An Eulerian Approach to the Large Displacement Analysis of Thin-Walled Frames

This paper presents a new approach for the geometrically nonlinear analysis of thin-walled space frames. The proposed approach employs an Eulerian (convected) system for the definition of local element freedoms, and is capable of representing the effects of large displacements, finite rotations and cross-sectional warping. The use of the Eulerian system has been shown to be advantageous in the context of adaptive elasto-plastic analysis, and the particular approach adopted has demonstrated a high level of accuracy which is quite insensitive to the size of the incremental load step. An important feature of the new approach is the separation of the transformations concerned with the effects of large displacements and finite rotations from the details of the element formulation, which allows the proposed approach to accommodate formulations of various degrees of sophistication. To demonstrate the accuracy of the new approach, a simple, yet powerful, finite element formulation is presented, which is capable of modelling thin-walled members with any open cross-sectional shape. Whilst such formulation is linear in the local system, its incorporation within the large displacement Eulerian approach allows geometrically nonlinear effects, such as lateral torsional buckling, to be accurately modelled. The incorporation of the local element response within a global nonlinear analysis capability based on the Eulerian approach is discussed, and essential requirements related to the coupling of warping freedoms of adjacent elements are outlined. Verification examples using ADAPTIC are finally presented to demonstrate the accuracy and efficiency of the proposed approach.