A nonlinear, beam finite element with variable, eccentric neutral axis. (15th May 2019) - Walls, Richard; Viljoen, Celeste; de Clercq, Hennie
Highlights: Beam finite element with eccentric, variable neutral axis. Non-linear materials and material softening considered. Computationally efficient finite element formulation. Case studies considering large deflections and material nonlinearity considered. Applicable to composite beams, bridge decks and other similar structures. Abstract: This paper presents a beam finite element and analysis methodology for structures with neutral axes (NA) that are eccentric to the positions about which they are modelled, and that change position during the process of an analysis. This NA shift occurs due to non-linear material behaviour (softening, cracking, etc.). The proposed formulation is based upon a modified corotational approach. It has been developed specifically for structures subjected to severe fires, although it is also applicable to the non-linear analysis of structures such as wind towers and bridge decks where the position of the neutral axis in a beam section changes due to material nonlinearity. The analysis formulation results in lower computational effort relative to contemporary analysis methods employing shell or volume elements, while providing comparable results. Four case studies that include material nonlinearity, large deflections and geometric nonlinearity are included to validate the proposed formulation, and results are compared to shell element models analysed using Abaqus. The contributions of this paper are: (a) the application of standard Euler beam theory in a novel manner to allow for adjusted position of neutral axes in beams, (b) the presentation of simple case studies that can be used for validating finite element methods, but which incorporate material, geometric and cross-sectional non-linearity, and (c) illustrating the influence of cross-sectional discontinuity and how it may influence results when using beam elements.