Predicting the Plastic Response of Circular Metal Plates Under Uniform Dynamic Load Using Deep Neural Network

Document Type : Impact Mechanics

Authors

1 Corresponding author: Assistant Professor, Faculty of Science, Imam Hossein University, Tehran, Iran

2 M.Sc Student, Faculty of Science, Imam Hossein University, Tehran, Iran

3 Assistant Professor, Faculty of Mechanical Engineering, University of Eyvanekey, Eyvanekey, Iran

Abstract

In the upcoming research, using deep neural networks, it is used to predict the maximum yield of circular metal sheets under uniform dynamic load. The neural network presented in this research was designed in the Python programming language and using the libraries available in it, including Tensorflow. The network is based on the regression problem and is of sequential type and includes 10 hidden layers which are the activation function in neurons of Leaky RELU type. The network optimizer algorithm was set to Adam and the objective function of the MSE problem and the number of network iterations was set to 700 times. The data set used in this article consists of 581 samples obtained from 16 series of experiments during the last forty years, which were standardized by the Scikit_learn library. The metal sheets are of 4 types: steel, aluminum, copper and titanium, and there is no separation between different metals.  The number of training data in the model was determined to be 443 equals to 75% of the data set. Also, the number of experimental and evaluator data was selected as 88 numbers equivalent to 15% and 50 numbers equivalent to 10% of the entire data set. Each sample has 8 features as neural network inputs and one label as output. The presented intelligent model among the 88 test data that was completely randomly selected from the data set was able to classify 76% of the data, approximately equivalent to 67 numbers, within the error range of less than 10% and 88% of the data, or in other words, equivalent to approximately 78 numbers within the error range. Predict less than 20%. The amount of the root mean square error index decreased 102 times compared to the analytical and traditional predictive relationships available in the research records. Also, the coefficient of determination criterion, which is an important indicator for evaluating the performance of neural networks based on regression problems, includes the value of 0.96.

Highlights

  • Using deep learning to predict the permanent deflection of metal sheets.
  • Using Adam's optimizer algorithm in deep neural network model architecture.
  • Determining optimal metaparameters based on evaluator search engines.

Keywords

Main Subjects

References

[1] Sakaridis E, Karathanasopoulos N, Mohr D. Machine-learning based prediction of crash response of tubular structures. International Journal of Impact Engineering. 2022;166:104240. DOI :10.1016/j.ijimpeng.2022.104240.
[2] Mostofi TM, Babaei H, Alitavoli M. Theoretical analysis on the effect of uniform and localized impulsive loading on the dynamic plastic behaviour of fully clamped thin quadrangular plates. Thin-Walled Structures. 2016;109:367-76. DOI :10.1016/j.tws.2016.10.009.
[3] Mirzababaie Mostofi T, Sayah Badkhor M, Babaei H. A study on plastic response of circular plates under uniformly and locally distributed dynamic loading. Journal of Solid and Fluid Mechanics. 2020;10(2):11-27. DOI :10.22044/JSFM.2020.9264.3091.
[4] Babaei H, Mostofi TM, Alitavoli M, Darvizeh A. Empirical modelling for prediction of large deformation of clamped circular plates in gas detonation forming process. Experimental Techniques. 2016;40(6):1485-94. DOI :10.1007/s40799-016-0063-3.
[5] Mostofi TM, Babaei H, Alitavoli M. The influence of gas mixture detonation loads on large plastic deformation of thin quadrangular plates: Experimental investigation and empirical modelling. Thin-Walled Structures. 2017;118:1-11. DOI :10.1016/j.tws.2017.04.031.
[6] Mostofi TM, Babaei H, Alitavoli M, Lu G, Ruan D. Large transverse deformation of double-layered rectangular plates subjected to gas mixture detonation load. International Journal of Impact Engineering. 2019;125:93-106. DOI :10.1016/j.ijimpeng.2018.11.005.
[7] Nurick G, Martin J. Deformation of thin plates subjected to impulsive loading—a review: Part i: Theoretical considerations. International Journal of Impact Engineering. 1989;8(2):159-70. DOI :10.1016/0734-743X(89)90015-8.
[8] Yuen SCK, Nurick G, Langdon G, Iyer Y. Deformation of thin plates subjected to impulsive load: Part III–an update 25 years on. International Journal of Impact Engineering. 2017;107:108-17. DOI :10.1016/j.ijimpeng.2016.06.010.
[9] Mirzababaie Mostofi T, Sayah Badkhor M, Ghasemi E. Experimental investigation and optimal analysis of the high-velocity forming process of bilayer plates. Journal of Solid and Fluid Mechanics. 2019;9(3):65-80. DOI :10.22044/JSFM.2019.8586.2953.
[10] Haghgoo M, Babaei H, Mostofi TM. 3D numerical investigation of the detonation wave propagation influence on the triangular plate deformation using finite rate chemistry model of LS-DYNA CESE method. International Journal of Impact Engineering. 2022;161:104108. DOI :10.1016/j.ijimpeng.2021.104108.
[11] Nasiri S, Sadegh-Yazdi M, Mousavi S, Ziya-Shamami M, Mostofi T. Repeated underwater explosive forming: Experimental investigation and numerical modeling based on coupled Eulerian–Lagrangian approach. Thin-Walled Structures. 2022;172:108860. DOI :10.1016/j.tws.2021.108860.
[12] Babaei H, Mirzababaie Mostofi T. Modeling and prediction of fatigue life in composite materials by using singular value decomposition method. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications. 2020;234(2):246-54. DOI :10.1177/1464420716660875.
[13] Nurick GN, Martin JB. Deformation of thin plates subjected to impulsive loading—a review Part II: Experimental studies. International Journal of Impact Engineering. 1989;8(2):171-86. DOI :10.1016/0734-743X(89)90015-8.
[14] Jacob N, Nurick G, Langdon G. The effect of stand-off distance on the failure of fully clamped circular mild steel plates subjected to blast loads. Engineering Structures. 2007;29(10):2723-36. DOI :10.1016/j.engstruct.2007.01.021.
[15] Nurick G, Martin J. Deformation of thin plates subjected to impulsive loading—a review part II: experimental studies. International journal of impact engineering. 1989;8(2):171-86. DOI :10.1016/0734-743X(89)90015-8.
[16] Goodfellow I, Bengio Y, Courville A. Deep learning: MIT press; 2016.
[17] Bishop CM, Nasrabadi NM. Pattern recognition and machine learning: Springer; 2006.
[18] Bengio Y. Practical recommendations for gradient-based training of deep architectures. InNeural networks: Tricks of the trade: Second edition 2012 May (pp. 437-478). Berlin, Heidelberg: Springer Berlin Heidelberg. DOI :10.1007/978-3-642-35289-8_26.
[19] Zhang A, Lipton ZC, Li M, Smola AJ. Dive into deep learning: Cambridge University Press; 2023. DOI :10.48550/arXiv.2106.11342.
[20] Florence A. Circular plate under a uniformly distributed impulse. International Journal of Solids and Structures. 1966;2(1):37-47. DOI :10.1016/0020-7683(66)90005-9.
[21] Wierzbicki T, Florence A. A theoretical and experimental investigation of impulsively loaded clamped circular viscoplastic plates. International Journal of solids and structures. 1970;6(5):553-68. DOI :10.1016/0020-7683(70)90030-2.
[22] Bodner SR, Symonds PS. Experiments on viscoplastic response of circular plates to impulsive loading. Journal of the Mechanics and Physics of Solids. 1979;27(2):91-113. DOI :10.1016/0022-5096(79)90013-9.
[23] Teeling-Smith R, Nurick G. The deformation and tearing of thin circular plates subjected to impulsive loads. International Journal of Impact Engineering. 1991;11(1):77-91. DOI :10.1016/0734-743X(91)90032-B.
[24] Nurick GN, Teeling-Smith RG. Predicting the onset of necking and hence rupture of thin plates loaded impulsively-an experimental view. InStructures Under Shock and Impact II: Proceedings of the Second International Conference, held in Portsmouth, UK, 16th–18th June, 1992 1992 (pp. 431-445). Thomas Telford Publishing.
[25] Thomas B. The effect of boundary conditions on thin plates subjected to impulsive loads. Dynamic Plasticity and Structural Behaviours. 1995;85.
[26] Nurick G, Gelman M, Marshall N. Tearing of blast loaded plates with clamped boundary conditions. International Journal of Impact Engineering. 1996;18(7-8):803-27. DOI :10.1016/S0734-743X(96)00026-7.
[27] Nurick G, Lumpp D. Deflection and tearing of clamped stiffened circular plates subjected to uniform impulsive blast loads. WIT Transactions on The Built Environment. 1970;25. DOI :10.2495/SUSI960361.
[28] Gharababaei H, Darvizeh A. Experimental and Analytical Investigation of Large Deformation of Thin Circular Plates Subjected to Localized and Uniform Impulsive Loading#. Mechanics Based Design of Structures and Machines. 2010;38(2):171-89. DOI :10.1080/15397730903554633.
[29] Zamani J, Safari K, Ghamsari A, Zamiri A. Experimental analysis of clamped AA5010 and steel plates subjected to blast loading and underwater explosion. The Journal of Strain Analysis for Engineering Design. 2011;46(3):201-12. DOI :10.1177/0309324710396601.
[30] Henchie TF, Yuen SCK, Nurick G, Ranwaha N, Balden V. The response of circular plates to repeated uniform blast loads: An experimental and numerical study. International Journal of Impact Engineering. 2014;74:36-45. DOI :10.1016/j.ijimpeng.2014.02.021.
[31] Babaei H, Mostofi TM, Sadraei SH. Effect of gas detonation on response of circular plate-experimental and theoretical. Structural Engineering and Mechanics. 2015;56(4):535-48. DOI :10.12989/sem.2015.56.4.535.
[32] Ziya-Shamami M, Babaei H, Mostofi TM, Khodarahmi H. Structural response of monolithic and multi-layered circular metallic plates under repeated uniformly distributed impulsive loading: An experimental study. Thin-Walled Structures. 2020;157:107024. DOI :10.1016/j.tws.2020.107024.
[33] Souza ML, da Costa CA, de Oliveira Ramos G. A machine-learning based data-oriented pipeline for Prognosis and Health Management Systems. Computers in Industry. 2023;148:103903. DOI :10.1016/j.compind.2023.103903.
[34] Ketkar N, Santana E. Deep learning with Python. Berkeley, CA: Apress; 2017. DOI :10.1007/978-1-4842-5364-9.
[35] Kingma DP, Ba J. Adam: A method for stochastic optimization. arXiv preprint arXiv:1412.6980. 2014. DOI :10.48550/arXiv.1412.6980.
[36] Abadi M, Agarwal A, Barham P, Brevdo E, Chen Z, Citro C, Corrado GS, Davis A, Dean J, Devin M, Ghemawat S. Tensorflow: Large-scale machine learning on heterogeneous distributed systems. arXiv preprint arXiv:1603.04467. 2016. DOI :10.48550/arXiv.1603.04467.
[37] Jones N. A theoretical study of the dynamic plastic behavior of beams and plates with finite-deflections. International Journal of Solids and Structures. 1971;7(8):1007-29. DOI :10.1016/0020-7683(71)90078-3.
[38] Soares CG. A mode solution for the finite deflections of a circular plate loaded impulsively. Engineering Transactions. 1981;29(1):99-114.
[39] Mostofi TM, Babaei H, Alitavoli M, Hosseinzadeh S. On dimensionless numbers for predicting large ductile transverse deformation of monolithic and multi-layered metallic square targets struck normally by rigid spherical projectile. Thin-Walled Structures. 2017;112:118-24. DOI :10.1016/j.tws.2016.12.014.
[40] Duffey TA. Large deflection dynamic response of clamped circular plates subjected to explosive loading. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); 1967.
[41] Babaei H, Mirzababaie Mostofi T. New dimensionless numbers for deformation of circular mild steel plates with large strains as a result of localized and uniform impulsive loading. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications. 2020;234(2):231-45. DOI :10.1177/1464420716654195.
[42] Babaei H, Mirzababaie Mostofi T, Armoudli E. On dimensionless numbers for the dynamic plastic response of quadrangular mild steel plates subjected to localized and uniform impulsive loading. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering. 2017;231(5):939-50. DOI :10.1177/0954408916650713.
[43] Cloete T, Nurick G. On the influence of radial displacements and bending strains on the large deflections of impulsively loaded circular plates. International Journal of Mechanical Sciences. 2014;82:140-8. DOI :10.1016/j.ijmecsci.2014.02.026.
[44] Lippmann H. Kinetics of the axisymmetric rigid-plastic membrane subject to initial impact. International Journal of Mechanical Sciences. 1974;16(5):297-303. DOI :10.1016/0020-7403(74)90046-0.
[45] C.K. De Wee, G.S. Langdon, G.N. Nurick. The influence of confined and unconfined explosions on the structural response of fully clamped mild steel plates. Undergraduate thesis, University of Cape Town, 2007.
[46] Mirzababaie Mostofi T, Babaei H. Plastic deformation of polymeric-coated aluminum plates subjected to gas mixture detonation loading: Part II: Analytical and empirical modelling. Journal of Solid and Fluid Mechanics. 2019;9(2):15-29. DOI :10.22044/JSFM.2019.7816.2778.
[47] Babaei H, Darvizeh A. Analytical study of plastic deformation of clamped circular plates subjected to impulsive loading. Journal of Mechanics of Materials and Structures. 2012;7(4):309-22. DOI :10.2140/jomms.2012.7.309.
[48] Gharababaei H, Darvizeh A, Darvizeh M. Analytical and experimental studies for deformation of circular plates subjected to blast loading. Journal of mechanical Science and Technology. 2010;24:1855-64. DOI :10.1007/s12206-010-0602-2.
 
Aerospace Mechanics
Volume 20, Issue 2 - Serial Number 76
Serial No. 75, Summer
July 2024
Pages 105-121

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History

  • Receive Date: 08 February 2024
  • Revise Date: 17 March 2024
  • Accept Date: 20 April 2024
  • Publish Date: 21 June 2024

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