending angles, etc) was proposed. This equation can solve several problems found in classical equations, which have many limitations such as only applies for small bending angles or must be solved using very complex schemes. Experiments were also conducted to confirm the theoretical predictions. The equation might be used to explain bending of palm fronds in a very simple way. The proposed equation may be used to obtain solution of several problems which are usually obtain with iteration procedures.