Stress and displacement analysis of thick sandwich plates with deformable auxetic cores using an enhanced third order global-local theory

In the present article, a high-order global-local theory with three-dimensional elasticity corrections is employed to trace the local and instantaneous variations of lateral deflections and stress components of sandwich plates with auxetic (negative Poisson ratio) cores under static loads. The governing equations are extracted based on Hamilton’s principle. The main novelties of the present research in comparison to the available literature are the presenting a higher-order global-local plate theory with equilibrium-based 3D-elasticity corrections, incorporation of the transverse flexibility of the core (a fact that is crucial when studying behaviors of thick or soft core sandwich plates) and investigation of the negative Poisson ratio (auxeticity) effects of the core material on the static (stress and displacment) responses. All these items are accomplished here, for the first time. Since the transverse shear stresses are extracted based on the 3D elasticity theory, in contract the traditional constitutive-based theories, the interlaminar continuity condition of the transverse shear stresses is met. The verification results show that the presented finite element formulation leads to highly accurate results, even for thick or soft core sandwich plates. Results reveal that auxeticity of the core material decreases the global and relative stresses and lateral deflections of the face sheets.