Key Considerations in Tracing the Postbuckling Response of Structures with Multi Winding Loops

Abstract

The postbuckling response of structures with multi winding loops is characterized by the appearance of multi adjacent equilibrium paths, which often makes the iterations difficult to converge to the desired path. In this paper, some key issues for tracing the postbuckling response of a structure using an incremental-iterative approach are discussed. Concerning the finite element equations used, it is essential that the corrector used for recovering the element forces from the element displacements be made as accurate as possible, and that the predictor for computing the structural displacements under given load increments, which are approximate by nature due to linearization involved, be accurate to the level not to misguide the iterations. As for the incremental-iterative scheme, it is required to be: (1) numerically stable when encountering the limit points, (Equation2) adjustable in load increments to reflect the stiffness variation, and (Equation3) self-adaptive in changing the loading direction. To demonstrate the ideas involved, some examples with highly complicated postbuckling responses will be solved in this paper. Keywords: CorrectorGeometric nonlinearityIncremental-iterative approachLarge strainSnap-back pointUpdated Lagrangian formulationLimit pointPostbucklingPredictor ACKNOWLEDGEMENT This study was made possible through a series of research projects granted by the National Science Council to the senior, including the one with NSC 78-0410-E002-30.