Elasticity solution for a 3D hollow cylinder axially loaded at the end faces

TL;DR

This paper derives an explicit elasticity solution for a hollow cylinder under axial end loads, using Fourier series expansion, with applications to engineering problems like cable-stayed bridges.

Contribution

It provides a novel explicit solution for the elasticity problem of a hollow cylinder with axial loads, including symmetry results and error estimates for series truncation.

Findings

Explicit Fourier series solution derived

Symmetry properties of the elasticity solution proven

Error bounds for series truncation provided

Abstract

Starting from an applicative problem related to the modeling of an element of a cable-stayed bridge, we compute the elasticity solution for a hollow cylinder loaded at the end faces with axial loads. We prove results of symmetry for the solution and we expand it in proper Fourier series; computing the Fourier coefficients in adapted power series, we provide the explicit solution. We consider an engineering case of study, applying the corresponding approximate formula and giving some estimates on the error committed with respect to the truncation of the series.