Nonlocal strain gradient isogeometric buckling analysis of variable-thickness bi-directionally functionally graded GPL-reinforced composite nanoplates with square and circular geometries

Abstract Driven by the demand for spatially tailored stiffness in aerospace nanostructures and nano-electromechanical systems, this study establishes a novel isogeometric analysis framework integrating nonlocal strain gradient theory (NSGT) and sinusoidal shear deformation theory to investigate the buckling behavior of variable-thickness bi-directionally functionally graded graphene platelet-reinforced composite nanoplates with square and circular geometries. The nanoplate thickness varies along both the length and width directions for square nanoplates, and along the radial direction for circular nanoplates. Meanwhile, the GPL volume fraction exhibits bi-directional gradation along the length and thickness directions for square nanoplates, and along the radial and thickness directions for circular nanoplates. Effective material properties are determined using the modified Halpin–Tsai micromechanical model. The governing equations, which incorporate both nonlocal softening and strain gradient hardening mechanisms, are discretized using non-uniform rational B-splines basis functions that inherently satisfy the higher-order continuity requirements imposed by NSGT. Following comprehensive validation against published benchmarks, extensive parametric studies demonstrate the effects of GPL distribution patterns, bidirectional gradient indexes, size-dependent parameters, thickness variation parameters, and boundary conditions on the critical buckling response.