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Stress Field Prediction in Cantilevered Structures Using Convolutional Neural Networks
Zhenguo Nie, Haoliang Jiang, Levent Burak Kara
TL;DR
Structural analysis needs to become faster without sacrificing accuracy as generative design and topology optimization advance. This paper uses CNNs to predict von Mises stress fields for 2D linear elastic cantilevered structures from geometry, loads, and boundary conditions, comparing SCSNet with StressNet. StressNet produced lower prediction errors, including a 2.04% mean relative error on testing, while the approach remains scoped to the studied problem setting.
Problem
Generative design and topology optimization increase the demand for structural analysis that is both fast and accurate.
Method
CNN architectures predict von Mises stress fields from image-based geometry, external loads, and displacement boundary conditions for 2D linear elastic cantilevered structures.
Results
StressNet achieved higher accuracy than SCSNet, with a 2.04% mean relative stress error on testing.
Takeaways & Limitations
The results support deep learning as a potential alternative for accelerating stress analysis in structural design and topology optimization.
Takeaways & Limitations
Future work is needed to reduce the need for extensive coverage of input geometries, boundary conditions, and loads.
Abstract
from arXiv · showhide
The demand for fast and accurate structural analysis is becoming increasingly more prevalent with the advance of generative design and topology optimization technologies. As one step toward accelerating structural analysis, this work explores a deep learning based approach for predicting the stress fields in 2D linear elastic cantilevered structures subjected to external static loads at its free end using convolutional neural networks (CNN). Two different architectures are implemented that take as input the structure geometry, external loads, and displacement boundary conditions, and output the predicted von Mises stress field. The first is a single input channel network called SCSNet as the baseline architecture, and the second is the multi-channel input network called StressNet. Accuracy analysis shows that StressNet results in significantly lower prediction errors than SCSNet on three loss functions, with a mean relative error of 2.04% for testing. These results suggest that deep learning models may offer a promising alternative to classical methods in structural design and topology optimization. Code and dataset are available at https://github.com/zhenguonie/stress_net
1 INTRODUCTION
The paper frames fast, accurate stress analysis as increasingly important for generative design and proposes CNN-based prediction for 2D linear elastic structures. It compares single-channel SCSNet with multi-channel StressNet, which encodes geometry, loads, and boundary conditions separately.
- Fast structural analysis is increasingly important as generative design and topology optimization impose higher speed demands without sacrificing accuracy.
- The work explores replacing conventional run-time stress analysis with a data-driven system that generates solutions instantaneously.
- Prior approaches include neural regression, simplified feature-vector representations, finite-element acceleration, and convolutional networks for mechanics problems.
- SCSNet is a single-channel architecture that augments a geometry feature representation with loads, whereas StressNet uses five separate input channels.
- StressNet achieved a 2.04% mean relative stress error and significantly higher accuracy than SCSNet in the reported tests.
2 BACKGROUND and RELATED WORK
The background describes finite element analysis as the conventional route for computing deformation and stress, while highlighting its computational cost. It then motivates CNN and ResNet architectures as data-driven alternatives for image-based mechanics and structural design tasks.
- Finite element analysis decomposes a structure into elements and computes coupled deformations and stresses from boundary and load conditions.
- The formulation assumes linear isotropic materials and small deformations in a two-dimensional field.
- Elemental stiffness matrices are assembled into a global stiffness matrix to determine nodal displacements, which are then converted into stresses.
- The von Mises stress is computed from the normal stress components σx and σy and the shear stress τxy.
- Large stiffness matrices make finite element analysis computationally costly, creating an opportunity for faster inner-loop simulations in structural design and optimization.
- CNNs process array-based representations through learned filters and pooling, while ResNet adds shortcut connections that support dynamically selected effective depth.
- Deep-learning mechanics applications include structural analysis, materials modeling, computational-mechanics enhancement, topology optimization, and stress-field prediction.
3 METHOD
The method predicts von Mises stress fields for 2D cantilevered structures from geometry, loads, and displacement boundary conditions using CNNs. It compares single-channel SCSNet with multi-channel StressNet, using FEM-generated data and image-based representations.
- Problem formulation: The approach predicts stress fields for 2D cantilevered structures with linear isotropic materials from geometry, external loads, and displacement boundary conditions.The structures are modeled as plane-strain problems with static loads applied at the free end.
- Dataset representation: 120,960 FEM samples represent 32 × 24-element domains, with inputs and von Mises stress fields encoded as images.The dataset uses 4-node quadrilateral elements of size 1 × 1 mm.
- SCSNet: SCSNet uses a single-channel convolutional autoencoder that encodes geometry and load position before reconstructing the von Mises stress field.Its encoder-decoder architecture includes convolutional and max-pooling layers.
- StressNet: StressNet uses five input channels for geometry, load components, and displacement-boundary-condition components.Its downsampling-and-upsampling architecture incorporates five Squeeze-and-Excitation ResNet modules.
- StressNet: Squeeze-and-Excitation blocks dynamically recalibrate feature channels to improve the network’s representational capacity.They use global average pooling, fully connected layers, reshaping, and element-wise rescaling.
- Loss function and metrics: MSE, MAE, and mean relative error evaluate differences between predicted and ground-truth 32 × 24 stress fields.The image fields are reshaped into one-dimensional arrays of length 768, and mean relative error is expressed as a percentage with smoothing term ϵ = 0.01.
4 RESULTS AND DISCUSSIONS
StressNet achieved substantially higher prediction accuracy than SCSNet, while both architectures converged reliably. Increasing training data reduced error, and StressNet accurately reproduced stress fields and maximum von Mises stress.
- Accuracy and performance: 1.56 seconds for SCSNet and 10.4 seconds for StressNet were required to render 120,960 FEM samples, versus approximately ten hours for FEM computation.Both neural architectures were trained on an NVIDIA GeForce GTX 1080Ti GPU and converged reliably.
- Accuracy and performance: StressNet predictions evolved from sparse nonzero points at epoch 1 to visually indistinguishable stress fields by epoch 100.The figure compares ground truth with predictions at epochs 1, 10, 100, and 5000.
- Effect of training data size: Increasing training data from 20,000 to 100,000 gradually reduced both MSE and MAE, although predicted fields appeared similar across training sizes.Different color bars indicated that visually similar outputs remained numerically different.
- Prediction of maximum stress: R^2 = 0.99 was obtained for predicting the ground-truth maximum von Mises stress on testing data.The authors evaluate this prediction because maximum stress is relevant to failure prediction.
- Effect of hierarchical architecture: The intermediate architecture using StressNet’s multiple input channels but SCSNet’s structure showed no training-accuracy improvement over SCSNet.The authors associate higher accuracy with deeper hierarchical architecture, while noting that deepening should account for image resolution, training size, and data variability.
- Comparison of architectures: 10.40% was SCSNet’s mean relative error, with reduced training time and acceptable accuracy relative to StressNet.The authors describe StressNet as an alternative to classical FEM when sufficient training data are available.
5 CONCLUSION
The paper presents two end-to-end neural architectures for predicting stress fields in cantilevered structures and finds that StressNet provides higher accuracy than SCSNet. Deeper networks improve prediction accuracy, while broader generalization remains future work.
- StressNet uses multiple input channels and SE-ResNet modules, while SCSNet uses a single input channel for stress-field prediction.
- 2.04% is the StressNet mean relative stress error on testing, with higher accuracy than SCSNet according to MSE and MAE results.
- Increasing training-data size gradually reduces MSE and MAE, although predicted stress fields remain desirably similar across dataset sizes.
- Input channel number has no significant effect on prediction accuracy, whereas deeper hierarchical architectures produce more accurate predictions.
- Future work aims to use generative deep learning to reduce the need for extensive coverage of input geometries, boundary conditions, and loads.