A High-Order Compact Finite Difference Decoupling Approach for Reissner-Mindlin Plate Bending

Abstract

This study presents a novel and computationally efficient framework for solving high-order Partial Differential Equations (PDEs), particularly polyharmonic equations, by systematically decomposing them into a sequence of coupled second-order problems. The core contribution lies in enhancing the classical decoupling strategies by introducing a Compact Finite Difference (CFD) scheme with improved numerical stability, accuracy, and flexibility. This method was previously applied to fourth-order differential equations in an earlier study. The current study extends the application of this method to sixth-order PDEs, particularly those arising in plate bending problems governed by the Reissner–Mindlin (R-M) theory. Specifically, a modified single-variable formulation proposed by the Bergan-Wang model was considered the study. The novelty of this approach lies in the streamlined reduction of polyharmonic operators using consistent Poisson-like solvers; a convergence-enhanced compact discretization applicable to various boundary conditions; and numerical benchmarking against recent Finite Element Methods (FEMs). Extensive simulations demonstrate the method's capability in computing accurate displacement and stress fields over different geometries and boundary types, suggesting its viability for complex engineering applications.