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ARTICLE

Bending Analysis of Functionally Graded Material and Cracked Homogeneous Thin Plates Using Meshfree Numerical Manifold Method

Shouyang Huang^*, Hong Zheng, Xuguang Yu, Ziheng Li, Zhiwei Pan

Key Laboratory of Urban Security and Disaster Engineering, Ministry of Education, Beijing University of Technology, Beijing, China

* Corresponding Author: Shouyang Huang. Email:

(This article belongs to the Special Issue: Advances in Numerical Modeling of Composite Structures and Repairs)

Computer Modeling in Engineering & Sciences 2026, 146(3), 11 https://doi.org/10.32604/cmes.2026.075929

Received 11 November 2025; Accepted 22 January 2026; Issue published 30 March 2026

Abstract

Functionally graded material (FGM) plates are widely used in various engineering structures owing to their tailor-made mechanical properties, whereas cracked homogeneous plates constitute a canonical setting in fracture mechanics analysis. These two classes of problems respectively embody material non-uniformity and geometric discontinuity, thereby imposing more stringent requirements on numerical methods in terms of high-order field continuity and accurate defect representation. Based on the classical Kirchhoff–Love plate theory, a numerical manifold method (MLS-NMM) incorporating moving least squares (MLS) interpolation is developed for bending analysis of FGM plates and fracture simulation of homogeneous plates with defects. The method constructs an H2-regular approximation with high-order continuous weighting functions and, combined with the separation of mathematical and physical covers, establishes a unified framework that accurately handles material gradients and cracks without mesh reconstruction. For the crack tip, a singular physical cover incorporating the Williams asymptotic field is introduced to achieve local enrichment, enabling the natural capture of displacement discontinuity and stress singularity. Stress intensity factors are extracted using the interaction integral method, and the dimensionless J-integral shows a maximum relative error below 1.2% compared with the reference solution. Numerical results indicate that MLS-NMM exhibits excellent convergence performance: using 676 mathematical nodes, the nondimensional central deflection of both FGM and homogeneous plates agrees with reference solutions with a maximum relative error below 0.81%, and no shear locking occurs. A systematic analysis reveals that for a simply supported on all four edges (SSSS)FGM square plate with a/h=10, the nondimensional central deflection increases by 212% as the gradient index nrises from 0 to 5. For a homogeneous plate containing a central crack with c/a=0.6, the nondimensional central deflection increases by approximately 46% compared with the intact plate. Under weak boundary constraints (e.g., SFSF), the deformation is markedly amplified, with the deflection reaching more than three times that under strong constraints (SCSC). The proposed method provides an efficient, reconstruction-free numerical tool for high-accuracy bending and fracture analyses of FGM and cracked thin-plate structures.

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