Font Size:     

This work presents a fully nonlinear geometrically-exact multi-parameter rod model that incorporates general in-plane cross-sectional changes as well as general out-of-plane crosssectional warping. The formulation constitutes an extension of the earlier works, in the sense that the restrictions to a rigid cross-section and to a Saint-Venant-like elastic warping are now removed from the theory. The de¯nition of energetically conjugated cross-sectional resultants in terms of generalized stresses and strains, based on the concept of a cross-section irector, simpli¯es the derivation of equilibrium equations and the enforcement of boundary conditions, in either weak or strong senses. In addition, the corresponding tangent bilinear weak form is obtained in a more expedient way, rendering always symmetric for hyper-elastic materials and conservative loadings. The de¯nition of a cross-section director allows also the introduction of independent degrees-of-freedom to describe both the in-plane cross-sectional changes and the out-of-plane warping. Fully three-dimensional ¯nite strain constitutive equations can therefore be employed with no spurious sti®ening. Finite rotations are treated consistently by the Euler-Rodrigues formula in a pure Lagrangean framework. Altogether, the present assumptions allow a consistent basis for the proper representation of pro¯le (distortional) deformations, which are typical of cold-formed thin-walled rod structures. This is one of the main features of the formulation, as the use of more complex shell models in order to capture such phenomena can be needless.