Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem

Our objective in this work is to demonstrate how physics-informed neural networks, a type of deep learning technology, can be utilized to examine the mechanical properties of a helicopter blade. The blade is regarded as a one-dimensional prismatic cantilever beam that is exposed to triangular loadin...

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Main Authors: Vishal Singh, Dineshkumar Harursampath, Sharanjeet Dhawan, Manoj Sahni, Sahaj Saxena, Rajnish Mallick
Format: Article
Language:English
Published: MDPI AG 2024-10-01
Series:Modelling
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Online Access:https://www.mdpi.com/2673-3951/5/4/80
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author Vishal Singh
Dineshkumar Harursampath
Sharanjeet Dhawan
Manoj Sahni
Sahaj Saxena
Rajnish Mallick
author_facet Vishal Singh
Dineshkumar Harursampath
Sharanjeet Dhawan
Manoj Sahni
Sahaj Saxena
Rajnish Mallick
author_sort Vishal Singh
collection DOAJ
description Our objective in this work is to demonstrate how physics-informed neural networks, a type of deep learning technology, can be utilized to examine the mechanical properties of a helicopter blade. The blade is regarded as a one-dimensional prismatic cantilever beam that is exposed to triangular loading, and comprehending its mechanical behavior is of utmost importance in the aerospace field. PINNs utilize the physical information, including differential equations and boundary conditions, within the loss function of the neural network to approximate the solution. Our approach determines the overall loss by aggregating the losses from the differential equation, boundary conditions, and data. We employed a physics-informed neural network (PINN) and an artificial neural network (ANN) with equivalent hyperparameters to solve a fourth-order differential equation. By comparing the performance of the PINN model against the analytical solution of the equation and the results obtained from the ANN model, we have conclusively shown that the PINN model exhibits superior accuracy, robustness, and computational efficiency when addressing high-order differential equations that govern physics-based problems. In conclusion, the study demonstrates that PINN offers a superior alternative for addressing solid mechanics problems with applications in the aerospace industry.
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series Modelling
spelling doaj-art-4fba5feda91b4847bcdc466f153c0b6c2024-12-27T14:42:05ZengMDPI AGModelling2673-39512024-10-01541532154910.3390/modelling5040080Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics ProblemVishal Singh0Dineshkumar Harursampath1Sharanjeet Dhawan2Manoj Sahni3Sahaj Saxena4Rajnish Mallick5Department of Mechanical Engineering, Thapar Institute of Engineering and Technology, Patiala 147004, Punjab, IndiaDepartment of Aerospace Engineering, Indian Institute of Science, Bengaluru 560012, Karnataka, IndiaDepartment of Mathematics, CCSHAU COA, Bawal 123501, Haryana, IndiaDepartment of Mathematics, Pandit Deendayal Energy University, Gandhinagar 382007, Gujarat, IndiaDepartment of Electrical and Instrumentation Engineering, Thapar Institute of Engineering and Technology, Patiala 147004, Punjab, IndiaDepartment of Mechanical Engineering, Thapar Institute of Engineering and Technology, Patiala 147004, Punjab, IndiaOur objective in this work is to demonstrate how physics-informed neural networks, a type of deep learning technology, can be utilized to examine the mechanical properties of a helicopter blade. The blade is regarded as a one-dimensional prismatic cantilever beam that is exposed to triangular loading, and comprehending its mechanical behavior is of utmost importance in the aerospace field. PINNs utilize the physical information, including differential equations and boundary conditions, within the loss function of the neural network to approximate the solution. Our approach determines the overall loss by aggregating the losses from the differential equation, boundary conditions, and data. We employed a physics-informed neural network (PINN) and an artificial neural network (ANN) with equivalent hyperparameters to solve a fourth-order differential equation. By comparing the performance of the PINN model against the analytical solution of the equation and the results obtained from the ANN model, we have conclusively shown that the PINN model exhibits superior accuracy, robustness, and computational efficiency when addressing high-order differential equations that govern physics-based problems. In conclusion, the study demonstrates that PINN offers a superior alternative for addressing solid mechanics problems with applications in the aerospace industry.https://www.mdpi.com/2673-3951/5/4/80physics-informed neural networkdeep neural networkartificial neural networkcomputational solid mechanicspartial differential equation
spellingShingle Vishal Singh
Dineshkumar Harursampath
Sharanjeet Dhawan
Manoj Sahni
Sahaj Saxena
Rajnish Mallick
Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem
Modelling
physics-informed neural network
deep neural network
artificial neural network
computational solid mechanics
partial differential equation
title Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem
title_full Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem
title_fullStr Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem
title_full_unstemmed Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem
title_short Physics-Informed Neural Network for Solving a One-Dimensional Solid Mechanics Problem
title_sort physics informed neural network for solving a one dimensional solid mechanics problem
topic physics-informed neural network
deep neural network
artificial neural network
computational solid mechanics
partial differential equation
url https://www.mdpi.com/2673-3951/5/4/80
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