"In this paper a procedure for obtaining a beam model from a thin plate theory, is introduced. The starting point is the theory proposed by Koiter which describes the deformation of the plate in a kinematically exact way. By assuming some fair constraints on the plate motion, its deformation measures can be described by means of four scalar parameters that are a measure of the elongation, two bending terms and the torsion of a 1D continuum. Given that the plate is thin and made up of a material that is isotropic elastic and linear in the 2D finite strains, its strain energy is written in terms of the 1D strains. The resulting function is then given a power expansion. Taking the derivative of this expression with respect to the 1D strain measures, the constitutive functions of the corresponding stress measures are obtained. Some samples show how the procedure can be used to study the mechanical behaviour of TWBs with open cross sections."
Gabriele, S., Rizzi, N.L., Varano, V. (2013). On the Postbuckling Behaviour of Thin Walled Beams with In-Plane Deformable Cross-Sections. In Proceedings of the Fourteenth International Conference on Civil, Structural and Envi- ronmental Engineering Computing. Stirlingshire : Civil-Comp Press [10.4203/ccp.102.99].