Nonlinear bending and buckling analysis of 3D-printed meta-sandwich curved beam with auxetic honeycomb core

Abstract

The present study investigates the static responses of a 3D-printed polymeric meta-sandwich curved beam with an auxetic honeycomb core, including buckling and nonlinear bending behavior. After extracting the mechanical properties of the core material, the nonlinear governing equations for the curved beam under two types of loading, namely uniform transverse and axial mechanical loads, are derived based on the first-order shear deformation theory and von-Kármán nonlinearity. After examining the convergence of the static responses and validating them by using the Ritz method, the influence of various geometrical parameters of the 3D-printed meta-sandwich structure on the results of buckling and nonlinear bending behavior as well as their optimization using the response surface methodology (RSM) are studied. The results indicate that by increasing the thickness-to-length ratio of the inclined wall, the critical load of the auxetic sandwich beam is enhanced due to improved stiffness, and its lateral displacement declines. The amount of buckling load increase from m = 0.005 to m = 0.1 is 1.92% in the clamped-clamped boundary conditions, 1.56% in the clamped-simply supported conditions, and 1.2% in the simply supported-simply supported edge conditions. Therefore, by selecting appropriate geometrical parameters for the core cells, the occurrence of instability can be delayed, leading to enhanced buckling resistance of the structure. Furthermore, optimizing the results by using the RSM showed that the highest critical load value and the lowest transverse deflection value of the meta-sandwich curved beam are obtained when θc = 15, n = 1, m = 0.1, 2θ0= 30, b = 0.07, λ= 1.1, h/h2= 1.2, and the edge conditions are of the clamped-clamped type.