A general beam finite element with deformable cross-section

A general beam finite element is proposed in the paper. The formulation of the element relies on the assumption that the beam-type structural response can be described by using the usual beam and 3D continuum theories. The be am behaviour is represented through the beam degrees of freedom of the glob al nodes on reference axis, and local effects are taken into account throug h the relative displacements of the cross-sectional nodes defining the in-p lane and out-of-plane deformations of the cross-section. Consistent derivat ions for small and large displacements within incremental analysis are pres ented. The cross-section is modeled by segments (cross-sectional elements) and can be of arbitrary shape, including thick- and thin-walled types. The element is formulated as a superelement consisting of the isoparametric sub elements (3D, shell, beam) with the relative displacements as the internal degrees of freedom of the element group, which is considered as a substruct ure. The relative displacements can be translations and rotations, dependin g on the type of the subelements. Continuity of the relative displacements is ensured within the element group, and connection of the beam elements wi th other finite element (FE) groups is realized through global (beam) degre es of freedom. Incompatible generalized displacements are implemented to su belements to improve their behavior. External loading of the element can co rrespond to global and cross-sectional nodes. The proposed beam superelemen t (BS) is easy for application within FE general purpose package las our pr ogram PAK) in the preparation of input and in the postprocessing. A number of typical examples illustrate accuracy of results obtained by use of the b eam superelement in linear and geometrically nonlinear analysis. (C) 2001 E lsevier Science B.V. All rights reserved.