Iterative global-local approach to consider the effects of local elasto-plastic deformations in the analysis of thin-walled members

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Journal Article
International Journal for Multiscale Computational Engineering, 2017, 15 (2), pp. 143 - 173
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© 2017 by Begell House, Inc. The aim of this study is to develop an iterative global-local analysis method to efficiently model the local deformation effects for the nonlinear elasto-plastic analysis of thin-walled beams. Thin-walled members are usually modeled by using beam-type one-dimensional finite elements, which are based on rigid cross-section assumption. Therefore, only deformations associated with the beam axis behavior such as flexural-, torsional-, or lateral buckling can be considered in these formulations, whereas local deformations, namely flange or web local buckling, can be captured by shell-type models. The proposed method allows the local use of shell elements in critical areas to incorporate the local deformation effects on the overall behavior of the thin-walled beam without necessitating a shell model for the whole structure. In this study, the local shell formulation is able to capture the elasto-plastic metal behavior based on the von Mises yield criterion and the associated flow rule for plane stress, which may cause unstable post-buckling response. In order to trace an unstable post-buckling curve, the iterative global-local analysis method is incorporated into the arc-length solution procedure. In order to improve the convergence characteristics, the procedure introduces strong discontinuities in the beam element formulation in the region of the local shell elements. These discontinuities are in the form of an internal enrichment considering additional local degrees of freedom associated with some penalty terms which adjust the tangent stiffness matrix of the beam for the prediction in the next step according to the effects of the local shell model in the previous step. Comparisons with full shell-type analysis are provided in order to illustrate the accuracy and efficiency of the method developed herein.
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