Analytical Modeling of Multi-sectioned Bi-stable Composites: Stiffness Variability and Embeddability

Abstract

Multi-stable composite laminates have been widely investigated for morphing applications due to distinct geometrical characteristics about each stable configuration. Recently, a mechanism for realizing on-demand stiffness adaptation in compliant structures has been proposed exploiting the stiffness variation from switching between the stable states of embedded bi-stable laminates. This allows for reducing the coupling between loading and morphing deformation modes, broadening the overall design space for morphing structures. However, the design of such embeddable laminates requires the study of multiple lamination domains to allow embedding within larger compliant structures. This process is currently done by computationally expensive simulations. We present an analytical model to predict the stable shapes and structural characteristics of multi-section, multi-stable composite laminates subject to two clamped boundary conditions. The analysis is conducted employing the Rayleigh-Ritz method using polynomial approximations of the displacement fields. The structural characteristics are predicted while constraining the laminate edges, thus extending previous models designed to account mainly for free edge boundary conditions. Our model is subsequently applied to explore the design space for characterizing the stability and variable stiffness properties of two different classes of bi-stable laminates. The presented model allows for the efficient design of multi-stable laminates embeddable within compliant structures.