Modelling and optimisation of bistable composite laminates

  • David Betts

Student thesis: Doctoral ThesisPhD


Asymmetric composite laminates can have a bistable response to loading. The potentially large structural deformations which can be achieved during snap-through from one stable state to another with small and removable energy input make them of interest for a wide range of engineering applications. After 30 years of research effort the shapes and response to applied loads of laminates of general layup can be quantitatively predicted. With attention switching to the incorporation of bistable laminates for practical applications, tools for the design and optimisation of actuated bistable devices are desirable. This thesis describes the analytical and experimental studies undertaken to develop novel modelling and optimisation techniques for the design of actuated asymmetric bistable laminates. These structures are investigated for practical application to morphing structures and the developing technology of piezoelectric energy harvesting. Existing analytical models are limited by the need for a numerical solver to determine stable laminate shapes. As the problem has multiple equilibria, convergence to the desired solution cannot be guaranteed and multiple initial guesses are required to identify all possible solutions. The approach developed in this work allows the efficient and reliable prediction of the stable shapes of laminates with off-axis ply orientations in a closed form manner. This model is validated against experimental data and finite element predictions, with an extensive sensitivity study presented to demonstrate the effect of uncertainty and imperfections in the laminate composition. This closed-form solution enables detailed optimisation studies to tailor the design of bistable devices for a range of applications. The first study considers tailoring of the directional stiffness properties of bistable laminates to provide resistance to externally applied loads while allowing low energy actuation. The optimisation formulation is constrained to guarantee bistability and to ensure a useful level of deformation. It is demonstrated that ‘cross-symmetric’ layups can provide stiffness in an arbitrary loading direction which is five times greater than in a chosen actuation direction.The optimisation formulation is extended to include a method of actuation, with a series of experimental and modelling studies presented to assess mechanical and smart actuators. Orthogonal piezoelectric macro-fibre composite actuators are identified as the most suitable method for both modelling and experimental actuation. The analytical model is extended to include piezoelectric loading in such a way as to maintain the reliable prediction of all loaded laminate shapes. Using this formulation piezo-laminate structures are identified which provide resistance to operating loads while still maintaining a useful structural deformation which is achievable within recommended operating voltage limits. A secondary study demonstrates that required actuation voltages can be reduced by up to 33% through the simultaneous use of the positive and negative voltage range of two oppositely oriented piezoelectric layers. Finally, the modelling and optimisation methods are applied to study piezoelectric composite laminates for electrical energy harvesting from ambient mechanical vibrations. The novel formulation aims to maximise the electrical energy output in an arrangement of piezoelectric layers excited by the alternating stress due to repeated mechanical actuation. Due to the complex mechanical-electrical coupling and the highly nonlinear behaviour, existing studies are limited to experimental demonstration with scope for improving designs for broadband harvesting identified. Enabled by the modelling formulation developed in this work, optimisation of the piezo-laminate structure demonstrates improved electrical energy generation. Through variation in laminate geometry, arbitrary stacking sequences and piezoelectric configurations, optimum designs are presented which differ from those considered experimentally, identifying wide scope for improvement of this developing technology.
Date of Award1 Jan 2012
Original languageEnglish
Awarding Institution
  • University of Bath
SponsorsEngineering and Physical Sciences Research Council
SupervisorHyunsun Kim (Supervisor) & Giles Hunt (Supervisor)


  • composite laminates
  • energy harvesting
  • bistability
  • optimisation

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