Nonlocal strain gradient analysis of honeycomb sandwich nanoscale plates.

• Size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. • The proposed approach utilizes a nonlocal strain-gradient isogeometric analysis which incorporates the effects of both nonlocality and strain gradient. • The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb and two outer skin layers reinforced with graphene nanoplatelets. • The length scale parameters can high-efficiently predict size effects. • Some novel benchmark numerical results are illustrated and introduced. Honeycomb structures, which are known for being lightweight and stiff, are still being researched and developed. They have been used in a wide range of industries, but their full potential has not yet been realized. In this study, a novel computational approach for exploring the size-dependent behaviors of auxetic honeycomb sandwich nanoplates is developed. The proposed approach employs a nonlocal strain-gradient isogeometric analysis integrating the influences of nonlocality and strain gradient into the nanoplate structures. The sandwich nanoplate consists of a core layer featuring an auxetic honeycomb with a negative Poisson's ratio, complemented by two outer skin layers reinforced with graphene nanoplatelets (GNPs). This configuration not only achieves exceptional lightweight characteristics through the utilization of auxetic honeycomb cells but also enhances structural stiffness by incorporating GNPs into the skin layers. The material properties of the core layer are determined using cellular cell formulas, while the reinforcement of the two outer skin layers with GNPs is calculated using the modified Halpin-Tsai model. Numerous numerical examples are conducted to investigate the influence of various parameters on the frequencies of the auxetic honeycomb sandwich nanoplates. Notably, the geometrical dimensions of the auxetic honeycomb cells and the nonlocal and length scale parameters emerge as significant influencers on the results. As the first analysis of honeycomb structures at small dimensions, our findings stand as valuable benchmarks for future analyses. [ABSTRACT FROM AUTHOR]