Buckling and free vibration analysis of sandwich plates with auxetic honeycomb core

Honeycomb sandwich structures, modeled as plates and shells, are widely used in modern technology, including aerospace, automotive, marine, and other engineering industries, due to their excellent strength-to-weight ratio. When designing components made of advanced composite materials, including metamaterials with a negative Poisson’s ratio, essential characteristics include strength, stiffness, low weight, and stability. It should be emphasized that in engineering practice, the assessment of structural stability is often more critical than evaluating stiffness or strength. In many cases, structural failure occurs due to instability phenomena such as buckling, when the applied load exceeds its critical value, or parametric resonance under dynamic excitation. This paper investigates the loads that cause buckling of a composite sandwich plate with a honeycomb auxetic core and functionally graded material (FGM) face sheets. The mathematical formulation is based on the refined first order shear deformation plate theory (FSDT). The solution algorithm includes several stages: determining the prebuckling state of the plate, calculating the critical load, and identifying stability and instability regions using the approach proposed by V. V. Bolotin. Various factors influencing the buckling behavior of the composite sandwich structure are analyzed and compared, including loading conditions, geometric parameters, and the thickness and width of the hexagonal honeycomb cells in the core. The obtained results are validated through comparison with available data in the literature.