Homogenization Model for Multistable Honeycomb Metastructures with Beam-like Behavior

Abstract

Reduced order models facilitate initial design space investigations and enable assessing the benefits of compliant structures utilized for shape adaptability. This work presents a simple model to determine the flexural rigidity of a beam-like, multistable metastructure used as a spar in a hybrid spanwise morphing wing. The model considers the more complex metabeam as a homogeneous beam described by Euler-Bernoulli beam theory with an equivalent flexural rigidity. The analytical model's validity is established by comparing the obtained static and dynamic responses to finite element simulations. A closed-form expression of the flexural rigidity is then given, drawing from the multistable honeycomb's material properties and the metabeam’s geometry. The model's limitations are addressed by examining several specific cases of the metabeam’s morphed configurations and a more complex metabeam structure.