Morphing structures: non-linear composite shells with irregular planforms

Abstract

The concept of morphing structures refers to devices that exhibit large scale shape changes, whilst maintaining load bearing capability, in response to distinctive operating conditions. This behavior comes from combinations of non-linear material or kinematic responses. Here, we limit our interests to shell type structures made from low strain, elastic materials that exhibit highly nonlinear kinematic behavior. Often, but not necessarily, the response can be bistable. Models predicting the multistability of shells often present a compromise between computational efficiency and accuracy of results. Moreover, they deal mainly with regular domains, such as rectangular or elliptical planforms. Few studies have been done to investigate the performance and the possible advantages of exploiting multistable structures with more general domains. In the present work, the multistability of thin shallow composite shells with irregular domains is investigated. An accurate and computationally efficient energy-based model is developed, in which 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 using Legendre polynomials and the membrane problem is solved in isolation by combining compatibility conditions and equilibrium equations. The result is the total potential energy as a function of curvatures only. Stable shapes are recovered by minimizing the total energy with respect to curvature. The accurate evaluation of the membrane energy is a key step in order to accurately capture the bifurcation points. Here the membrane problem is solved using the Differential Quadrature Method (DQM), which provides accuracy at a relatively small computational cost. However, DQM is limited to rectangular domains. For this reason, blending functions are used to map the irregular physical domain into a regular computational domain. This approach allows multistable shells with arbitrary convex planforms to be described without affecting the computational efficiency and the accuracy of the proposed model.