On the Kelvin Problem

TL;DR

This paper presents a solution to the Kelvin problem, determining the unique stress field in an isotropic elastic space under a concentrated load by leveraging the problem's symmetries.

Contribution

It introduces a symmetry-based method to solve the Kelvin problem, providing a clear and unique stress field solution.

Findings

Derived the unique balanced and compatible stress field.

Utilized symmetry properties to simplify the problem.

Provided insights into elastic space behavior under concentrated loads.

Abstract

The Kelvin problem of an isotropic elastic space subject to a concentrated load is solved in a manner that exploits the problem's built-in symmetries so as to determine in the first place the unique balanced and compatible stress field.