Small scale analysis of porosity-dependent functionally graded triply periodic minimal surface nanoplates using nonlocal strain gradient theory.

• Small scale analysis of functionally graded triply periodic minimal surface (FG-TPMS) nanoplates. • The generalized weak form formulation for the FG-TPMS nanoplate is proposed. • A fitting technique based on a two-phase piece-wise function for porous structures of TPMS. • The length scale parameters can high-efficiently predict size effects. • Novel benchmark numerical results are illustrated and introduced. In recent years, the triply periodic minimal surface (TPMS) has emerged as a remarkable solution for constructing structures, drawing inspiration from natural architectures. TPMS offers several outstanding features, including porous architectures with high interconnectivity, smooth surfaces and the ability to achieve mathematically controllable geometry features. However, it is evident that the current research has not fully harnessed the extensive potential and benefits of TPMS structures. In this paper, a groundbreaking approach for analyzing functionally graded triply periodic minimal surface (FG-TPMS) nanoplate, which is utilized a novel nonlocal strain gradient isogeometric analysis, is provided. Three patterns of the FG-TPMS nanoplate, namely Primitive (P), Gyroid (G) and I-gragh and Wrapped Package-graph (IWP), are utilized in this study. The primary focus is to investigate size dependent problems with two types of density distributions. The proposed model successfully incorporates both nonlocal effects and strain gradient effects into nanoplate structures. The paper demonstrates how the mechanisms responsible for both reducing and enhancing stiffness in the nanoplate can be understood by fine-tuning the nonlocal and strain gradient parameters. The findings of this study offer promising prospects for future design and optimization as they provide a robust approach to address the complex mechanical behavior observed in the FG-TPMS nanoplate. The proposed model not only captures the behavior accurately but also opens up new avenues for exploring the capabilities of FG-TPMS structures. [ABSTRACT FROM AUTHOR]