Closed-form expressions of shear deformability tensors associated with a new beam model

The application of a recent beam model requires the evaluation of a suitably defined shear deformability tensor in order to ensure both energetic and geometric consistency with the 3D Saint Venant model subjected to non-uniform flexure and torsion. Actually, whatever is the position of the shearing force, the beam model provides the same elastic energy and the same tip displacement of the barycentric axis of the 3D Saint Venant model. The expression of the shear deformability tensor is rather involved since it depends upon three harmonic functions, namely the warping and the warpage functions associated, respectively, with torsion and shear. For this reason, in order to promote its use and shed some light on its properties, we derive explicit expressions of the shear deformability tensor for circular, elliptical and rectangular sections exploiting the relevant analytical formulas of the warping and warpage functions. Copyright (C) 2022 The Authors.

Automated summary

This study derives explicit expressions of the shear deformability tensor for circular, elliptical, and rectangular sections and proposes a beam model applicable to non-uniform flexure and torsion of the 3D Saint Venant model.