FFT-based homogenisation for efficient concurrent multiscale modelling of thin plate structures

Abstract This paper presents a novel approach to concurrent multiscale analysis, where structures are formulated at both microscopic and macro levels for simulation purposes. The proposed method employs a plate model to formulate structures at both scales, and homogenisation is performed using the FFT-based approach, offering higher efficiency compared to conventional methods. Additionally, the macroscopic tangent operator of the microscopic model is derived through an algorithmically consistent process within the FFT-based framework, incorporating the application of Lippman–Schwinger equations as outlined in this work. The effectiveness of the proposed method is demonstrated through case studies in real simulations, revealing comparable results to traditional multiscale schemes in addressing multiscale thin plate structures. Importantly, the method significantly reduces computing time and memory usage, attributed to the efficiency of plate modelling and the FFT-based homogenisation strategy.