This repository contains the implementation of a Graph Neural Network (GNN) framework for predicting buckling behavior of thin-walled structures with and without 1D stiffeners, as presented in the Master's thesis by Ömer Kurt at Middle East Technical University.
This research develops a novel approach to structural analysis using Graph Neural Networks as surrogate models, specifically focusing on predicting buckling behavior of thin-walled structures. The framework addresses computational challenges in traditional finite element analysis by providing an efficient machine learning-based alternative that maintains engineering-grade accuracy while achieving computational speeds approximately two orders of magnitude faster than conventional methods.
- Comprehensive Data Generation Pipeline: Automated generation of diverse structural geometries using Bezier curves
- Advanced Graph Representation: Novel approach incorporating super nodes and virtual edges for enhanced information flow
- Rotational/Translational Invariance: PCA-based coordinate transformation ensuring generalization across different orientations
- Dual Architecture Support: Implementation of both GraphSAGE and CustomGNN architectures
- Multi-scale Analysis: Support for both non-stiffened and stiffened structures
- Efficient Buckling Prediction: Accurate prediction of critical buckling eigenvalues
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Data Generation Framework
- Bezier curve-based shape generation system creating diverse yet physically meaningful geometries
- Systematic load case generation with comprehensive coverage of realistic loading scenarios
- Advanced dataset balancing methodology addressing inherent biases in structural response distributions
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Architectural Innovations
- Novel coordinate transformation approach based on principal component analysis
- Enhanced information flow mechanisms through virtual edges and super node architecture
- Specialized pooling strategies optimized for global property prediction
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Practical Applications
- Demonstrated effectiveness in buckling behavior prediction
- Significant computational efficiency gains (100× faster than traditional FEA)
- Framework for rapid stiffener layout optimization
- Validation MAPE: 5.5%
- Test MAPE: 6.73%
- Validation MAPE: 12.5%
- Test MAPE: 17.64%
- Shape dimensions: 700-1000mm
- Material: Aluminum alloy (E=76 GPa, ν=0.3)
- Analysis types: Linear static and linear buckling
- Dataset sizes: 40,000 (non-stiffened) and 80,000 (stiffened) cases
- Base architecture: GraphSAGE with 6 layers
- Hidden dimension: 512
- Enhanced features: Super node for global information aggregation
- Pooling: Mean pooling for buckling prediction
- GPUs: NVIDIA Tesla V100 and P100 (16GB VRAM)
- Batch size: 16 (memory-constrained)
- Training time: ~10 hours for base dataset
- Python 3.8+
- PyTorch 1.10+
- PyTorch Geometric
- NumPy, SciPy, scikit-learn
- MSC Nastran (for FEA validation)
- Currently limited to 2D thin-walled structures
- Linear analysis only (no post-buckling behavior)
- Isotropic materials only
- Future extensions could include:
- 3 D structures and complex assemblies
- Non-linear analysis capabilities
- Composite materials
If you use this work in your research, please cite:
@mastersthesis{kurt2025graph,
title={Graph Neural Networks as Surrogate Models for Structural Analysis: A Study on Buckling Behavior},
author={Kurt, {"O}mer},
year={2025},
school={Middle East Technical University (Turkey)}
}
The full thesis is available at: https://open.metu.edu.tr/handle/11511/113521
This research was conducted at Middle East Technical University and Turkish Aerospace Industries under the supervision of Prof. Dr. Ulaş Yaman. Computational resources were provided by TRUBA (Turkish National e-Infrastructure).