A general computational framework for designing morphing structures

Structural morphing is a bio-inspired design strategy that aims to conform structures to different operating environments, typically by adapting the geometrical shape in a compliant manner. Composites play an enabling role for larger-scale morphing structures as multi-functionality is readily incorporated in the manufacturing process. To date there is no predominantly accepted technique of analysing and designing these structures, especially in a manner that integrates easily with established tools used in industry. One potential candidate in this respect is generalised path-following, which combines a numerical continuation algorithm with the geometrical versatility of the finite element method. Morphing composites often take the form of multistable laminates which, as the name suggests, are driven by instabilities. The two (or more) stable states that are exploited in a multistable laminate are typically a product of postbuckling or other forms of prestress, and the ensuing snap-through phenomenon is a catastrophic event (in a mathematical sense) in itself. In this respect, a generalised path-following algorithm is ideally suited for analysing these structures as it is capable of detecting critical instability points, switching to secondary bifurcated branches, and evaluating the parametric response of critical points with respect to any other parameter. We show that the full complexity of multi-snap events of bistable laminates is robustly captured by this algorithm, and that the ability to determine loci of instability points with respect to additional parameters is especially useful for rapid parametric studies.