Assessment of homogenization solutions for dynamic problems of periodic plate structures

Composite periodic plates with in-plane microstructures present significant challenges for numerical simulation due to their intricate microstructures. In this paper, the effective engineering elastic constants were derived based on the asymptotic homogenization method (AHM) for the dynamic problem of periodic plate structures. Moreover, the poor accuracy of out-of-plane deformations achieved by the AHM was revealed and explained in mechanics for plates with only in-plane periodicity. Then, a multiscale plate homogenization method (PHM) was presented based on the first-order shear deformation theory (FSDT) and the equivalent principle of internal energy at macroscopic and microscopic scales. The effective engineering elastic constants were, respectively, derived in accordance with the obtained in-plane and out-of-plane effective stiffness solved by the PHM. Numerical simulation results show that the AHM agrees well with the in-plane deformations, but with poor calculation accuracy for out-of-plane deformations for periodic plates with only in-plane periodicity. Besides, the proposed PHM can well predict both the in-plane and out-of-plane deformations of the periodic plate structures. In addition, the calculation accuracy of the equivalent engineering elastic constants obtained by those with the in-plane and out-of-plane equivalent stiffness performs differently, and a suitable material homogenization analysis method depends on the main deformation characteristics of periodic plates.