Dynamic snap-through of bi-stable laminates with simply supported at four corners under impact loads

In this paper, nonlinear dynamic responses of bi-stable laminate being simply supported on four corner points, which is subjected to various impact loads, are analyzed from theoretical viewpoints. Consider a four layers asymmetric cross-ply bi-stable laminate composited by the carbon fiber reinforced resin matrix. A novel configuration function that satisfies the boundary condition is proposed to predict the equilibrium configuration. Then, employing the first order shear deformation theory, the von Kàrmàn strains and Hamilton principle, nonlinear dynamic equations of motion expressed by two curvatures are derived. To obtain the two stable configurations of the laminate, the inertia terms are ignored. With the aids of static equilibrium equation, the side length and curvature of the system are solved by using NLPSolve functions in the Maple software. The stable configurations are verified by comparing present results with those reported in available literatures. Consider the incremental load loading, the decreasing loading, the sinusoidal loading, the step loading, the triangular loading and periodic loading, the nonlinear dynamic response of the bi-stable laminate are discussed. The dynamic snap-through behavior, the intra-well oscillations and inter-wall oscillations are studied by numerical simulation in detail.