Graph Neural Network for Stress Predictions in Stiffened Panels Under Uniform Loading

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during conceptual design of a structure or a product. In this study, we propose a novel graph embedding technique for efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite-element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural geometry on the prediction performance. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding method as robust reduced-order models for 3D structures.

Physics-informed Neural Network: The Effect of Reparameterization in Solving Differential Equations

Differential equations are used to model and predict the behaviour of complex systems in a wide range of fields, and the ability to solve them is an important asset for understanding and predicting the behaviour of these systems. Complicated physics mostly involves difficult differential equations, which are hard to solve analytically. In recent years, physics-informed neural networks have been shown to perform very well in solving systems with various differential equations. The main ways to approximate differential equations are through penalty function and reparameterization. Most researchers use penalty functions rather than reparameterization due to the complexity of implementing reparameterization. In this study, we quantitatively compare physics-informed neural network models with and without reparameterization using the approximation error. The performance of reparameterization is demonstrated based on two benchmark mechanical engineering problems, a one-dimensional bar problem and a two-dimensional bending beam problem. Our results show that when dealing with complex differential equations, applying reparameterization results in a lower approximation error.