Abstract
A numerical procedure for tracing the load-deflection path of tubular beam-columns and frames is presented. Nonlinearities arising from both the change of geometry and material yielding are included, incorporating the effects of arbitrarily large rotations and strain unloading. This numerical scheme is based on a compatible relationship between the incremental and the total equilibrium equations, as opposed to the generally available methods. An updated Lagrangian formulation, coupled with the numerical minimum residual displacement method, is employed for the solution of the nonlinear simultaneous equations. The proposed scheme is validated against a number of examples of which the results by other methods are available. The present method is capable of tracing the equilibrium paths of tubular struts with complex loading and boundary conditions using the incremental-iterative method throughout; suppression of iterations as required in other methods is not needed. This leads to a significant improvement in efficiency and accuracy because of the non-existence of the drift-off numerical error.
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