Non-linear analysis of thin-walled members of open cross-section

The paper presents a means of determining the non-linear stiffness matrices from expressions for the first and second variation of the Total Potential of a thin-walled open section finite element that lead to non-linear stiffness equations. These non-linear equations can be solved for moderate to large displacements. The variations of the Total Potential have been developed elsewhere by the authors, and their contribution to the various non-linear matrices is stated herein. It is shown that the method of solution of the non-linear stiffness matrices is problem dependent. The finite element procedure is used to study non-linear torsion that illustrates torsional hardening, and the Newton-Raphson method is deployed for this study. However, it is shown that this solution strategy is unsuitable for the second example, namely that of the post-buckling response of a cantilever, and a direct iteration method is described. The good agreement for both of these problems with the work of independent researchers validates the non-linear finite element method of analysis. Copyright (C) 1999 John Wiley & Sons, Ltd.