Sub-cell-free weighted least-squares integration methods with and without stabilization terms for higher-order shear deformation analysis of isotropic plates

Abstract

ABSTRACT This paper presents a sub-cell-free weighted least-squares integration (SCF-WLSI) framework for higher-order shear deformation analysis of isotropic plates, formulated in two variants: un-stabilized (u-SCF-WLSI) and stabilized (s-SCF-WLSI). Advancing the estimation-based direct simulation on nodal networks (EDISONN) approach, the method evaluates the discrete weak form directly at nodes, eliminating background quadrature meshes and sub-cell partitions. Its foundation pairs a moving weighted least-squares gradient operator with a two-ring Hessian operator. To suppress spurious zero-energy modes from direct nodal integration, s-SCF-WLSI incorporates a parameter-free stabilization stiffness using the nodal polar moment of inertia as an intrinsic length scale, restoring C 1 variational consistency. Benchmark evaluations across static bending, free vibration, and buckling in thin and thick plates demonstrate optimal convergence for both variants. Crucially, the free vibration on centrally clustered nodal domains (e.g., circular plates) reveals a vital distinction: while u-SCF-WLSI achieves accurate frequency eigenvalues, local rank deficiency induces sharp, non-physical spikes in mode shapes; s-SCF-WLSI completely eliminates these eigenvector artifacts, recovering smooth, physically admissible mode shapes without degrading eigenvalue precision. Consequently, while u-SCF-WLSI offers maximum efficiency for well-resolved meshes, s-SCF-WLSI provides an indispensable, spurious-mode-free framework required when accurate mode shapes and robustness on non-uniform nodal distributions are needed.

The authors' abstract, as published at the source. Engineering Analysis with Boundary Elements, 2026 · DOI ↗