Self‐Consistent Clustering Analysis for Homogenisation of Heterogeneous Plates

ABSTRACT This work introduces a reduced‐order model (ROM) for plate structures with periodic microstructures by coupling the self‐consistent clustering analysis (SCA) method with the Lippmann‐Schwinger equation, thereby enabling rapid multi‐scale homogenisation of heterogeneous plates. For the first time, a plate‐specific SCA scheme is derived featuring two key components: (i) an offline‐online strategy that combines Green's functions with k ‐means data compression, and (ii) an online self‐consistent update that exploits the weak sensitivity of the reference medium. The framework handles both linear and non‐linear problems in classical plate theory (CPT) and first‐order shear deformation theory, and its performance is verified on linear isotropic perforated plates and woven composites, as well as on non‐linear elasto‐plastic perforated plates and woven composites with damage. Across all cases, the proposed model matches the accuracy of fast Fourier transform (FFT)‐based direct numerical simulation (DNS) while reducing computational cost by over an order of magnitude. Furthermore, the potential of dynamic adaptive clustering to balance improved computational accuracy with associated increased computational cost is discussed.