This paper models the large periodic plate structure as Kirchhoff-Love plates and introduces a novel implementation of asymptotic homogenization (NIAH) to enable an efficient calculation of the structural stiffness. Compared to full finite element models, applying NIAH to a unit-cell model greatly reduces computational costs. This paper systematically presents the derivation and finite element formulation of asymptotic homogenization (AH), and the development of NIAH. Benchmark cases, including solid, thin-walled, multi-material plates, and a plate with octagonal holes, are used to validate the NIAH implementation. A series of representative fish cage designs are analyzed to investigate the influence of pontoon components, structural layouts, and material distribution on structural stiffness. To ensure the reliability of the calculations, the choice of unit-cell model and the sensitivity of the results to mesh density and unit-cell size are also discussed.