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2024 | OriginalPaper | Buchkapitel

Machine Learning Assisted Development of Eight Node Hexahedral Finite Element

verfasst von : Tadala Venkata Krishna Subhash, Ankit, Dipjyoti Nath, Sachin Singh Gautam

Erschienen in: Recent Advances in Aerospace Engineering

Verlag: Springer Nature Singapore

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Abstract

The finite element method (FEM) is a popular numerical technique for solving partial differential equations (PDEs) arising in computational modeling. Several engineering problems, such as those involving fluid flows, electromagnetics, heat transfer, and structural analysis, have been effectively solved using FEM. It is the most powerful tool currently in structural analysis. Recently, machine learning (ML) approaches have been used to enhance the performance of FEM. The main aim of this study is to build an artificial neural network (ANN) model using deep learning, a popular and powerful ML algorithm that can estimate the elemental stiffness matrices of 3D 8-noded hexahedral elements with very high accuracy. The performance of the model is evaluated by comparing it with Cook’s beam problem. The model predicts the displacement of the beam with an error of 0.74%.

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Fußnoten
1
All units are normalized units.
 
Literatur
1.
Zurück zum Zitat Zienkiewicz O, Taylor R, Zhu JZ (2013) The finite element method: its basis and fundamentals, 7th edn. Butterworth-Heinemann, Elsevier Zienkiewicz O, Taylor R, Zhu JZ (2013) The finite element method: its basis and fundamentals, 7th edn. Butterworth-Heinemann, Elsevier
2.
Zurück zum Zitat Goodfellow I, Bengio Y, Courville A (2016) Deep Learning. MIT Press Goodfellow I, Bengio Y, Courville A (2016) Deep Learning. MIT Press
3.
Zurück zum Zitat Mitchell T (1997) Machine learning. McGraw-Hill Education Mitchell T (1997) Machine learning. McGraw-Hill Education
4.
Zurück zum Zitat Lagaris IE, Likas A, Fotiadis DI (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Networks 9(5):987–1000CrossRef Lagaris IE, Likas A, Fotiadis DI (1998) Artificial neural networks for solving ordinary and partial differential equations. IEEE Trans Neural Networks 9(5):987–1000CrossRef
5.
Zurück zum Zitat Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686–707MathSciNetCrossRef Raissi M, Perdikaris P, Karniadakis GE (2019) Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. J Comput Phys 378:686–707MathSciNetCrossRef
6.
Zurück zum Zitat Liu X, Athanasiou CE, Padture NP, Sheldon BW, Gao H (2020) A machine learning approach to fracture mechanics problems. Acta Mater 190:105–112CrossRef Liu X, Athanasiou CE, Padture NP, Sheldon BW, Gao H (2020) A machine learning approach to fracture mechanics problems. Acta Mater 190:105–112CrossRef
7.
Zurück zum Zitat Ozarde AP, Narayan J, Yadav D, McNay GH, Gautam SS (2020) Optimization of diesel engine’s liner geometry to reduce head gasket’s fretting damage. SAE Int J Engines 14(1):81–97CrossRef Ozarde AP, Narayan J, Yadav D, McNay GH, Gautam SS (2020) Optimization of diesel engine’s liner geometry to reduce head gasket’s fretting damage. SAE Int J Engines 14(1):81–97CrossRef
8.
Zurück zum Zitat Gautam SS, Khan K (2020) Detection of fretting fatigue using machine learning algorithms. In: 3rd structural integrity conference and exhibition (sice 2020) structural integrity at multiple length scales (e-Conference), IIT Bombay Gautam SS, Khan K (2020) Detection of fretting fatigue using machine learning algorithms. In: 3rd structural integrity conference and exhibition (sice 2020) structural integrity at multiple length scales (e-Conference), IIT Bombay
9.
Zurück zum Zitat Nowell D, Nowell P (2020) A machine learning approach to the prediction of fretting fatigue life. Tribol Int 141:105913CrossRef Nowell D, Nowell P (2020) A machine learning approach to the prediction of fretting fatigue life. Tribol Int 141:105913CrossRef
10.
Zurück zum Zitat Vithalbhai SK, Gautam SS (2021) A machine learning approach to fretting fatigue problem. In: Proceedings of the international conference on futuristic technologies (e-conference)—structural health monitoring, energy harvesting, green material and biomechanics. IIT Delhi Vithalbhai SK, Gautam SS (2021) A machine learning approach to fretting fatigue problem. In: Proceedings of the international conference on futuristic technologies (e-conference)—structural health monitoring, energy harvesting, green material and biomechanics. IIT Delhi
11.
Zurück zum Zitat Gouravaraju S, Narayan J, Sauer RA, Gautam SS (2023) A Bayesian regularization-backpropagation neural network model for peeling computations. J Adhes 99(1):92–115CrossRef Gouravaraju S, Narayan J, Sauer RA, Gautam SS (2023) A Bayesian regularization-backpropagation neural network model for peeling computations. J Adhes 99(1):92–115CrossRef
12.
Zurück zum Zitat Oishi A, Yagawa G (2020) A surface-to-surface contact search method enhanced by deep learning. Comput Mech 65(4):1125–1147MathSciNetCrossRef Oishi A, Yagawa G (2020) A surface-to-surface contact search method enhanced by deep learning. Comput Mech 65(4):1125–1147MathSciNetCrossRef
13.
Zurück zum Zitat Oishi A, Yagawa G (2017) Computational mechanics enhanced by deep learning. Comput Methods Appl Mech Eng 327:327–351MathSciNetCrossRef Oishi A, Yagawa G (2017) Computational mechanics enhanced by deep learning. Comput Methods Appl Mech Eng 327:327–351MathSciNetCrossRef
14.
Zurück zum Zitat Vithalbhai SK, Nath D, Agrawal V, Gautam SS (2022) Artificial neural network assisted numerical quadrature in finite element analysis in mechanics. Materials Today: Proceedings 66:1645–1650 Vithalbhai SK, Nath D, Agrawal V, Gautam SS (2022) Artificial neural network assisted numerical quadrature in finite element analysis in mechanics. Materials Today: Proceedings 66:1645–1650
15.
Zurück zum Zitat Chinchkar R, Nath D, Gautam SS (2023) Design of efficient quadrature scheme in finite element using deep learning. Advances in engineering design: select proceedings of FLAME 2022, pp. 21–29, Springer, Singapore Chinchkar R, Nath D, Gautam SS (2023) Design of efficient quadrature scheme in finite element using deep learning. Advances in engineering design: select proceedings of FLAME 2022, pp. 21–29, Springer, Singapore
16.
Zurück zum Zitat Khoei A, Moslemi H, Seddighian M (2020) An efficient stress recovery technique in adaptive finite element method using artificial neural network. Eng Fract Mech 237:107231CrossRef Khoei A, Moslemi H, Seddighian M (2020) An efficient stress recovery technique in adaptive finite element method using artificial neural network. Eng Fract Mech 237:107231CrossRef
17.
Zurück zum Zitat Liang L, Liu M, Martin C, Sun W (2018) A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis. J R Soc Interface 15(138):20170844CrossRef Liang L, Liu M, Martin C, Sun W (2018) A deep learning approach to estimate stress distribution: a fast and accurate surrogate of finite-element analysis. J R Soc Interface 15(138):20170844CrossRef
18.
Zurück zum Zitat Saikia BB, Nath D, Gautam SS (2023) Application of machine learning in efficient stress recovery in finite element analysis. Mater Today: Proc 78:359–363 Saikia BB, Nath D, Gautam SS (2023) Application of machine learning in efficient stress recovery in finite element analysis. Mater Today: Proc 78:359–363
19.
Zurück zum Zitat Saikia BB, Nath D, Gautam S S (2024) Machine learning models for stress recovery in finite element method. In: Recent trends in computational mechanics and simulation: select proceedings of ICCMS 2022, Springer, Singapore (in press) Saikia BB, Nath D, Gautam S S (2024) Machine learning models for stress recovery in finite element method. In: Recent trends in computational mechanics and simulation: select proceedings of ICCMS 2022, Springer, Singapore (in press)
20.
Zurück zum Zitat Nath D, Neog DR, Gautam SS (2024) Application of machine learning and deep learning in finite element analysis: a comprehensive review. Archives of computational methods in engineering, pp. 1–40 Nath D, Neog DR, Gautam SS (2024) Application of machine learning and deep learning in finite element analysis: a comprehensive review. Archives of computational methods in engineering, pp. 1–40
22.
Zurück zum Zitat Nath SS, Nath D, Gautam SS (2022) Design of efficient finite elements using deep learning approach. In: Biennial international conference on future learning aspects of mechanical engineering. Springer Nature Singapore, Singapore, pp 11–20 Nath SS, Nath D, Gautam SS (2022) Design of efficient finite elements using deep learning approach. In: Biennial international conference on future learning aspects of mechanical engineering. Springer Nature Singapore, Singapore, pp 11–20
23.
Zurück zum Zitat Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. In: International conference on machine learning. PMLR, 2015, pp 448–456 Ioffe S, Szegedy C (2015) Batch normalization: accelerating deep network training by reducing internal covariate shift. In: International conference on machine learning. PMLR, 2015, pp 448–456
25.
Zurück zum Zitat Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. In: Proceedings of the thirteenth international conference on artificial intelligence and statistics. JMLR workshop and conference proceedings, pp 249–256 Glorot X, Bengio Y (2010) Understanding the difficulty of training deep feedforward neural networks. In: Proceedings of the thirteenth international conference on artificial intelligence and statistics. JMLR workshop and conference proceedings, pp 249–256
26.
Zurück zum Zitat Cook RD, Malkus DS, Plesha ME, Witt RJ (2007) Concepts and applications of finite element analysis. John Wiley & Sons Cook RD, Malkus DS, Plesha ME, Witt RJ (2007) Concepts and applications of finite element analysis. John Wiley & Sons
Metadaten
Titel
Machine Learning Assisted Development of Eight Node Hexahedral Finite Element
verfasst von
Tadala Venkata Krishna Subhash
Ankit
Dipjyoti Nath
Sachin Singh Gautam
Copyright-Jahr
2024
Verlag
Springer Nature Singapore
DOI
https://doi.org/10.1007/978-981-97-1306-6_20

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