An Improved Beam Theory for Arbitrary Cross-Sectional Shapes

The objective of this research is to systematically deduce a more accurate 1D beam model from 3D continuum considerations. This new approach results in a finite element analysis of a 3D "slice" of the cross-section, by which spanwise derivatives of the section-averaged displacement and rotation are connected to section forces and moments. The intent of this method is to produce a more accurate solution that can be applied for cross-section deformation and finite deformation of the beam, while still remaining within the framework of a reduced-order theory.