A Closed Form Solution for Reissner's Planar Finite-Strain Beam Using Jacobi Elliptical Functions

TL;DR

This paper presents an exact analytical solution for large-deflection finite-strain planar beams using Jacobi elliptical functions, including buckling analysis under various boundary conditions.

Contribution

It introduces a novel closed-form solution for Reissner's finite-strain beam problem, extending analytical methods with numerical validation and buckling behavior analysis.

Findings

Analytical solution expressed via Jacobi elliptical functions

Numerical examples demonstrating solution accuracy

Buckling factors derived for different boundary conditions

Abstract

In the article we introduce an analytical solution for Reissner's large-deflection finite-strain planar beam subject to an end force and a bending moment. The solution is given in terms of Jacobi elliptical functions. The obtained analytical solution is enhanced with numerical examples. A buckling and post buckling behavior of a beam under axial compressive load applied at the end and subject to various boundary conditions is also discussed in some details. In particular, the buckling factor is derived for each case of the boundary conditions.