NATURAL APPROACH FOR GEOMETRIC NONLINEAR-ANALYSIS OF THIN-WALLED FRAMES

A new stiffness matrix for geometrically non‐linear analysis of three‐dimensional beam‐columns with bisymmetrical, thin‐walled, I‐type cross‐sections is presented. The displacement field is described in terms of natural and rigid‐body displacements and both Cartesian and natural matrices are derived. A novelty of the resulting method is the use of this dual description in all aspects of the analysis including the computer implementation. A companion paper1 that introduces the plastic behaviour of the material also justifies the need for this dual approach as a means to separate nodal forces from stress resultants in the cross‐section of the 3D beam‐column element. The current development uses the updated Lagrangian formulation and corrections in the element matrix are made to properly consider the behaviour under finite rotation. It is shown that accuracy and convergence of the solution process can be improved if the natural matrices derived here are used in a new force recovery process that is insensitive to rigid‐body displacements. Copyright © 1990 John Wiley & Sons, Ltd