FFT-based homogenisation for Thin Plate Structures

This paper introduces an FFT-based homogenisation approach designed to mitigate the computational demands associated with conventional numerical methods for thin plate structures. The periodic Lippman-Schwinger is proposed equation as an approach to solve the governing equation of both Classical and First-order plate models in cell problems, achieving an explicit solution by Green's function obtained from the Fourier space. The paper provides comprehensive details on the developed method, its algorithmic implementation, and its potential application demonstrated through two case studies focused on complex plate structures. The findings reveal a significant alignment with the results derived from Finite Element Method (FEM), with an added advantage of marked time efficiency observed within the FFT-based approach.