Low Energy Clamped Planar Elastica

TL;DR

This paper introduces a new method for estimating clamped planar elastica that is faster, more robust, and more likely to produce low-energy solutions compared to standard discretisation techniques, without relying on elliptic function solutions.

Contribution

The paper presents a novel estimation method for clamped planar elastica that improves speed, robustness, and energy minimization over existing discretisation approaches.

Findings

The new method is quicker than standard discretisation.

It is more robust in estimating elastica.

It tends to produce lower energy elastica solutions.

Abstract

A method is given for estimating clamped plane elastica. Arguments are made, and evidence is provided by way of illustrative examples, suggesting that the new method is quicker and more robust than standard discretisation, and more likely to give elastica of low energy. Just as for standard discretisation, no use is made of the known solutions for elastica in terms of elliptic functions.