Variational asymptotic beam sectional analysis – An updated version

This paper discusses three recent updates to the variational asymptotic beam sectional analysis (VABS). The first update is a change to the warping constraints in terms of three-dimensional variables, so that one-dimensional beam variables are treated with more rigor. The second update, although its formulation has only been analytically derived but has not been implemented yet, is the incorporation of the effects due to applied loads. The third update is a more accurate energy transformation to generalized Timoshenko form, which is a crucial aspect in finding the stiffness constants to the generalized Timoshenko beam theory. Examples are presented to demonstrate that the updated energy transformation may yield significantly different stiffness predictions from previous versions of VABS and to show that the updated version is indeed more accurate. In addition to the updates, this paper includes a comprehensive derivation of the geometrically-exact nonlinear one-dimensional beam theory and the asymptotically-correct cross-sectional analysis that together form the basis of VABS.