Thermo-mechanical postbuckling analysis of sandwich cylindrical shells with functionally graded auxetic GRMMC core surrounded by an elastic medium

In this paper, modeling and analysis of postbuckling of sandwich cylindrical shells surrounded by an elastic medium are presented. The sandwich cylindrical shells consist of two metal face sheets and auxetic graphene-reinforced metal matrix composite (GRMMC) core with in-plane negative Poisson’s ratio (NPR). Two cases of the compressive postbuckling of sandwich cylindrical shells under axial compression in thermal environments and the thermal postbuckling of sandwich cylindrical shells caused by a uniform temperature rise are considered. Each ply of auxetic GRMMC core possesses in-plane NPR and can have different graphene volume fraction to achieve a piece-wise functionally graded (FG) distribution through the thickness domain of the core. The thermo-mechanical properties of both metal face sheets and the GRMMC core are temperature dependent. The governing equations are formulated based on the Reddy’s third order shear deformation shell theory coupled with von Kármán kinematic nonlinearity. The shell-foundation interaction and the thermal effects are considered in the modeling. Applying a singular perturbation technique in conjunction with a two-step perturbation approach, we obtain the postbuckling solutions for perfect and imperfect sandwich cylindrical shells. The effects of the FG pattern, the face sheet-to-core-to-face sheet thickness ratio, and the foundation stiffness on the postbuckling behaviors of sandwich cylindrical shells with auxetic GRMMC core are studied in detail.