Buckling analysis of bio-inspired helicoidal functionally graded CNT-reinforced laminated nanoplates with antisymmetric angle-ply architecture

:This study presents a novel Galerkin-based analytical framework for the comprehensive investigation of the buckling behavior of advanced functionally graded (FG), antisymmetric angle-ply (AP), bio-inspired helicoidal (BiH) laminated composite nanoplates. To the best of our knowledge, this is the first analytical exploration of such hybrid nanoscale structures, integrating both material and geometrical gradation effects. The proposed model accounts for nanoscale reinforcement via randomly dispersed single-walled carbon nanotubes (SWCNTs) in conjunction with FG fibrous reinforcements, thereby enhancing both mechanical performance and multifunctionality. The governing stability equations are rigorously derived through the principle of virtual work, incorporating higher-order shear deformation theory (HSDT) and an advanced nonlocal strain gradient elasticity theory to capture essential small-scale effects and microstructural interactions. Three distinct helicoidal carbon nanotube (CNT) arrangements are considered: helicoidal-linear (HL), helicoidal-exponential (HE), and helicoidal-semicircular (HS), alongside four CNT distribution profiles: uniform distribution (UD), functionally graded X-type (FG-X), functionally graded O-type (FG-O), and functionally graded asymmetric (FG-A). The combined influence of these reinforcement schemes and helicoidal architectures is systematically examined to characterize their impact on the global buckling resistance of the nanoplates. A detailed parametric investigation is conducted to explore the effects of volume fraction, layer thickness ratio, gradient index, aspect ratio, and various boundary condition types. The findings provide deep insights into the synergistic interplay between reinforcement topology, material gradation, and scale-dependent behaviors, thus offering valuable guidelines for the optimal design and deployment of next-generation nanostructured composite systems in aerospace, biomedical, and structural applications.