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A novel analysis-prediction approach for geometrically nonlinear problems using group method of data handling. (English) Zbl 1441.74116
Summary: A novel analysis-prediction (ANP) approach for geometrically nonlinear problems of solid mechanics is for the first time proposed in this paper. The key concept of this approach is: (1) A part of equilibrium path is traced by numerical analysis; (2) Data of this part is then used for training predictive network; (3) Applying the trained network, the rest of the equilibrium path is simply traced by pure prediction without using any analysis. As an illustration for ANP approach, the analysis package is in this study established based on isogeometric shell analysis using the first-order shear deformation shell theory (FSDT). As the main advantage of the proposed approach, computational cost is significantly lower than that of the conventional approach based on pure numerical analysis. In addition, the predictive networks are built via group method of data handling (GMDH) known as a self-organizing deep learning method for time series forecasting problems without requirement of big data. Some numerical examples are provided to confirm the high accuracy and efficiency of the proposed approach. The approach not only could be applied to a wide range of computational mechanics problems in which nonlinear response occurs but also to other computational engineering fields.

MSC:
74K25 Shells
65D07 Numerical computation using splines
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
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References:
[1] Rezaiee-Paj, M.; Naserian, R., Geometrical nonlinear analysis based on optimization technique, Appl. Math. Model., 53, 32-48 (2018) · Zbl 07166409
[2] Peterson, A.; Petersson, H., On finite element analysis of geometrically nonlinear problems, Comput. Methods Appl. Mech. Engrg., 51, 1, 277-286 (1985) · Zbl 0552.73064
[3] Sze, K.; Liu, X.; Lo, S., Popular benchmark problems for geometric nonlinear analysis of shells, Finite Elem. Anal. Des., 40, 11, 1551-1569 (2004)
[4] Vu-Bac, N.; Duong, T. X.; Lahmer, T.; Zhuang, X.; Sauer, R. A.; Park, H. S.; Rabczuk, T., A NURBS-based inverse analysis for reconstruction of nonlinear deformations of thin shell structures, Comput. Methods Appl. Mech. Engrg., 331, 427-455 (2018)
[5] Areias, P.; Rabczuk, T., Finite strain fracture of plates and shells with configurational forces and edge rotations, Internat. J. Numer. Methods Engrg., 94, 12, 1099-1122 (2013) · Zbl 1352.74316
[6] Rabczuk, T.; Areias, P. M.A.; Belytschko, T., A meshfree thin shell method for non-linear dynamic fracture, Internat. J. Numer. Methods Engrg., 72, 5, 524-548 (2007) · Zbl 1194.74537
[7] Nguyen, T. N.; Thai, C. H.; Nguyen-Xuan, H.; Lee, J., Geometrically nonlinear analysis of functionally graded material plates using an improved moving kriging meshfree method based on a refined plate theory, Compos. Struct., 193, 268-280 (2018)
[8] Li, W.; Nguyen-Thanh, N.; Zhou, K., Geometrically nonlinear analysis of thin-shell structures based on an isogeometric-meshfree coupling approach, Comput. Methods Appl. Mech. Engrg., 336, 111-134 (2018)
[9] Nguyen-Thanh, N.; Zhou, K.; Zhuang, X.; Areias, P.; Nguyen-Xuan, H.; Bazilevs, Y.; Rabczuk, T., Isogeometric analysis of large-deformation thin shells using RHT-splines for multiple-patch coupling, Spec. Issue Isogeometric Anal.: Prog. Chall., 316, 1157-1178 (2017)
[10] Thai, S.; Thai, H. T.; Vo, T. P.; Nguyen-Xuan, H., Nonlinear static and transient isogeometric analysis of functionally graded microplates based on the modified strain gradient theory, Eng. Struct., 153, 598-612 (2017)
[11] Nguyen, H. X.; Atroshchenko, E.; Nguyen-Xuan, H.; Vo, T. P., Geometrically nonlinear isogeometric analysis of functionally graded microplates with the modified couple stress theory, Comput. Struct., 193, 110-127 (2017)
[12] Phung-Van, P.; Ferreira, A.; Nguyen-Xuan, H.; Wahab, M. Abdel., An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates, Composites B, 118, 125-134 (2017)
[13] Nguyen, T. N.; Ngo, T. D.; Nguyen-Xuan, H., A novel three-variable shear deformation plate formulation: Theory and Isogeometric implementation, Comput. Methods Appl. Mech. Engrg., 326, 376-401 (2017)
[14] Crisfield, M., A faster modified Newton – raphson iteration, Comput. Methods Appl. Mech. Engrg., 20, 3, 267-278 (1979) · Zbl 0434.73086
[15] Riks, E., The application of Newton’s method to the problem of elastic stability, J. Appl. Mech., 39, 1060 (1972) · Zbl 0254.73047
[16] Riks, E., An incremental approach to the solution of snapping and buckling problems, Int. J. Solids Struct., 15, 7, 529-551 (1979) · Zbl 0408.73040
[17] Leonetti, L.; Liguori, F.; Magisano, D.; Garcea, G., An efficient isogeometric solid-shell formulation for geometrically nonlinear analysis of elastic shells, Comput. Methods Appl. Mech. Engrg., 331, 159-183 (2018)
[18] Crisfield, M., A fast incremental/iterative solution procedure that handles snap-through, Comput. Struct., 13, 1, 55-62 (1981) · Zbl 0479.73031
[19] Rezaiee-Paj, M.; Naserian, R., Using residual areas for geometrically nonlinear structural analysis, Ocean Eng., 105, 327-335 (2015)
[20] Rezaiee-Paj, M.; Estiri, H., Geometrically nonlinear analysis of shells by various dynamic relaxation methods, World J. Eng., 14, 5, 381-405 (2017)
[21] Rezaiee-Paj, M.; Estiri, H., Finding equilibrium paths by minimizing external work in dynamic relaxation method, Appl. Math. Model., 40, 23, 10300-10322 (2016) · Zbl 1443.74101
[22] Rezaiee-Paj, M.; Estiri, H., Comparative analysis of three-dimensional frames by dynamic relaxation methods, Mech. Adv. Mater. Struct., 25, 6, 451-466 (2018)
[23] Rezaiee-Paj, M.; Afsharimoghadam, H., An incremental iterative solution procedure without predictor step, Eur. J. Comput. Mech., 27, 1, 58-87 (2018)
[24] Maghami, A.; Shahabian, F.; Hosseini, S. M., Path following techniques for geometrically nonlinear structures based on Multi-point methods, Comput. Struct., 208, 130-142 (2018)
[25] Mei, Y.; Hurtado, D. E.; Pant, S.; Aggarwal, A., On improving the numerical convergence of highly nonlinear elasticity problems, Comput. Methods Appl. Mech. Engrg., 337, 110-127 (2018)
[26] Thai, C. H.; Nguyen, T. N.; Rabczuk, T.; Nguyen-Xuan, H., An improved moving Kriging meshfree method for plate analysis using a refined plate theory, Comput. Struct., 176, 34-49 (2016)
[27] Nguyen, T. N.; Thai, C. H.; Nguyen-Xuan, H., A novel computational approach for functionally graded isotropic and sandwich plate structures based on a rotation-free meshfree method, Thin-Walled Structures, 107, 473-488 (2016)
[28] Hughes, T.; Cottrell, J.; Bazilevs, Y., Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 39, 4135-4195 (2005) · Zbl 1151.74419
[29] Atroshchenko, E.; Tomar, S.; Xu, G.; Bordas, S. P.A., Weakening the tight coupling between geometry and simulation in isogeometric analysis: From sub- and super-geometric analysis to geometry-independent field approximation (GIFT, Internat. J. Numer. Methods Engrg., 114, 10, 1131-1159 (2018)
[30] Reddy, J. N., Reddy JN Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (2003), CRC Press
[31] Nguyen, T. N.; Thai, C. H.; Nguyen-Xuan, H.; Lee, J., NURBS-Based analyses of functionally graded carbon nanotube-reinforced composite shells, Compos. Struct., 203, 349-360 (2018)
[32] Nguyen, T. N.; Thai, C. H.; Luu, A. T.; Nguyen-Xuan, H.; Lee, J., NURBS-Based postbuckling analysis of functionally graded carbon nanotube-reinforced composite shells, Comput. Methods Appl. Mech. Engrg., 347, 983-1003 (2019)
[33] Hale, J. S.; Brunetti, M.; Bordas, S. P.A.; Maurini, C., Simple and extensible plate and shell finite element models through automatic code generation tools, Comput. Struct., 209, 163-181 (2018)
[34] Brunetti, A.; Buongiorno, D.; Trotta, G. F.; Bevilacqua, V., Computer vision and deep learning techniques for pedestrian detection and tracking: A survey, Neurocomputing, 300, 17-33 (2018)
[35] Vo, T.; Nguyen, T.; Le, C. T., Race recognition using deep convolutional neural networks, Symmetry, 10, 11, 564 (2018)
[36] Xiong, W.; Lu, Z.; Li, B.; Hang, B.; Wu, Z., Automating smart recommendation from natural language API descriptions via representation learning, Future Gener. Comput. Syst., 87, 382-391 (2018)
[37] Zhao, R.; Yan, R.; Chen, Z.; Mao, K.; Wang, P.; Gao, R. X., Deep learning and its applications to machine health monitoring, Mech. Syst. Signal Process., 115, 213-237 (2019)
[38] Le, T.; Vo, B.; Fujita, H.; Nguyen, N. T.; Baik, S. W., A fast and accurate approach for bankruptcy forecasting using squared logistics loss with GPU-based extreme gradient boosting, Inform. Sci., 494, 294-310 (2019)
[39] Le, T.; Son, L. Hoang.; Vo, M. T.; Lee, M. Y.; Baik, S. W., A cluster-based boosting algorithm for bankruptcy prediction in a highly imbalanced dataset, Symmetry, 10, 7, 250 (2018)
[40] Le, T.; Lee, M. Y.; Park, J. R.; Baik, S. W., Oversampling techniques for bankruptcy prediction: Novel features from a transaction dataset, Symmetry, 10, 4, 79 (2018)
[41] Nguyen, N. P.; Hong, S. K., Fault-tolerant control of quadcopter UAVs using robust adaptive sliding mode approach, Energies, 12, 1, 95 (2019)
[42] Lee, S.; Ha, J.; Zokhirova, M.; Moon, H.; Lee, J., Background information of deep learning for structural engineering, Arch. Comput. Methods Eng., 25, 1, 121-129 (2018) · Zbl 1390.68538
[43] Mosavi, A.; Rabczuk, T., Learning and Intelligent Optimization for Material Design Innovation (2017), Springer International Publishing
[44] Mosavi, A.; Rabczuk, T.; Varkonyi-Koczy, A. R., Reviewing the Novel Machine Learning Tools for Materials Design (2018), Springer International Publishing
[45] Anitescu, C.; Atroshchenko, E.; Alajlan, N.; Rabczuk, T., Artificial neural network methods for the solution of second order boundary value problems, Comput. Mater. Continua, 59, 1, 345-359 (2019)
[46] Rappel, H.; Beex, L. A.A.; Bordas, S. P.A., Bayesian Inference to identify parameters in viscoelasticity, Mech. Time-Dependent Mater., 22, 2, 221-258 (2018)
[47] Rappel, H.; Beex, L. A.A.; Hale, J. S.; Noels, L.; Bordas, S. P.A., A tutorial on Bayesian inference to identify material parameters in solid mechanics, Arch. Comput. Methods Eng. (2019)
[48] Rappel, H.; Beex, L. A.A.; Noels, L.; Bordas, S. P.A., Identifying elastoplastic parameters with bayes’ theorem considering output error, input error and model uncertainty, Probab. Eng. Mech., 55, 28-41 (2019)
[49] Goodfellow, I.; Bengio, Y.; Courville, A., Deep Learning (2016), MIT Press · Zbl 1373.68009
[50] Samuel, A. L., Some studies in machine learning using the game of checkers, IBM J. Res. Dev., 3, 3, 210-229 (1959)
[51] Längkvist, M.; Karlsson, L.; Loutfi, A., A review of unsupervised feature learning and deep learning for time-series modeling, Pattern Recognit. Lett., 42, 11-24 (2014)
[52] Hochreiter, S.; Schmidhuber, J., Long short-term memory, Neural Comput., 9, 8, 1735-1780 (1997)
[53] Sezer, O. B.; Ozbayoglu, A. M., Algorithmic financial trading with deep convolutional neural networks: Time series to image conversion approach, Appl. Soft Comput., 70, 525-538 (2018)
[54] Minh, D. L.; Sadeghi-Niaraki, A.; Huy, H. D.; Min, K.; Moon, H., Deep learning approach for short-term stock trends prediction based on two-stream gated recurrent unit network, IEEE Access, 6, 55392-55404 (2018)
[55] Dang, L. M.; Hassan, S. I.; Im, S.; Mehmood, I.; Moon, H., Utilizing text recognition for the defects extraction in sewers CCTV inspection videos, Comput. Ind., 99, 96-109 (2018)
[56] Dang, L. M.; Hassan, S. I.; Im, S.; Lee, J.; Lee, S.; Moon, H., Deep learning based computer generated face identification using convolutional neural network, Appl. Sci., 8, 12, 2610 (2018)
[57] Ivakhnenko, A. G., Polynomial theory of complex systems, IEEE Trans. Syst. Man Cybern., SMC-1, 4, 364-378 (1971)
[58] Ivakhnenko, A., The group method of data handling in long-range forecasting, Technol. Forecast. Soc. Change, 12, 2, 213-227 (1978)
[59] Dorn, M.; Braga, A. L.; Llanos, C. H.; Coelho, L. S., A GMDH polynomial neural network-based method to predict approximate three-dimensional structures of polypeptides, Expert Syst. Appl., 39, 15, 12268-12279 (2012)
[60] Pham, D. T.; Liu, X., Modelling and prediction using GMDH networks of Adalines with nonlinear preprocessors, Internat. J. Systems Sci., 25, 11, 1743-1759 (1994) · Zbl 0825.93040
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