Incorporating local effects in the predictor step of the iterative global-local analysis of beams

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Journal Article
International Journal for Multiscale Computational Engineering, 2016, 14 (5), pp. 455 - 477
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© 2016 by Begell House, Inc. The aim of the study is to develop a stiffness modification technique that considers the effects of local deformations/damages within the predictor step of iterative global-local analysis. The procedure is based on internal springs introduced in a beam element formulation whose constants are obtained according to the force vs. displacement results of the global-local analysis. Within the beam element formulation, strong discontinuities are introduced in the form of an internal enrichment considering additional local degrees of freedom associated with the deformations of local springs. Determination of the spring constants introduced in this study is an inverse problem, as given independent end-displacements and end-forces, corresponding spring stiffness terms are sought. Discussions on the heuristic nature of this problem are included and a regularization option is introduced to give rise to a unique solution for the problem. Nevertheless, it is shown that by using the proposed approach the number of iterations can be significantly reduced within the iterative global-local analysis algorithm. In the corrector step of the global-local analysis a local membrane finite element model is used to obtain the internal stress field.
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