Thermally induced multistable configurations of variable stiffness composite plates: Semi-analytical and finite element investigation

Multistable structures used in morphing applications are conventionally achieved by using unsymmetric laminates with straight fibers. An ideal morphing system always calls for a structure with highly anisotropic internal architecture. With the advancement of fiber placement technology, it is possible to manufacture fibers even with curvilinear paths or so-called variable stiffness (VS) composites. The aim of this study is to explore the bistable shapes generated by changing various angle parameters that define a VS composite for elucidating novel morphing structures. A semi-analytical model based on the Rayleigh-Ritz method was developed to investigate the thermally induced multistable behavior particularly taking into account the curvilinear paths of VS composites. This approach provides a computationally efficient means to determine all the stable solutions with reasonable accuracy. The proposed methodology requires the definition of appropriate shape functions for the out-of-plane displacement and strain field. This is used to: (i) identify the multiple potential solutions and (ii) to perform the subsequent stability assessment of the solutions obtained. To check the accuracy and robustness of the proposed method, the results for different cases are compared with a nonlinear finite element analysis. A parametric study is further conducted to analyze the effect of changing fiber orientation on the multistable shapes. A rich design space of VS composite is demonstrated with multiple bistable shapes having different values of out-of-plane displacements and curvatures.