GXBeam: A Pure Julia Implementation of Geometrically Exact Beam Theory


geometrically exact beam theory, flexible structures, aeroelastic, Julia, finite element, nonlinear beam, large deflection beam, derivatives, automatic differentiation


When the cross sections of a three-dimensional structure are small compared to the length of the structure, beam theory may be used to efficiently model the structure’s three-dimensional behavior. Applications of beam theory include, but are not limited to, the structural modeling of buildings, bridges, aircraft, helicopter blades, and wind turbines. When deflections are small, linear beam theories may be used to model the behavior of slender structures. When deflections become significant, such as encountered when modeling high aspect ratio wings or large wind turbine blades, nonlinearities associated with geometric deformations must be accounted for.

GXBeam is a geometrically exact beam theory package which is written completely in the Julia programming language. It was originally based on the open source code GEBT and its associated papers, which adopt the mixed formulation of geometrically exact beam theory presented by Hodges. When combined with a beam cross sectional analysis, such as a variational asymptotic beam sectional analysis, this geometrically exact beam theory formulation constitutes an efficient and accurate replacement for a full three-dimensional structural analysis.

Original Publication Citation

McDonnell, T., and Ning, A., “GXBeam: A Pure Julia Implementation of Geometrically Exact Beam Theory,” Journal of Open Source Software, Vol. 7, No. 73, p. 3997, May 2022. doi:10.21105/joss.03997

Document Type

Peer-Reviewed Article

Publication Date


Permanent URL



Journal of Open Source Software




Ira A. Fulton College of Engineering


Mechanical Engineering

University Standing at Time of Publication

Associate Professor