Firsts steps for a fully exact thin-walled rod model incorporating generic cross-sectional distortion

Resumo

Thin-walled frame structures consisted of profiles or rod members are often subject to loadings that induce local effects on the profiles ́ webs and flanges. For some elements, local instability is the main design constraint. This work aims to present the first steps towards a thin-walled kinematically-exact rod formulation with cross-sectional local effects on its kinematical assumptions. The model ́s displacement field allows for the traditional cross-sectional rigid body motion, along with wall ́s mid-line in- and out-of-plane deformations (first-order in-plane distortion and out-of-plane warping, respectively, herein called primary deformations) and a kinematically-exact rotation for out-of-mid-line points (herein called secondary deformation). Accordingly, rigid body motion is parametrized as usual for geometrically exact models, whilst primary deformations are described by means of the Generalized Beam Theory (GBT) concept. The (shell-like) rotation that defines the secondary deformation, in turn, is obtained as a function of the walls ́ mid-line displacement field and is parametrized using Kirchhoff-Love shell assumptions. This is an ongoing research, and only the kinematical description, the related weak form (for future FEM discretization) are presented. Its linearization is only conceptually briefed by now. Neither constitutive equations nor numerical implementation are addressed here.