Generalized thin-walled beam models for flexural-torsional analysis

With non-uniform warping being an important mode of deformation, supplementary to the other six modes of stretching, shearing, twisting, and bending, we utilize a fairly comprehensive one-dimensional beam theory for the development of a simple finite element model for the analysis of arbitrary thin-walled beams under general loadings and boundary conditions. The formulation is valid for both open- and closed-type sections, and this is accomplished by using a kinematical description accounting for both flexural and warping torsional effects. To eliminate the shear/warping locking in this C⁰-element, a generalized mixed variational principle is utilized, in which both displacement and strain fields are approximated separately. In this, the strain parameters are of the interelement-independent type, and are therefore eliminated on the element level by applying the relevant stationarity conditions of the employed 'modified' Hellinger-Reissner functional, thus leading to the standard form of stiffness equations for implementation. A rather extensive set of numerical simulations are given to demonstrate the versatility of the models in practical applications involving usage of such components in their stand-alone forms as well as in plate/shell stiffening.