Bending and vibration analyses of functionally graded auxetic doubly curved shells via dual mesh control domain model

Abstract

This paper presents a novel dual mesh control domain (DMCD) model for the static bending and free vibration analysis of functionally graded (FG) graphene origami (GOri)-enabled auxetic metamaterial (GOEAM) doubly curved shells within the framework of the first-order shear deformation theory and modified Sanders assumptions. The shell consists of multilayered GOEAMs where the GOri content varies across the shell thickness in a layer-wise manner, leading to graded variations in auxetic and other material properties. Genetic programming (GP)-assisted micromechanical models are employed to estimate the material properties, including Poisson’s ratio, Young’s modulus, coefficient of thermal expansion (CTE), and mass density of the GOEAM in each layer. Governing equations are derived by the principle of virtual work and numerically solved using the dual mesh control domain method (DMCDM). The accuracy and convergence of the DMCD model are first verified, followed by a systematic investigation of the effects of GOri content, folding degree, temperature, and length-to-thickness ratio on the bending deflection, normal stress and fundamental frequency of FG-GOEAM doubly curved shells. The numerical results provide valuable insights for designing FG-GOEAM doubly curve shells in aerospace engineering with tunable negative Poisson’s ratio and enhanced mechanical properties.