Session: 01-05-02: Applications of Artificial Intelligence/Machine Learning for Aerospace Structures

Paper Number: 138338

138338 - Scalable Finite Element Analysis Neural Network (Fea-Net) Model for Structures and Materials Analysis 

Scientific Machine Learning (SciML) is a rapidly evolving field for many engineering analyses and simulations. SciML has been used extensively to solve various engineering problems with partial differential equations as the governing equations, such as mechanical stress analysis of materials and structures. SciML integrates physics knowledge and data-driven methods aiming to achieve the best parts of both sides. Specifically, physics-guided/informed machine learning is one of the major approaches for this type of analysis. There are many ways to include physics in machine learning, such as including physics at the input, output (loss), and model. The proposed study focuses on the inclusion of physics in the model, which significantly enhances the interpretability of ML results.

Finite element analysis (FEA) is one of the most widely used structural and material mechanical methods. The proposed method aims to design suitable neural networks inspired by the finite element method. It is well known that high-fidelity FEA is time-consuming, which is critical for complex structural analysis or dense-mesh material analysis. Thus, a scalable finite element analysis neural network (FEA-Net) is proposed in this study to enhance the efficiency under high-dimensional conditions. The proposed model contributes to three main aspects. Firstly, the model, based on the finite element method, offers a physically interpretable representation. Secondly, it incorporates a data-driven solver to alleviate the computational demands on time and memory. Thirdly, the model is applicable and demonstrated for multiple material systems in both 2D and 3D, providing a more realistic simulation framework for complex structures and materials.

Methods

First, this model combines the FEA and CNN methods. FEA for mechanical response establishes the solution domain with smaller meshes, transforming the original Partial Differential Equation (PDE) into a system of linear equations. The convolution operation models the mapping from the system response image to the system loading image within the mesh. Next, the model applies the multi-grid communication and smoothing operators between grids. The smoothers for each grid level are modified from the Jacobi smoother kernel, and the modification is learned from a three-layer convolutional neural network. Third, the model extends the 2D application fields to 3D, utilizing a 3x3x3 filter kernel matrix based on the simplest 8-node linear element (cube). By adding physical knowledge to this model, the model can achieve the true prediction for the mechanical response for different materials beyond the training data.

Preliminary results

The scalable FEA-Net model is demonstrated on several numerical examples with different loading and boundary conditions. The model can identify not only homogenous material structure but also multiphases material. It performs better on convergence speed and computation times compared to the traditional FEA method. In conclusion, this study presents a novel scalable FEA-Net model. It combines the FEA and CNN method with multigrid formulation, which is super-efficient and highly interpretable.

Presenting Author: Xiaoyun Fan Arizona State University

Presenting Author Biography: Graduate student in Arizona State University
Major in Mechanical Engineering