Abstract
Morphing shells are nonlinear structures that have the ability to change shape and adopt multiple stable states. By exploiting the concept of morphing, designers may devise adaptable structures, capable of accommodating a wide range of service conditions, minimising design complexity and cost. At present, models predicting shell multistability are often characterised by a compromise between computational efficiency and result accuracy. This paper addresses the main challenges of describing the multistable behaviour of thin composite shells, such as bifurcation points and snap-through loads, through the development of an accurate and computationally efficient energy-based method. The membrane and the bending components of the total strain energy are decoupled by using the semi-inverse formulation of the constitutive equations. Transverse displacements are approximated by using Legendre polynomials and the membrane problem is solved in isolation by combining compatibility conditions and equilibrium equations. This approach provides the strain energy as a function of curvature only, which is of particular interest, as this decoupled representation facilitates efficient solution. The minima of the energy with respect to the curvature components give the multiple stable configurations of the shell. The accurate evaluation of the membrane energy is a key step in order to correctly capture the multiple configurations of the structure. Here, the membrane problem is solved by adopting the Differential Quadrature Method (DQM), which provides accurate results at a relatively small computational cost. The model is benchmarked against three exemplar case studies taken from the literature.
Highlights
Multistable structures may play an important role in future engineering designs due to their potential for reconfiguration between different states
This paper focuses on the latter kind, which are either bespoke to specific problems, and of limited applicability, or more general which often necessitate a compromise between computational efficiency and accuracy
Case-Study 1: Snap-Through Load The computational efficiency of the proposed model is evaluated in terms of the number of degrees of freedom, or Lagrangian parameters, required to obtain converged results
Summary
Multistable structures may play an important role in future engineering designs due to their potential for reconfiguration between different states. A large variety of morphing concepts have been developed These often utilise stiffness-tailored nonlinear structures to provide shape changing features. Eckstein et al [11] extended Hyer’s work to describe the multimode morphing of thermally-actuated initially cylindrical shells, in which temperature-dependent material properties were modelled. In all of these works, simple shape functions were employed to keep computational cost to a minimum, with the limiting assumption that transverse displacements could only capture constant curvatures, whereas in reality, satisfaction of zero forces at free boundaries creates significant nonlinear variation of curvatures into the interior of the structure [12, 7]. The high order of the set of complete polynomials implied a large computational cost, a loss of efficiency of the method
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