Ritz-Based Analysis of Functionally Graded Sandwich Plates with Reentrant Auxetic Core

Abstract

This study investigates the free vibration, buckling response, and optimal design of functionally graded sandwich plates with a reentrant auxetic core. A Ritz-based formulation is utilized, combining global in-plane admissible functions with a spectral through-thickness representation. The auxetic core is modeled as a homogenized orthotropic continuum. The results show that natural frequency monotonically decreases with the increase of the relative density, indicating the dominance of the mass effects on the dynamic response. On the other hand, the critical buckling load increases with density, confirming the stiffness-dominated nature of the stability behavior. The effect of material gradation is strongly dependent on the chosen law: power-law and exponential distributions have a great impact on both responses, while the sigmoid distribution gives almost invariant results, showing more stable structural behavior. The geometric parameters of the auxetic core lead to significant nonlinear effects, with the strut length exhibiting a non-monotonic behavior and the reentrant angle always improving the buckling resistance. The optimization results show a clear tradeoff between mass, frequency, and buckling performance, with feasible solutions forming a narrow Pareto region. The best compromise is found at an intermediate density level ([Formula: see text]) with a power-law distribution.