Economical Computational Approach Using Finite Difference Method for Evaluating Equivalent Moduli of Composite Perforated Plates
摘要
An agile computational framework for investigating the elastic behavior of composite multi-circular-holed (MCH) plates under in-plane loading was presented by means of the integration of the displacement potential method (DPM) into the finite difference method (FDM) (denoted as DPM-FDM). This novel approach effectively overcomes the challenge of imposing boundary conditions which is an obstacle that often limits FDM’s applicability in solid mechanics, distinguishing it from other methods. Implementing stress and displacement boundary conditions, unlike traditional computational methods like the finite element method (FEM), has notably enhanced the accuracy of boundary conditions for field variables in the method presented. The employment of the DPM not only derives governing equations and boundary conditions from a single scalar potential function, but also substantially reduces computational complexity. This advantage becomes particularly pronounced in scenarios involving structural discontinuities, as explored in this study focusing on perforated plates. To demonstrate the efficacy and credibility of the FDM developed, a comprehensive comparative analysis was conducted to determine stress displacement fields in symmetric cross-ply perforated plates. The results were benchmarked against the finite element solutions. Finally, utilizing an economically viable DPM-FDM and a homogenization approach, equivalent moduli were extracted for symmetric cross-ply MCH plates subjected to uniform in-plane biaxial loading, as well as uniform shear loading, providing designers with practical property data for rapid structural analysis. These advances extend the applicability of FDM-DPM to complex perforated composites and offer a significant scientific stride in modeling and analysis of composite MCH plate design.