A semi-discretized thin-walled beam element including distortion

A straight beam of constant cross section is considered. The strain components associated with the displacements are found as

Here ws(s) and wn(s) describes the local displacements of the centerline, ψ(z) is the function which describes the variation along the beam and (s) describes the axial (warping) displacement mode. The local components are clearly described in (Andreassen 2012). The notation indicates the two dimensions of the cross section planes and the single dimension associated with the variation along the beam.