Supervised learning for finite element analysis of holes under biaxial load - Lau, Jia Tai (Nanyang Technological University, 2020)
This paper presents a novel approach of using supervised learning with a shallow neural network to increase the efficiency for the finite element analysis of holes under biaxial load. The objective of this approach is to reduce the number of elements in the finite element analysis while maintaining good accuracy. The training of neural network will be done based on the coarse mesh of a hole on an infinite width plate under biaxial load against its analytical solution. Three common backpropagation network algorithms are evaluated. They are the Conjugate Gradient Descent, Levenberg-Marquardt algorithm, and Bayesian Regularization. In addition, tangent sigmoid and pure linear transfer functions will be evaluated. Subsequently, the neural network will be used to predict the maximum stress for holes of different configurations such as hole in a finite width plate (2D), multiple holes (2D), staggered holes (2D) and hole in an infinite plate (3D). In the infinite width problem, Levenberg-Marquardt algorithm with pure linear transfer function and Bayesian Regularization with tangent sigmoid transfer function offer the highest accuracy in testing of the neural network model. This is done using the displacement values of all 6 nodes as training parameters. However, this setup has poor prediction accuracy when it is applied to holes of different configurations. To improve the prediction accuracy, the training would be done solely based on the non-zero displacements of the nodes associated to the element with highest stress. After applying this setup with Levenberg-Marquardt algorithm to train the neural network, the trained neural network is used to predict the maximum stresses for other 2D problems. The predictions are based on their respective coarse mesh with only 2 elements along the hole quarter perimeter. In this way, prediction errors of under 5% are achieved for all the listed hole configurations. In contrast, the conventional FEM with the respective coarse mesh for the above 2D hole configurations have errors of above 20%. To achieve similar accuracy, the conventional FEM would require at least 6 elements along the perimeter. Furthermore, this setup is also effective in predicting the maximum stress in the 3D infinite width problem, attaining prediction errors of less than 2% with only 2 elements along the perimeter. In contrast, the same coarse mesh using conventional FEM have errors of above 35%. To achieve similar accuracy for the 3D problem, the conventional FEM would require more than 8 elements along the perimeter. This result shows that supervised learning has great potential in enhancing the efficiency of the finite element analysis with less elements while attaining satisfactory results.