Conference Room 3546D
The Department of Civil and Environmental Engineering
Michigan State University
Ph.D. Dissertation Defense
Beyond Finite Element: Physics-Informed Neural Network for Stress Prediction
By
Hamed Bolandi
Advisor: Dr. Nizar Lajnef
When: Wednesday, March 29, 2023
From 1:00 – 3:00 PM
Where: Civil & Environmental Engineering
Conference Room 3546D
Join Zoom Meeting
https://msu.zoom.us/j/91920781136
Meeting ID: 919 2078 1136
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Abstract
This Multidisciplinary research proposes deep neural networks to bypass the Finite Element Analysis (FEA) and predict high-resolution stress distributions on loaded steel plates with variable loading, geometries, and boundary conditions. FEA for structures has been broadly used to conduct stress analysis of various civil and mechanical engineering structures. Conventional methods, such as FEA, provide high-fidelity solutions but require solving large linear systems that can be computationally intensive.
The existing workflow for FEM applications includes: (i) modeling the geometry and its components, (ii) specifying material properties, boundary conditions, and loading, (iii) Applying mesh strategy, and (iv) stress analysis which may be time-consuming based on the complexity of the model. Instead, Deep learning (DL) techniques can generate solutions significantly faster than conventional run-time analysis. This can prove extremely valuable in real-time structural assessment applications. In this work, The Convolutional Neural network (CNN) was designed and trained to use the geometry, boundary conditions, and static load as input to predict the stress contours in intact steel plates. Furthermore, we predict high-resolution stress distributions on damaged steel plates using CNNs augmented with custom loss functions that use physics rules to bypass the need for Finite Element Analysis.
We embedded physics constraints into the loss function to enforce the model training, precisely capturing stress concentrations around the tips of various structural damage configurations. The proposed technique’s performance was compared to Finite-Element simulations using partial differential equation (PDE) solver. There is also an emerging need for the prediction of dynamic stress distribution since Catastrophic failure of structural components is often caused by lateral loads, such as earthquakes and winds. Thus, accurate predictions of dynamic stress distribution are useful during highly disruptive events to guide corrective actions. Neuro-DynaStress is proposed to predict the entire sequence of stress distribution based on Finite Element simulations using a partial differential equation (PDE) solver.
More specifically, CNN, along with the multi-head attention transformer and feature alignment, is used to extract features and capture the data’s temporal dependence. The model was designed and trained to use the geometry, boundary conditions, and sequence of loads as input and predict the sequences of high-resolution von Mises stress contours. Moreover, to increase the accuracy of dynamic stress prediction, we propose Physics Informed Neural Network (PINN). The PINN-Stress model can predict the entire sequence of stress distribution based on Finite Element simulations using a PDE solver. Using automatic differentiation, we embed a partial differential equation into a deep neural network’s loss function to incorporate information from measurements and PDEs. In order to force our model to learn the physical constraints, we minimize the violation of the equation of motion and also minimize the boundary condition violation to fully enforce the underlying PDE. The PINN-Stress model can predict the sequence of normal and shear stress distribution in almost real-time and can generalize better than the model without PINN. Our model is also able to predict von Mises stress using the von Mises equation.
