Buckling analysis of super-light composite cylinders with auxetic core and isotropic facing sheets with variable thickness: An analytical approach

An analytical method is presented to determine the axial buckling load of composite cylindrical shells with honeycomb core layer and nonuniform thickness using the first-order shear deformation theory, the nonlinear von Karman theory, and the Hooke law relations. The composite shell consists of two isotropic inner and outer layers with non-uniform thicknesses and one honeycomb core with constant thicknesses and adjustable Poisson's ratio. The equilibrium equations are a system of nonlinear differential equations with variable coefficients, and they are derived by employing the virtual work principle. The equilibrium equations have been solved analytically using the matched asymptotic expansion method of the perturbation technique. The stability equations extracted using the adjacent criterion include a system of linear homogenous equations with variable coefficients. By solving these equations, the buckling load is obtained analytically. A parametric study investigates the effects of different geometrical and mechanical parameters such as the honeycomb structure on the buckling load. The metamaterial honeycomb core layer has an adjustable Poisson's ratio, and the effect of negative/positive Poisson's ratio has been studied on the buckling behavior. The accuracy of the presented method is studied by comparing the results with the finite element method and some other references in special cases.