Morphing shell structures: A refined, computationally-efficient solution of the governing equations

Morphing shells are nonlinear structures with 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 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 an accurate and computationally efficient energy-based method. The membrane and the bending components of the total strain energy are decoupled 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. The result is the total strain energy as function of curvatures only. The minima of the energy with respect to the curvatures 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 accuracy of results at a relatively small computational cost.