Neutrally stable double-curved shells by inflection point propagation

Abstract

Elastic structures that can deflect without springback, known as neutrally stable structures, form a remarkable group within their field, since they require the energetic state to remain unchanged during elastic deformation. Several examples in the literature obtain this state of neutral stability by the application of pre-stress, either as a result of manufacturing processes or the application of imposed boundary conditions. In this paper, we present a new class of neutrally stable structure that exhibits neutral stability as part of a continuous deformation process, while also allowing a stress-free configuration to exist. The transition of a double-curved compliant shell from its stress-free stable equilibrium towards its second stable equilibrium, through a range of neutrally stable equilibrium configurations forms the basis of this investigation. To design this neutrally stable shell, an optimization is employed to obtain an ideal set of variables that defines a varying thickness profile. Numerical analysis of the resulting optimized shell structure predicts a substantial region of near-constant energy and associated near-zero loads within this unique deformation mode. Additively manufactured prototypes demonstrate the validity of the modeled results by featuring a continuous equilibrium within the range of motion. These results lay the foundation for compliant beam elements with a neutrally stable bending degree of freedom.