Geometrically Nonlinear Flexibility-Based Frame Finite Element

Abstract

The paper presents a new element for geometrically nonlinear analysis of frame structures. The proposed formulation is flexibility based and uses force interpolation functions for the bending moment variation that depend on the transverse displacements and strictly satisfy equilibrium in the deformed configuration. The derivation of the governing equations and their consistent linearization are substantially more involved than for stiffness-based elements. Nonetheless, the element offers significant advantages over existing stiffness-based approaches, since no discretization error occurs and all governing equations are satisfied exactly. Consequently, fewer elements are needed to yield results of comparable accuracy. This is demonstrated with the analysis of several simple example structures by comparing the results from flexibility and stiffness-based elements.