Generalised path-following for well-behaved nonlinear structures

Groh, R.M.J. and Avitabile, D. and Pirrera, A. (2018) Generalised path-following for well-behaved nonlinear structures. Computer Methods in Applied Mechanics and Engineering, 331 . pp. 394-426. ISSN 0045-7825

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Recent years have seen a research revival in structural stability analysis. This renewed interest stems from a paradigm shift regarding the role of buckling instabilities in engineering design—from detrimental sources of catastrophic failure to novel opportunities for functionality. Novel nonlinear structures take the form of optimised thin-walled structures that operate safely in the post-buckling regime; shape-morphing structures that exploit multi-stability to snap and pop between different configurations; and meta-materials that derive novel material properties from a cascade of choreographed instabilities. Hence, elastic instabilities are no longer considered as structural failures but rather exploited for repeatable well-behaved adaptations. In this article we focus on shape-morphing—a bio-inspired design strategy that intends to conform structures to different operating conditions. Computational tools that integrate easily with established methods used in industry, and that are capable of capturing the full phase diagram of compound instabilities and entangled post-buckling paths typical of these structures, are limited. Such a capability is crucial, however, as confidence in predictive tools can be key in enabling non-conventional designs. One potential candidate in this regard is generalised path-following, which combines the computational robustness of numerical continuation algorithms with the geometric versatility of the finite element method. In this paper we collate an array of successful computational tools introduced by other researchers, and introduce our own developments, to present a modelling framework fit for analysing and designing with well-behaved nonlinear structures in industry and academia. Particularly, we show that the full complexity of multi-snap events of morphing composite laminates is robustly captured by generalised path-following algorithms, and that the ability to determine loci of singular points with respect to a set of parameters is especially useful for tracing the boundaries of bistability in parameter space. Furthermore, we shed new insight into the mechanics of multi-stable laminates, showing that the multi-stability and snapping behaviour of these structures is much richer than previously assumed, featuring many unstable post-buckling branches and localised regions of stability.

Item Type: Article
Keywords: Generalised path-following; Nonlinear structures; Multi-functionality; Bifurcations; Morphing; Composites
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1016/j.cma.2017.12.001
Depositing User: Eprints, Support
Date Deposited: 07 Feb 2018 10:02
Last Modified: 08 Feb 2018 16:29

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