Nonlinear thermo-mechanical bending and stability analysis of CNT-reinforced auxetic sandwich beams using a peridynamic differential operator framework

This study investigates the nonlinear bending, thermal buckling, and post-buckling behavior of sandwich beams composed of carbon nanotube–reinforced composite (CNTRC) face sheets and a reentrant auxetic core. The mechanical response of the beam is modeled using the first-order shear deformation theory (FSDT) combined with von Kármán nonlinear strain–displacement relations. The governing nonlinear differential equations are derived using Hamilton’s principle and solved numerically through the Peridynamic Differential Operator (PDDO), a nonlocal mesh-free discretization technique. This work demonstrates the capability of the PDDO to efficiently solve nonlinear eigenvalue problems arising in thermal buckling analysis of sandwich beams. The material properties of the CNTRC face sheets are determined using micromechanical relations based on the rule of mixtures, while temperature-dependent properties are considered for both the face sheets and the core. The proposed formulation is validated through comparisons with existing analytical and numerical results available in the literature. A comprehensive parametric study is conducted to investigate the effects of face sheet thickness ratio, CNT volume fraction, and auxetic core geometric parameters on bending, buckling, and post-buckling responses. The results indicate that increasing the CNT volume fraction significantly enhances the critical buckling temperature, while variations in core geometry and face sheet thickness ratio strongly influence the nonlinear structural response.