Bistable Structures for Morphing Applications Using Anisotropic Shells

Student thesis: Doctoral ThesisDoctor of Philosophy (PhD)


An investigation into the thermally-induced bistability of composite plates and shells is presented. The principal aim is to provide novel capabilities for analytical modelling and optimum design for potential morphing applications.One possible mechanism for obtaining bistability is by tailoring the thermal expansion coefficient of plies within a laminate. For instance, unsymmetric laminates may warp and assume two stable configurations upon cooling down from cure to room temperature.Such behaviour is inherently nonlinear in nature and presents complex details that, despite being crucial for the feasibility of potential morphing applications, are not captured in sufficient fidelity by the models available in the literature.In the current approach, the equilibrium equations are discretised using polynomial bases, and solved following a Ritz approach. As a novelty, use is made of suitably derived, non-dimensional lamination theories. This ameliorated the inher- ently poor conditioning properties of Ritz discretisations and, as a consequence, to use high-order approximations. The increased degrees of freedom within the models are shown to be the first analytical solutions to accurately reflect the underlying mechanics and several characteristic details.Furthermore, Ritz discretisations are complemented by numerical continuation routines based on pseudo-arclength algorithms. This approach provides the means for a systematic and parametric exploration of the design space. Subsequently, a tool for optimal design is obtained that offers key advantages over the more conventional natural continuation method or commercial FE software.Since bistable laminates feature very large displacements, a further aim was to assess whether the Lagrangian equilibrium equations on which the models are based were adequate or whether a Eulerian description would be necessary. Undertaking this study required a detailed understanding of the strain descriptors. With regard to shells, this led to the formulation of a consistent first-order shear deformation theory, which gives novel insight into the structural mechanics of curved panels.
Date of Award2011
Original languageEnglish
Awarding Institution
  • The University of Bristol
SupervisorPaul M Weaver (Supervisor)

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