<p>Existing studies on graphene platelet (GPL)-reinforced composite plates have mainly focused on through-thickness functional gradation, limiting their adaptability under multidirectional loading. This study develops a bidirectionally functionally graded GPL-reinforced composite plate, where the GPL content continuously varies along both in-plane (length or radial) and thickness directions following independent power-law distributions. An integrated isogeometric analysis framework based on the first-order shear deformation theory is developed to examine their free vibration and buckling behaviors. Effective properties are evaluated via a modified Halpin–Tsai model, and the NURBS-discretized governing equations are validated against benchmark results, demonstrating excellent accuracy. Comprehensive parametric studies investigate the effects of GPL weight fraction, distribution patterns, bidirectional gradient indexes, and length-to-thickness ratio on the structural responses of square and circular plates. Results show that the configuration concentrating GPLs near the top and bottom surfaces as well as the mid-span (for square plates) or intermediate radial regions (for circular plates) generally provides the most effective reinforcement configuration. Notably, while this specific configuration maintains its superiority status across the entire in-plane gradient (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$k_{x}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>x</mi> </msub> </math></EquationSource> </InlineEquation> or <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$k_{r}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>r</mi> </msub> </math></EquationSource> </InlineEquation>) range, its superiority diminishes at exceedingly large thickness gradient indexes <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$k_{z}$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>k</mi> <mi>z</mi> </msub> </math></EquationSource> </InlineEquation>. In such extreme scenarios, it no longer yields the highest natural frequency for either square or circular plates, nor does it provide the highest buckling resistance for circular plates, highlighting distinct multi-dimensional stiffness redistributions induced by the coupled gradient effects.</p>

Isogeometric analysis of bidirectionally functionally graded graphene platelet-reinforced composite plates: beyond unidirectional graphene reinforcement

期刊论文
发表日期：

2026年4月12日

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Ruhui Cheng,
Shijie Zheng

摘要

Existing studies on graphene platelet (GPL)-reinforced composite plates have mainly focused on through-thickness functional gradation, limiting their adaptability under multidirectional loading. This study develops a bidirectionally functionally graded GPL-reinforced composite plate, where the GPL content continuously varies along both in-plane (length or radial) and thickness directions following independent power-law distributions. An integrated isogeometric analysis framework based on the first-order shear deformation theory is developed to examine their free vibration and buckling behaviors. Effective properties are evaluated via a modified Halpin–Tsai model, and the NURBS-discretized governing equations are validated against benchmark results, demonstrating excellent accuracy. Comprehensive parametric studies investigate the effects of GPL weight fraction, distribution patterns, bidirectional gradient indexes, and length-to-thickness ratio on the structural responses of square and circular plates. Results show that the configuration concentrating GPLs near the top and bottom surfaces as well as the mid-span (for square plates) or intermediate radial regions (for circular plates) generally provides the most effective reinforcement configuration. Notably, while this specific configuration maintains its superiority status across the entire in-plane gradient ( $k_{x}$ $k_{x}$ or $k_{r}$ $k_{r}$ ) range, its superiority diminishes at exceedingly large thickness gradient indexes $k_{z}$ $k_{z}$ . In such extreme scenarios, it no longer yields the highest natural frequency for either square or circular plates, nor does it provide the highest buckling resistance for circular plates, highlighting distinct multi-dimensional stiffness redistributions induced by the coupled gradient effects.