On Stability of Non-inflectional Elastica

TL;DR

This paper analyzes the stability of non-inflectional elastica under various boundary conditions, establishing conditions for stability and revealing that Dirichlet boundary conditions guarantee unconditional stability.

Contribution

It provides a comprehensive stability analysis of non-inflectional elastica under different boundary conditions, including new criteria based on boundary derivative signs.

Findings

Dirichlet boundary conditions ensure unconditional stability.

Stability under mixed and Neumann conditions depends on endpoint tangent angle derivatives.

Sufficient stability criteria are derived for non-inflectional elastica.

Abstract

This study considers the stability of a non-inflectional elastica under a conservative end force subject to the Dirichlet, mixed, and Neumann boundary conditions. It is demonstrated that the non-inflectional elastica subject to the Dirichlet boundary conditions is unconditionally stable, while for the other two boundary conditions, sufficient criteria for stability depend on the signs of the second derivatives of the tangent angle at the endpoints.