# Some features of bending of a rod under a strong longitudinal compression

## TL;DR

This paper analyzes the bending behavior of rods under strong longitudinal compression, linking the process to Laplace equation perturbations and describing initial bending stages near singularities using Hardy integrals.

## Contribution

It establishes a connection between rod bending under compression and Laplace equation perturbations, providing a new description of initial bending stages near singularities.

## Key findings

- Bending dynamics correspond to perturbations of the 2D Laplace equation.
- Rapid increase domains of bending originate near singularity points.
- Initial bending stages are characterized using Hardy integrals.

## Abstract

Considered typical processes of rod bending under strong longitudinal compression. The dynamic equation of bending correspponds to a perturbation of the two- dimensional Laplace equation. It is established that, for these processes, expanding of do- mains of rapid increasing of bending begins in small neighborhoods of singularity points of solutions of the limiting Laplace's equation. The initial stages of these increases are described using the Hardy integral.