On the finite element analysis of the spatial response of curved beams with arbitrary thin-walled sections

A three-dimensional, two-field, variational formulation is employed to derive the differential equations governing the stretching, shearing, bending, twisting, as well as warping modes of deformations in a spatially curved beam subjected to general loading and boundary conditions. Correspondingly, a simple two-noded finite element model was developed and utilized in a number of numerical simulations. In particular, attention was given to the significant curvature effects on the results in cases involving unsymmetric cross-section of the thin-walled type, in which any inconsistencies introduced when using the classical notion of two different reference lines, i.e., centroid and shear center, for sectional deformations may lead to large errors.