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 beam behaviour is represented through the beam degrees of freedom of the global nodes on reference axis, and local effects are taken into account through the relative displacements of the cross-sectional nodes defining the in-plane and out-of-plane deformations of the cross-section. Consistent derivations for small and large displacements within incremental analysis are presented. 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 subelements (3D, shell, beam) with the relative displacements as the internal degrees of freedom of the element group, which is considered as a substructure. The relative displacements can be translations and rotations, depending on the type of the subelements. Continuity of the relative displacements is ensured within the element group, and connection of the beam elements with other finite element (FE) groups is realized through global (beam) degrees of freedom. Incompatible generalized displacements are implemented to subelements to improve their behavior. External loading of the element can correspond to global and cross-sectional nodes. The proposed beam superelement (BS) is easy for application within FE general purpose package (as our program PAK) in the preparation of input and in the postprocessing. A number of typical examples illustrate accuracy of results obtained by use of the beam superelement in linear and geometrically nonlinear analysis.