A numerical Bézier extraction method is proposed for nanoplates with sophisticated geometries reinforced by lightweight, functionally graded materials, providing a tool for practical engineering design. The approach combines a quasi-3D formulation with the modified strain-gradient theory to evaluate size-dependent transient vibration and buckling behaviors in porous multi-patch microplates. A new hybrid formulation of normal and shear functions is introduced in the quasi-3D theory to more accurately represent displacements through the plate thickness. This approach is employed to satisfy the higher-order \(C^{2}\) -continuity requirement, enabling the solution of the modified strain-gradient theory (MSGT). Using the rule of mixtures and the material length-scale parameters, the effective properties are evaluated as functions of the gradient index and three porosity distributions. Using the principle of virtual work, the governing equations for both classical and non-classical motions, including natural frequencies and mechanical buckling behavior, are formulated. The proposed method demonstrates excellent accuracy for a wide range of multi-patch microplates, from simple to complex geometries. Detailed numerical examples are presented to examine the effects of stretching strain, size dependency, porosity distributions, gradient index, and boundary conditions on the dynamic, transient vibration, and buckling responses of porous microplates. To conclude, the consideration of size-dependent effects is crucial for accurately capturing the natural frequencies and buckling behavior of microplates at the micron scale. The role of porosity distributions in transient vibration and buckling is assessed, providing important insights for practical engineering design and lightweight structures.
