An efficient semi-analytical framework to tailor snap-through loads in bistable variable stiffness laminates

Multistable laminates are potential candidates for adaptive structures due to the existence of multiple stable states. Commonly, such bistable shapes are generated from the cool-down process of the unsymmetric laminates from the curing temperature. In this work, we exploit unsymmetric variable stiffness laminates with curvilinear fiber paths to generate similar bistable shapes as unsymmetric cross-ply laminates, but with the possibility to tailor the snap-through loads. Snap-through is a complex phenomenon in that is difficult to characterize using simple analytical models. An accurate yet computationally efficient semi-analytical model is proposed to compute the snap-through forces of bistable variable stiffness (VS) laminates. The differential equations resulting from the compatibility and the in-plane equilibrium equations are solved with negligible numerical error using the Differential Quadrature Method (DQM). As a result, the in-plane stress resultants and the total potential energy is written in terms of curvatures. The out-of-plane displacements are expressed in the form of Legendre polynomials where the unknown coefficients of the displacement function are found using the Rayleigh-Ritz formulation. The calculated snap-through loads are then compared with the Finite Element (FE) results. A parametric study is conducted to explore the tailoring capabilities of VS laminates for snap-through loads.