Nonlinear Static and Dynamic Stability Analysis of Graphene Origami-Enabled Auxetic Metamaterial Plates with Geometric Imperfections

Nonlinear static and dynamic stability analysis of graphene origami (GOri)-enabled auxetic metamaterial plates with geometric imperfections is presented. The Poisson’s ratio, Young’s modulus, density, and coefficient of thermal expansion of GOri-enabled auxetic metamaterial (GOEAM) are obtained by genetic programming-assisted micromechanical models. Taking into account the effect of thermal environment, the control equation of GOEAM plates with geometric imperfections is established based on the first-order shear deformation theory and Hamilton’s principle. A nonautonomous system of nonlinear ordinary differential equations with parametric excitation is obtained by the Galerkin method. The critical buckling load and instability region are determined by the eigenvalue of Jacobian matrix and Bolotin’s approach. The results indicate that increasing the scale coefficient of imperfections and weight fraction of GOri will enhance the excitation frequency and critical buckling load of the structure, while increasing the temperature and degree of GOri folding will decrease the stability of the structure. Meanwhile, the presence of imperfections can lead to significant deformation and displacement of the structure subjected to surface internal forces.