A multiscale co-rotational method for geometrically nonlinear shape morphing of 2D fluid actuated cellular structures

Abstract

This work investigates geometrically nonlinear shape morphing behaviors of the adaptive bio-inspired fluid actuated cellular structures. An efficient multiscale co-rotational method based on the multiscale finite element framework is proposed for the geometrically nonlinear analysis of the fluidic cellular structures composed of periodical microscopic fluid inclusions. In this method, the multiscale base functions are firstly constructed to establish the relationship between the small-scale fluctuations of the microstructures and the macroscopic deformation on the coarse scale mesh. And then the co-rotational formulation is integrated to the multiscale method to decompose the geometrically nonlinear motion of the coarse-grid element into rigid-body motion and pure deformational displacements. With these formulations, the large displacement-small strain nonlinear problems of the fluid actuated cellular structures can be resolved on the multiscale co-rotational coarse-grid elements with little work. The numerical results indicate that the present multiscale algorithm is simple, accurate and highly efficient and can provide an alternative to model the fluid actuated actuators for morphing wings.