Nonlinear thermal stability of plates with auxetic FG-CNTRC core and FG-CNTRC face sheets considering temperature-dependent material properties

Abstract

This study examines the nonlinear thermal stability of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) sandwich plates incorporating an auxetic core and resting on a two-parameter Pasternak elastic foundation using an analytical framework. The material properties of the FG-CNTRC constituents are assumed to be temperature-dependent, and the structural response is evaluated under a uniform temperature rise. The auxetic core is characterized through a homogenization scheme in which its effective properties are derived from FG-CNTRC cell walls with carbon nanotubes aligned along the re-entrant members. This modeling strategy enables the directional reinforcement effect of CNTs to be consistently transferred to the equivalent orthotropic behavior of the auxetic core. A higher-order shear deformation theory combined with von Kármán geometric nonlinearity is employed to describe the kinematics of the sandwich plates. By applying an energy-based formulation, the nonlinear governing equations are expressed and subsequently solved by Ritz method with admissible trigonometric functions. Closed-form expressions for the critical thermal buckling temperature are obtained, and the nonlinear postbuckling equilibrium paths are determined. The comprehensive investigations are conducted to assess the influences of CNT volume fraction, grading patterns, auxetic geometric parameters, foundation, and temperature-dependent effects on both the nonlinear stability responses.