Static bending and baseline free-vibration assessment of Type-A functionally graded sandwich plates with a homogenized auxetic core

This paper examines the static bending response and the baseline free-vibration trends of Type-A functionally graded sandwich plates with Al/ZrO₂ face layers and a homogenized auxetic core. The numerical analysis is carried out within a linear small-strain framework by using a previously verified higher-order shear deformation assumed-strain quadrilateral element, employed here as a computational vehicle rather than as a new finite element development. The free-vibration sweep is restricted to the square simply supported baseline configuration used for literature comparison, whereas the static investigation is extended to four boundary conditions, several slenderness and aspect ratios, multiple gradation exponents, and two layer schemes. The results show that a stiff auxetic core reduces transverse deflection and the top-surface normal stress across all boundary conditions, but increases the monitored shear quantity at the selected edge probe, revealing a clear static stiffness–shear trade-off. A soft auxetic core, in contrast, increases all three monitored static response measures. The extended campaign further shows that increasing the slenderness ratio a / h strongly amplifies deflection, increasing the aspect ratio reduces all monitored static responses, and that the face-sheet gradation interacts with the auxetic core in a metric-dependent manner: more ceramic-dominant faces favor lower deflection and lower monitored shear, whereas more metal-dominant faces reduce the present normalized top-surface stress metric. For the monitored static metrics considered here, the 2–1–2 layer scheme performs less favorably than 1–2–1, particularly for the stiff auxetic core. In the baseline free-vibration sweep, negative core Poisson’s ratio is not uniformly beneficial: frequency gains are concentrated mainly in the stiff-core region and should be interpreted as baseline modal trends rather than as an independently re-benchmarked validation set. Because the core is represented by equivalent isotropic properties, the results are best interpreted as structural-level response maps within the investigated linearized parameter space rather than as topology-specific design rules.