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Optimization of Patch Shape for FGM Plates Using The NSGA-II Algorithm Cover

Optimization of Patch Shape for FGM Plates Using The NSGA-II Algorithm

Acta Mechanica et Automatica
Volume 19 (2025): Issue 4 (December 2025)
By: Soufiane ABBAS,  Mohamed Ikhlef CHAOUCH,  Hinde LAGHFIRI and  Mohamed BENGUEDIAB  
Open Access
|Dec 2025

Figures & Tables

Fig. 1.

Geometry of a functionally graded material plate
Geometry of a functionally graded material plate

Fig. 3.

Distribution of stress components at the tip of a crack
Distribution of stress components at the tip of a crack

Fig. 4.

The Three Fundamental Modes of Crack Tip Deformation: (a) Mode I - Opening; (b) Mode II - Sliding; (c) Mode III - Tearing
The Three Fundamental Modes of Crack Tip Deformation: (a) Mode I - Opening; (b) Mode II - Sliding; (c) Mode III - Tearing

Fig. 2.

Illustration of a cracked plate with width w and crack length 2a
Illustration of a cracked plate with width w and crack length 2a

Fig. 5.

The material gradient plate (FGM)
The material gradient plate (FGM)

Fig. 6.

Boundary conditions imposed on the structure
Boundary conditions imposed on the structure

Fig. 7.

Comparison of Numerical and Analytical Stress Intensity Factors (K1) at Different Applied Stress Levels
Comparison of Numerical and Analytical Stress Intensity Factors (K1) at Different Applied Stress Levels

Fig. 8.

FGM Plate Reinforced with Carbon Fiber-Reinforced Polymer (CFRP) Patches under Tensile Loading with Ceramic-Metal Gradient Layers and Patch Optimization Paths
FGM Plate Reinforced with Carbon Fiber-Reinforced Polymer (CFRP) Patches under Tensile Loading with Ceramic-Metal Gradient Layers and Patch Optimization Paths

Fig. 9.

Optimization Flowchart Using NSGA-II and Pareto Front Method to Identify Optimal Patch Geometries through Abaqus Simulations
Optimization Flowchart Using NSGA-II and Pareto Front Method to Identify Optimal Patch Geometries through Abaqus Simulations

Fig. 10.

Flowchart of the NSGA-II Multi-Objective Optimization Process for Patch Geometry and Stress Intensity Factor Minimization
Flowchart of the NSGA-II Multi-Objective Optimization Process for Patch Geometry and Stress Intensity Factor Minimization

Fig. 11.

Influence of Parameters ηc and ηm on Volume Reduction (V) as a Function of (k1) with NSGA-II Pareto Front Optimization.
Influence of Parameters ηc and ηm on Volume Reduction (V) as a Function of (k1) with NSGA-II Pareto Front Optimization.

Fig. 12.

Evolution of the Pareto Front with NSGA-II Optimization for Different Population Sizes
Evolution of the Pareto Front with NSGA-II Optimization for Different Population Sizes

Fig. 13.

Convergence of the NSGA-II Algorithm with Respect to the Number of Generations
Convergence of the NSGA-II Algorithm with Respect to the Number of Generations

Fig. 14.

Patch Dashboard for Multi-Objective Optimization of Crack Repair: Trade-offs Between Volume and Stress Intensity Factor (K1); a) 2a=10 mm, b) 2a=18mm, c) 2a=26mm
Patch Dashboard for Multi-Objective Optimization of Crack Repair: Trade-offs Between Volume and Stress Intensity Factor (K1); a) 2a=10 mm, b) 2a=18mm, c) 2a=26mm

Mechanical properties of composite patch and adhesive

Composite patchAdhesive
E1(GPa)1352.1547
E2(GPa)9
E3(GPa)9
G12(GPa)5
G13(GPa)5
G23(GPa)8
ν120.30.34
ν130.3
V230.02

Material properties of metal and ceramic

MaterialYoung's modulus (GPa)Poisson's ratioMass density (kg/m3)
Aluminum (Al)700.32702
Zirconia (ZrO2)1510.33000
DOI: https://doi.org/10.2478/ama-2025-0087 | Journal eISSN: 2300-5319 | Journal ISSN: 1898-4088
Journal RSS Feed
Language: English
Page range: 779 - 789
Submitted on: Jan 28, 2025
|
Accepted on: Oct 19, 2025
|
Published on: Dec 31, 2025
Published by: Bialystok University of Technology
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year
Keywords:
FGM,
Evolutionary algorithm,
NSGA-II,
Pareto Front Analysis,
Crack Propagation
Related subjects:
Engineering,
Electrical engineering,
Electronics,
Mechanical engineering,
Mechanics,
Bioengineering and biomedical engineering,
Biomechanics,
Civil engineering,
Environmental engineering

© 2025 Soufiane ABBAS, Mohamed Ikhlef CHAOUCH, Hinde LAGHFIRI, Mohamed BENGUEDIAB, published by Bialystok University of Technology
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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